Daily Papers

In this work, we study how well the learned weights of a neural network utilize the space available to them. This notion is related to capacity, but additionally incorporates the interaction of the network architecture with the dataset. Most learned weights appear to be full rank, and are therefore not amenable to low rank decomposition. This deceptively implies that the weights are utilizing the entire space available to them. We propose a simple data-driven transformation that projects the weights onto the subspace where the data and the weight interact. This preserves the functional mapping of the layer and reveals its low rank structure. In our findings, we conclude that most models utilize a fraction of the available space. For instance, for ViTB-16 and ViTL-16 trained on ImageNet, the mean layer utilization is 35% and 20% respectively. Our transformation results in reducing the parameters to 50% and 25% respectively, while resulting in less than 0.2% accuracy drop after fine-tuning. We also show that self-supervised pre-training drives this utilization up to 70%, justifying its suitability for downstream tasks.

Most state-of-the-art approaches for weather and climate modeling are based on physics-informed numerical models of the atmosphere. These approaches aim to model the non-linear dynamics and complex interactions between multiple variables, which are challenging to approximate. Additionally, many such numerical models are computationally intensive, especially when modeling the atmospheric phenomenon at a fine-grained spatial and temporal resolution. Recent data-driven approaches based on machine learning instead aim to directly solve a downstream forecasting or projection task by learning a data-driven functional mapping using deep neural networks. However, these networks are trained using curated and homogeneous climate datasets for specific spatiotemporal tasks, and thus lack the generality of numerical models. We develop and demonstrate ClimaX, a flexible and generalizable deep learning model for weather and climate science that can be trained using heterogeneous datasets spanning different variables, spatio-temporal coverage, and physical groundings. ClimaX extends the Transformer architecture with novel encoding and aggregation blocks that allow effective use of available compute while maintaining general utility. ClimaX is pre-trained with a self-supervised learning objective on climate datasets derived from CMIP6. The pre-trained ClimaX can then be fine-tuned to address a breadth of climate and weather tasks, including those that involve atmospheric variables and spatio-temporal scales unseen during pretraining. Compared to existing data-driven baselines, we show that this generality in ClimaX results in superior performance on benchmarks for weather forecasting and climate projections, even when pretrained at lower resolutions and compute budgets.

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant for applications that require joint compression and retrieval, and in scenarios involving distributional shifts due to processing. We show that the proposed formulation extends the classical minimum entropy coupling framework by integrating a bottleneck, allowing for a controlled degree of stochasticity in the coupling. We explore the decomposition of the Minimum Entropy Coupling with Bottleneck (MEC-B) into two distinct optimization problems: Entropy-Bounded Information Maximization (EBIM) for the encoder, and Minimum Entropy Coupling (MEC) for the decoder. Through extensive analysis, we provide a greedy algorithm for EBIM with guaranteed performance, and characterize the optimal solution near functional mappings, yielding significant theoretical insights into the structural complexity of this problem. Furthermore, we illustrate the practical application of MEC-B through experiments in Markov Coding Games (MCGs) under rate limits. These games simulate a communication scenario within a Markov Decision Process, where an agent must transmit a compressed message from a sender to a receiver through its actions. Our experiments highlight the trade-offs between MDP rewards and receiver accuracy across various compression rates, showcasing the efficacy of our method compared to conventional compression baseline.

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction. The study presents a neural operator based on the dynamic mode decomposition algorithm (DMD), mapping functional spaces, which combines DMD and deep learning (DL) for spatiotemporal processes efficient modeling. Solving PDEs for various initial and boundary conditions requires significant computational resources. The method suggested automatically extracts key modes and system dynamics using them to construct predictions, reducing computational costs compared to traditional numerical methods. The approach has demonstrated its efficiency through comparative analysis of performance with closest analogues DeepONet and FNO in the heat equation, Laplaces equation, and Burgers equation solutions approximation, where it achieves high reconstruction accuracy.

Multimodal functional neuroimaging enables systematic analysis of brain mechanisms and provides discriminative representations for brain-computer interface (BCI) decoding. However, its acquisition is constrained by high costs and feasibility limitations. Moreover, underrepresentation of specific groups undermines fairness of BCI decoding model. To address these challenges, we propose a unified representation framework for multimodal functional neuroimaging via generative artificial intelligence (AI). By mapping multimodal functional neuroimaging into a unified representation space, the proposed framework is capable of generating data for acquisition-constrained modalities and underrepresented groups. Experiments show that the framework can generate data consistent with real brain activity patterns, provide insights into brain mechanisms, and improve performance on downstream tasks. More importantly, it can enhance model fairness by augmenting data for underrepresented groups. Overall, the framework offers a new paradigm for decreasing the cost of acquiring multimodal functional neuroimages and enhancing the fairness of BCI decoding models.

Vision-Language-Action (VLA) models have gained much attention from the research community thanks to their strength in translating multimodal observations with linguistic instructions into robotic actions. Despite their recent advancements, VLAs often overlook the explicit reasoning and only learn the functional input-action mappings, omitting these crucial logical steps for interpretability and generalization for complex, long-horizon manipulation tasks. In this work, we propose ReFineVLA, a multimodal reasoning-aware framework that fine-tunes VLAs with teacher-guided reasons. We first augment robotic datasets with reasoning rationales generated by an expert teacher model, guiding VLA models to learn to reason about their actions. Then, we use ReFineVLA to fine-tune pre-trained VLAs with the reasoning-enriched datasets, while maintaining their inherent generalization abilities and boosting reasoning capabilities. In addition, we conduct an attention map visualization to analyze the alignment among visual attention, linguistic prompts, and to-be-executed actions of ReFineVLA, showcasing its ability to focus on relevant tasks and actions. Through the latter step, we explore that ReFineVLA-trained models exhibit a meaningful attention shift towards relevant objects, highlighting the enhanced multimodal understanding and improved generalization. Evaluated across manipulation tasks, ReFineVLA outperforms the state-of-the-art baselines. Specifically, it achieves an average increase of 5.0% success rate on SimplerEnv WidowX Robot tasks, improves by an average of 8.6% in variant aggregation settings, and by 1.7% in visual matching settings for SimplerEnv Google Robot tasks. The source code will be publicly available.

Functional magnetic resonance imaging (fMRI) is an indispensable tool in modern neuroscience, providing a non-invasive window into whole-brain dynamics at millimeter-scale spatial resolution. However, fMRI is constrained by issues such as high operation costs and immobility. With the rapid advancements in cross-modality synthesis and brain decoding, the use of deep neural networks has emerged as a promising solution for inferring whole-brain, high-resolution fMRI features directly from electroencephalography (EEG), a more widely accessible and portable neuroimaging modality. Nonetheless, the complex projection from neural activity to fMRI hemodynamic responses and the spatial ambiguity of EEG pose substantial challenges both in modeling and interpretability. Relatively few studies to date have developed approaches for EEG-fMRI translation, and although they have made significant strides, the inference of fMRI signals in a given study has been limited to a small set of brain areas and to a single condition (i.e., either resting-state or a specific task). The capability to predict fMRI signals in other brain areas, as well as to generalize across conditions, remain critical gaps in the field. To tackle these challenges, we introduce a novel and generalizable framework: NeuroBOLT, i.e., Neuro-to-BOLD Transformer, which leverages multi-dimensional representation learning from temporal, spatial, and spectral domains to translate raw EEG data to the corresponding fMRI activity signals across the brain. Our experiments demonstrate that NeuroBOLT effectively reconstructs unseen resting-state fMRI signals from primary sensory, high-level cognitive areas, and deep subcortical brain regions, achieving state-of-the-art accuracy with the potential to generalize across varying conditions and sites, which significantly advances the integration of these two modalities.

The web provides a rich, open-domain environment with textual, structural, and spatial properties. We propose a new task for grounding language in this environment: given a natural language command (e.g., "click on the second article"), choose the correct element on the web page (e.g., a hyperlink or text box). We collected a dataset of over 50,000 commands that capture various phenomena such as functional references (e.g. "find who made this site"), relational reasoning (e.g. "article by john"), and visual reasoning (e.g. "top-most article"). We also implemented and analyzed three baseline models that capture different phenomena present in the dataset.

Neural decoding, the process of understanding how brain activity corresponds to different stimuli, has been a primary objective in cognitive sciences. Over the past three decades, advancements in functional Magnetic Resonance Imaging and machine learning have greatly improved our ability to map visual stimuli to brain activity, especially in the visual cortex. Concurrently, research has expanded into decoding more complex processes like language and memory across the whole brain, utilizing techniques to handle greater variability and improve signal accuracy. We argue that "seeing" involves more than just mapping visual stimuli onto the visual cortex; it engages the entire brain, as various emotions and cognitive states can emerge from observing different scenes. In this paper, we develop algorithms to enhance our understanding of visual processes by incorporating whole-brain activation maps while individuals are exposed to visual stimuli. We utilize large-scale fMRI encoders and Image generative models pre-trained on large public datasets, which are then fine-tuned through Image-fMRI contrastive learning. Our models hence can decode visual experience across the entire cerebral cortex, surpassing the traditional confines of the visual cortex. We first compare our method with state-of-the-art approaches to decoding visual processing and show improved predictive semantic accuracy by 43%. A network ablation analysis suggests that beyond the visual cortex, the default mode network contributes most to decoding stimuli, in line with the proposed role of this network in sense-making and semantic processing. Additionally, we implemented zero-shot imagination decoding on an extra validation dataset, achieving a p-value of 0.0206 for mapping the reconstructed images and ground-truth text stimuli, which substantiates the model's capability to capture semantic meanings across various scenarios.

Cycle consistency has long been exploited as a powerful prior for jointly optimizing maps within a collection of shapes. In this paper, we investigate its utility in the approaches of Deep Functional Maps, which are considered state-of-the-art in non-rigid shape matching. We first justify that under certain conditions, the learned maps, when represented in the spectral domain, are already cycle consistent. Furthermore, we identify the discrepancy that spectrally consistent maps are not necessarily spatially, or point-wise, consistent. In light of this, we present a novel design of unsupervised Deep Functional Maps, which effectively enforces the harmony of learned maps under the spectral and the point-wise representation. By taking advantage of cycle consistency, our framework produces state-of-the-art results in mapping shapes even under significant distortions. Beyond that, by independently estimating maps in both spectral and spatial domains, our method naturally alleviates over-fitting in network training, yielding superior generalization performance and accuracy within an array of challenging tests for both near-isometric and non-isometric datasets. Codes are available at https://github.com/rqhuang88/Spatiallyand-Spectrally-Consistent-Deep-Functional-Maps.

As requirements drift with rapid iterations, agile development becomes the dominant paradigm. Goal-driven Requirements Elicitation (RE) is a pivotal yet challenging task in agile project development due to its heavy tangling with adaptive planning and efficient collaboration. Recently, AI agents have shown promising ability in supporting requirements analysis by saving significant time and effort for stakeholders. However, current research mainly focuses on functional RE, and research works have not been reported bridging the long journey from goal to user stories. Moreover, considering the cost of LLM facilities and the need for data and idea protection, privately hosted small-sized LLM should be further utilized in RE. To address these challenges, we propose Goal2Story, a multi-agent fleet that adopts the Impact Mapping (IM) framework while merely using cost-effective sLLMs for goal-driven RE. Moreover, we introduce a StorySeek dataset that contains over 1,000 user stories (USs) with corresponding goals and project context information, as well as the semi-automatic dataset construction method. For evaluation, we proposed two metrics: Factuality Hit Rate (FHR) to measure consistency between the generated USs with the dataset and Quality And Consistency Evaluation (QuACE) to evaluate the quality of the generated USs. Experimental results demonstrate that Goal2Story outperforms the baseline performance of the Super-Agent adopting powerful LLMs, while also showcasing the performance improvements in key metrics brought by CoT and Agent Profile to Goal2Story, as well as its exploration in identifying latent needs.

Recent voxel-wise multimodal brain encoding studies have shown that multimodal large language models (MLLMs) exhibit a higher degree of brain alignment compared to unimodal models in both unimodal and multimodal stimulus settings. More recently, instruction-tuned multimodal models have shown to generate task-specific representations that align strongly with brain activity. However, prior work evaluating the brain alignment of MLLMs has primarily focused on unimodal settings or relied on non-instruction-tuned multimodal models for multimodal stimuli. To address this gap, we investigated brain alignment, that is, measuring the degree of predictivity of neural activity recorded while participants were watching naturalistic movies (video along with audio) with representations derived from MLLMs. We utilized instruction-specific embeddings from six video and two audio instruction-tuned MLLMs. Experiments with 13 video task-specific instructions show that instruction-tuned video MLLMs significantly outperform non-instruction-tuned multimodal (by 15%) and unimodal models (by 20%). Our evaluation of MLLMs for both video and audio tasks using language-guided instructions shows clear disentanglement in task-specific representations from MLLMs, leading to precise differentiation of multimodal functional processing in the brain. We also find that MLLM layers align hierarchically with the brain, with early sensory areas showing strong alignment with early layers, while higher-level visual and language regions align more with middle to late layers. These findings provide clear evidence for the role of task-specific instructions in improving the alignment between brain activity and MLLMs, and open new avenues for mapping joint information processing in both the systems. We make the code publicly available [https://github.com/subbareddy248/mllm_videos].

Reconstructions of visual perception from brain activity have improved tremendously, but the practical utility of such methods has been limited. This is because such models are trained independently per subject where each subject requires dozens of hours of expensive fMRI training data to attain high-quality results. The present work showcases high-quality reconstructions using only 1 hour of fMRI training data. We pretrain our model across 7 subjects and then fine-tune on minimal data from a new subject. Our novel functional alignment procedure linearly maps all brain data to a shared-subject latent space, followed by a shared non-linear mapping to CLIP image space. We then map from CLIP space to pixel space by fine-tuning Stable Diffusion XL to accept CLIP latents as inputs instead of text. This approach improves out-of-subject generalization with limited training data and also attains state-of-the-art image retrieval and reconstruction metrics compared to single-subject approaches. MindEye2 demonstrates how accurate reconstructions of perception are possible from a single visit to the MRI facility. All code is available on GitHub.

Rust's compile-time safety guarantees make it ideal for safety-critical systems, creating demand for translating legacy C codebases to Rust. While various approaches have emerged for this task, they face inherent trade-offs: rule-based solutions face challenges in meeting code safety and idiomaticity requirements, while LLM-based solutions often fail to generate semantically equivalent Rust code, due to the heavy dependencies of modules across the entire codebase. Recent studies have revealed that both solutions are limited to small-scale programs. In this paper, we propose EvoC2Rust, an automated framework for converting entire C projects to equivalent Rust ones. EvoC2Rust employs a skeleton-guided translation strategy for project-level translation. The pipeline consists of three evolutionary stages: 1) it first decomposes the C project into functional modules, employs a feature-mapping-enhanced LLM to transform definitions and macros and generates type-checked function stubs, which form a compilable Rust skeleton; 2) it then incrementally translates the function, replacing the corresponding stub placeholder; 3) finally, it repairs compilation errors by integrating LLM and static analysis. Through evolutionary augmentation, EvoC2Rust combines the advantages of both rule-based and LLM-based solutions. Our evaluation on open-source benchmarks and six industrial projects demonstrates EvoC2Rust's superior performance in project-level C-to-Rust translation. On average, it achieves 17.24% and 14.32% improvements in syntax and semantic accuracy over the LLM-based approaches, along with a 96.79% higher code safety rate than the rule-based tools. At the module level, EvoC2Rust reaches 92.25% compilation and 89.53% test pass rates on industrial projects, even for complex codebases and long functions.

We propose a novel zero-shot approach to computing correspondences between 3D shapes. Existing approaches mainly focus on isometric and near-isometric shape pairs (e.g., human vs. human), but less attention has been given to strongly non-isometric and inter-class shape matching (e.g., human vs. cow). To this end, we introduce a fully automatic method that exploits the exceptional reasoning capabilities of recent foundation models in language and vision to tackle difficult shape correspondence problems. Our approach comprises multiple stages. First, we classify the 3D shapes in a zero-shot manner by feeding rendered shape views to a language-vision model (e.g., BLIP2) to generate a list of class proposals per shape. These proposals are unified into a single class per shape by employing the reasoning capabilities of ChatGPT. Second, we attempt to segment the two shapes in a zero-shot manner, but in contrast to the co-segmentation problem, we do not require a mutual set of semantic regions. Instead, we propose to exploit the in-context learning capabilities of ChatGPT to generate two different sets of semantic regions for each shape and a semantic mapping between them. This enables our approach to match strongly non-isometric shapes with significant differences in geometric structure. Finally, we employ the generated semantic mapping to produce coarse correspondences that can further be refined by the functional maps framework to produce dense point-to-point maps. Our approach, despite its simplicity, produces highly plausible results in a zero-shot manner, especially between strongly non-isometric shapes.

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.

We present UniTEX, a novel two-stage 3D texture generation framework to create high-quality, consistent textures for 3D assets. Existing approaches predominantly rely on UV-based inpainting to refine textures after reprojecting the generated multi-view images onto the 3D shapes, which introduces challenges related to topological ambiguity. To address this, we propose to bypass the limitations of UV mapping by operating directly in a unified 3D functional space. Specifically, we first propose that lifts texture generation into 3D space via Texture Functions (TFs)--a continuous, volumetric representation that maps any 3D point to a texture value based solely on surface proximity, independent of mesh topology. Then, we propose to predict these TFs directly from images and geometry inputs using a transformer-based Large Texturing Model (LTM). To further enhance texture quality and leverage powerful 2D priors, we develop an advanced LoRA-based strategy for efficiently adapting large-scale Diffusion Transformers (DiTs) for high-quality multi-view texture synthesis as our first stage. Extensive experiments demonstrate that UniTEX achieves superior visual quality and texture integrity compared to existing approaches, offering a generalizable and scalable solution for automated 3D texture generation. Code will available in: https://github.com/YixunLiang/UniTEX.

Domain adaptation in reinforcement learning (RL) mainly deals with the changes of observation when transferring the policy to a new environment. Many traditional approaches of domain adaptation in RL manage to learn a mapping function between the source and target domain in explicit or implicit ways. However, they typically require access to abundant data from the target domain. Besides, they often rely on visual clues to learn the mapping function and may fail when the source domain looks quite different from the target domain. To address these problems, we propose a novel framework Online Prototype Alignment (OPA) to learn the mapping function based on the functional similarity of elements and is able to achieve the few-shot policy transfer within only several episodes. The key insight of OPA is to introduce an exploration mechanism that can interact with the unseen elements of the target domain in an efficient and purposeful manner, and then connect them with the seen elements in the source domain according to their functionalities (instead of visual clues). Experimental results show that when the target domain looks visually different from the source domain, OPA can achieve better transfer performance even with much fewer samples from the target domain, outperforming prior methods.

Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for improved accuracy and generality. However, most existing methods in this area restrict the learning aspect only to the feature functions and still rely on axiomatic modeling for formulating the training loss or for functional map regularization inside the networks. This limits both the accuracy and the applicability of the resulting approaches only to scenarios where assumptions of the axiomatic models hold. In this work, we show, for the first time, that both in-network regularization and functional map training can be replaced with data-driven methods. For this, we first train a generative model of functional maps in the spectral domain using score-based generative modeling, built from a large collection of high-quality maps. We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections. Remarkably, we demonstrate that the learned models are category-agnostic, and can fully replace commonly used strategies such as enforcing Laplacian commutativity or orthogonality of functional maps. Our key technical contribution is a novel distillation strategy from diffusion models in the spectral domain. Experiments demonstrate that our learned regularization leads to better results than axiomatic approaches for zero-shot non-rigid shape matching. Our code is available at: https://github.com/daidedou/diffumatch/

We introduce ReMatching, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm, can target shape-matching tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

We present a new dataset, Functional Map of the World (fMoW), which aims to inspire the development of machine learning models capable of predicting the functional purpose of buildings and land use from temporal sequences of satellite images and a rich set of metadata features. The metadata provided with each image enables reasoning about location, time, sun angles, physical sizes, and other features when making predictions about objects in the image. Our dataset consists of over 1 million images from over 200 countries. For each image, we provide at least one bounding box annotation containing one of 63 categories, including a "false detection" category. We present an analysis of the dataset along with baseline approaches that reason about metadata and temporal views. Our data, code, and pretrained models have been made publicly available.

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. Functional diffusion is very versatile as images, videos, audio, 3D shapes, deformations, \etc, can be handled by the same framework with minimal changes. In addition, functional diffusion is especially suited for irregular data or data defined in non-standard domains. In our work, we derive the necessary foundations for functional diffusion and propose a first implementation based on the transformer architecture. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.

We introduce the task of predicting functional 3D scene graphs for real-world indoor environments from posed RGB-D images. Unlike traditional 3D scene graphs that focus on spatial relationships of objects, functional 3D scene graphs capture objects, interactive elements, and their functional relationships. Due to the lack of training data, we leverage foundation models, including visual language models (VLMs) and large language models (LLMs), to encode functional knowledge. We evaluate our approach on an extended SceneFun3D dataset and a newly collected dataset, FunGraph3D, both annotated with functional 3D scene graphs. Our method significantly outperforms adapted baselines, including Open3DSG and ConceptGraph, demonstrating its effectiveness in modeling complex scene functionalities. We also demonstrate downstream applications such as 3D question answering and robotic manipulation using functional 3D scene graphs. See our project page at https://openfungraph.github.io

We address the problem of aligning real-world 3D data of garments, which benefits many applications such as texture learning, physical parameter estimation, generative modeling of garments, etc. Existing extrinsic methods typically perform non-rigid iterative closest point and struggle to align details due to incorrect closest matches and rigidity constraints. While intrinsic methods based on functional maps can produce high-quality correspondences, they work under isometric assumptions and become unreliable for garment deformations which are highly non-isometric. To achieve wrinkle-level as well as texture-level alignment, we present a novel coarse-to-fine two-stage method that leverages intrinsic manifold properties with two neural deformation fields, in the 3D space and the intrinsic space, respectively. The coarse stage performs a 3D fitting, where we leverage intrinsic manifold properties to define a manifold deformation field. The coarse fitting then induces a functional map that produces an alignment of intrinsic embeddings. We further refine the intrinsic alignment with a second neural deformation field for higher accuracy. We evaluate our method with our captured garment dataset, GarmCap. The method achieves accurate wrinkle-level and texture-level alignment and works for difficult garment types such as long coats. Our project page is https://jsnln.github.io/iccv2023_intrinsic/index.html.

In the realm of computer vision and graphics, accurately establishing correspondences between geometric 3D shapes is pivotal for applications like object tracking, registration, texture transfer, and statistical shape analysis. Moving beyond traditional hand-crafted and data-driven feature learning methods, we incorporate spectral methods with deep learning, focusing on functional maps (FMs) and optimal transport (OT). Traditional OT-based approaches, often reliant on entropy regularization OT in learning-based framework, face computational challenges due to their quadratic cost. Our key contribution is to employ the sliced Wasserstein distance (SWD) for OT, which is a valid fast optimal transport metric in an unsupervised shape matching framework. This unsupervised framework integrates functional map regularizers with a novel OT-based loss derived from SWD, enhancing feature alignment between shapes treated as discrete probability measures. We also introduce an adaptive refinement process utilizing entropy regularized OT, further refining feature alignments for accurate point-to-point correspondences. Our method demonstrates superior performance in non-rigid shape matching, including near-isometric and non-isometric scenarios, and excels in downstream tasks like segmentation transfer. The empirical results on diverse datasets highlight our framework's effectiveness and generalization capabilities, setting new standards in non-rigid shape matching with efficient OT metrics and an adaptive refinement module.

Functional grasping is essential for humans to perform specific tasks, such as grasping scissors by the finger holes to cut materials or by the blade to safely hand them over. Enabling dexterous robot hands with functional grasping capabilities is crucial for their deployment to accomplish diverse real-world tasks. Recent research in dexterous grasping, however, often focuses on power grasps while overlooking task- and object-specific functional grasping poses. In this paper, we introduce FunGrasp, a system that enables functional dexterous grasping across various robot hands and performs one-shot transfer to unseen objects. Given a single RGBD image of functional human grasping, our system estimates the hand pose and transfers it to different robotic hands via a human-to-robot (H2R) grasp retargeting module. Guided by the retargeted grasping poses, a policy is trained through reinforcement learning in simulation for dynamic grasping control. To achieve robust sim-to-real transfer, we employ several techniques including privileged learning, system identification, domain randomization, and gravity compensation. In our experiments, we demonstrate that our system enables diverse functional grasping of unseen objects using single RGBD images, and can be successfully deployed across various dexterous robot hands. The significance of the components is validated through comprehensive ablation studies. Project page: https://hly-123.github.io/FunGrasp/ .

We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

In this paper, we propose a real-world benchmark for studying robotic learning in the context of functional manipulation: a robot needs to accomplish complex long-horizon behaviors by composing individual manipulation skills in functionally relevant ways. The core design principles of our Functional Manipulation Benchmark (FMB) emphasize a harmonious balance between complexity and accessibility. Tasks are deliberately scoped to be narrow, ensuring that models and datasets of manageable scale can be utilized effectively to track progress. Simultaneously, they are diverse enough to pose a significant generalization challenge. Furthermore, the benchmark is designed to be easily replicable, encompassing all essential hardware and software components. To achieve this goal, FMB consists of a variety of 3D-printed objects designed for easy and accurate replication by other researchers. The objects are procedurally generated, providing a principled framework to study generalization in a controlled fashion. We focus on fundamental manipulation skills, including grasping, repositioning, and a range of assembly behaviors. The FMB can be used to evaluate methods for acquiring individual skills, as well as methods for combining and ordering such skills to solve complex, multi-stage manipulation tasks. We also offer an imitation learning framework that includes a suite of policies trained to solve the proposed tasks. This enables researchers to utilize our tasks as a versatile toolkit for examining various parts of the pipeline. For example, researchers could propose a better design for a grasping controller and evaluate it in combination with our baseline reorientation and assembly policies as part of a pipeline for solving multi-stage tasks. Our dataset, object CAD files, code, and evaluation videos can be found on our project website: https://functional-manipulation-benchmark.github.io

A long standing goal in neuroscience has been to elucidate the functional organization of the brain. Within higher visual cortex, functional accounts have remained relatively coarse, focusing on regions of interest (ROIs) and taking the form of selectivity for broad categories such as faces, places, bodies, food, or words. Because the identification of such ROIs has typically relied on manually assembled stimulus sets consisting of isolated objects in non-ecological contexts, exploring functional organization without robust a priori hypotheses has been challenging. To overcome these limitations, we introduce a data-driven approach in which we synthesize images predicted to activate a given brain region using paired natural images and fMRI recordings, bypassing the need for category-specific stimuli. Our approach -- Brain Diffusion for Visual Exploration ("BrainDiVE") -- builds on recent generative methods by combining large-scale diffusion models with brain-guided image synthesis. Validating our method, we demonstrate the ability to synthesize preferred images with appropriate semantic specificity for well-characterized category-selective ROIs. We then show that BrainDiVE can characterize differences between ROIs selective for the same high-level category. Finally we identify novel functional subdivisions within these ROIs, validated with behavioral data. These results advance our understanding of the fine-grained functional organization of human visual cortex, and provide well-specified constraints for further examination of cortical organization using hypothesis-driven methods.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

Model merging is an efficient post-training strategy for integrating knowledge from multiple finetuned checkpoints of a shared foundation model. Existing methods operate in the parameter space, combining task vectors to mitigate conflicts, but remain constrained by parameter inconsistencies. We propose Functional Dual Anchors (FDAs), a framework that instead models the input-representation space. FDAs are synthetic inputs whose induced gradients align with task vectors, capturing task-specific functional shifts relative to the pretrained model. This perspective bridges joint multi-task training and post-hoc merging, offering both robustness and flexibility. We further introduce a principled initialization scheme and show that FDAs are complementary to parameter-space model merging. Comprehensive experiments demonstrate the effectiveness of FDAs in model merging.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

The field of Automatic Machine Learning (AutoML) has recently attained impressive results, including the discovery of state-of-the-art machine learning solutions, such as neural image classifiers. This is often done by applying an evolutionary search method, which samples multiple candidate solutions from a large space and evaluates the quality of each candidate through a long training process. As a result, the search tends to be slow. In this paper, we show that large efficiency gains can be obtained by employing a fast unified functional hash, especially through the functional equivalence caching technique, which we also present. The central idea is to detect by hashing when the search method produces equivalent candidates, which occurs very frequently, and this way avoid their costly re-evaluation. Our hash is "functional" in that it identifies equivalent candidates even if they were represented or coded differently, and it is "unified" in that the same algorithm can hash arbitrary representations; e.g. compute graphs, imperative code, or lambda functions. As evidence, we show dramatic improvements on multiple AutoML domains, including neural architecture search and algorithm discovery. Finally, we consider the effect of hash collisions, evaluation noise, and search distribution through empirical analysis. Altogether, we hope this paper may serve as a guide to hashing techniques in AutoML.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting the flexibility of data-driven discovery, while many deep-learning pipelines treat functions as fixed-grid vectors, ignoring inherent continuity. In this paper, we introduce Functional Attention with a Mixture-of-Experts (FAME), an end-to-end, fully data-driven framework for function-on-function regression. FAME forms continuous attention by coupling a bidirectional neural controlled differential equation with MoE-driven vector fields to capture intra-functional continuity, and further fuses change to inter-functional dependencies via multi-head cross attention. Extensive experiments on synthetic and real-world functional-regression benchmarks show that FAME achieves state-of-the-art accuracy, strong robustness to arbitrarily sampled discrete observations of functions.

Canonical surface mapping generalizes keypoint detection by assigning each pixel of an object to a corresponding point in a 3D template. Popularised by DensePose for the analysis of humans, authors have since attempted to apply the concept to more categories, but with limited success due to the high cost of manual supervision. In this work, we introduce SHIC, a method to learn canonical maps without manual supervision which achieves better results than supervised methods for most categories. Our idea is to leverage foundation computer vision models such as DINO and Stable Diffusion that are open-ended and thus possess excellent priors over natural categories. SHIC reduces the problem of estimating image-to-template correspondences to predicting image-to-image correspondences using features from the foundation models. The reduction works by matching images of the object to non-photorealistic renders of the template, which emulates the process of collecting manual annotations for this task. These correspondences are then used to supervise high-quality canonical maps for any object of interest. We also show that image generators can further improve the realism of the template views, which provide an additional source of supervision for the model.

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.

We introduce Brain-JEPA, a brain dynamics foundation model with the Joint-Embedding Predictive Architecture (JEPA). This pioneering model achieves state-of-the-art performance in demographic prediction, disease diagnosis/prognosis, and trait prediction through fine-tuning. Furthermore, it excels in off-the-shelf evaluations (e.g., linear probing) and demonstrates superior generalizability across different ethnic groups, surpassing the previous large model for brain activity significantly. Brain-JEPA incorporates two innovative techniques: Brain Gradient Positioning and Spatiotemporal Masking. Brain Gradient Positioning introduces a functional coordinate system for brain functional parcellation, enhancing the positional encoding of different Regions of Interest (ROIs). Spatiotemporal Masking, tailored to the unique characteristics of fMRI data, addresses the challenge of heterogeneous time-series patches. These methodologies enhance model performance and advance our understanding of the neural circuits underlying cognition. Overall, Brain-JEPA is paving the way to address pivotal questions of building brain functional coordinate system and masking brain activity at the AI-neuroscience interface, and setting a potentially new paradigm in brain activity analysis through downstream adaptation.

Addressing the uncertainty and variability in the quality of 3D printed metals can further the wide spread use of this technology. Process mapping for new alloys is crucial for determining optimal process parameters that consistently produce acceptable printing quality. Process mapping is typically performed by conventional methods and is used for the design of experiments and ex situ characterization of printed parts. On the other hand, in situ approaches are limited because their observable features are limited and they require complex high-cost setups to obtain temperature measurements to boost accuracy. Our method relaxes these limitations by incorporating the temporal features of molten metal dynamics during laser-metal interactions using video vision transformers and high-speed imaging. Our approach can be used in existing commercial machines and can provide in situ process maps for efficient defect and variability quantification. The generalizability of the approach is demonstrated by performing cross-dataset evaluations on alloys with different compositions and intrinsic thermofluid properties.

Despite its fruitful applications in remote sensing, image super-resolution is troublesome to train and deploy as it handles different resolution magnifications with separate models. Accordingly, we propose a highly-applicable super-resolution framework called FunSR, which settles different magnifications with a unified model by exploiting context interaction within implicit function space. FunSR composes a functional representor, a functional interactor, and a functional parser. Specifically, the representor transforms the low-resolution image from Euclidean space to multi-scale pixel-wise function maps; the interactor enables pixel-wise function expression with global dependencies; and the parser, which is parameterized by the interactor's output, converts the discrete coordinates with additional attributes to RGB values. Extensive experimental results demonstrate that FunSR reports state-of-the-art performance on both fixed-magnification and continuous-magnification settings, meanwhile, it provides many friendly applications thanks to its unified nature.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

Attention heads are one of the building blocks of large language models (LLMs). Prior work on investigating their operation mostly focused on analyzing their behavior during inference for specific circuits or tasks. In this work, we seek a comprehensive mapping of the operations they implement in a model. We propose MAPS (Mapping Attention head ParameterS), an efficient framework that infers the functionality of attention heads from their parameters, without any model training or inference. We showcase the utility of MAPS for answering two types of questions: (a) given a predefined operation, mapping how strongly heads across the model implement it, and (b) given an attention head, inferring its salient functionality. Evaluating MAPS on 20 operations across 6 popular LLMs shows its estimations correlate with the head's outputs during inference and are causally linked to the model's predictions. Moreover, its mappings reveal attention heads of certain operations that were overlooked in previous studies, and valuable insights on function universality and architecture biases in LLMs. Next, we present an automatic pipeline and analysis that leverage MAPS to characterize the salient operations of a given head. Our pipeline produces plausible operation descriptions for most heads, as assessed by human judgment, while revealing diverse operations.

Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.

While large language models (LLMs) appear to be increasingly capable of solving compositional tasks, it is an open question whether they do so using compositional mechanisms. In this work, we investigate how feedforward LLMs solve two-hop factual recall tasks, which can be expressed compositionally as g(f(x)). We first confirm that modern LLMs continue to suffer from the "compositionality gap": i.e. their ability to compute both z = f(x) and y = g(z) does not entail their ability to compute the composition y = g(f(x)). Then, using logit lens on their residual stream activations, we identify two processing mechanisms, one which solves tasks compositionally, computing f(x) along the way to computing g(f(x)), and one which solves them directly, without any detectable signature of the intermediate variable f(x). Finally, we find that which mechanism is employed appears to be related to the embedding space geometry, with the idiomatic mechanism being dominant in cases where there exists a linear mapping from x to g(f(x)) in the embedding spaces. We fully release our data and code at: https://github.com/apoorvkh/composing-functions .

Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the mechanisms underlying this functional organization remain unclear. Here, building on work from the vision literature, we develop TopoLM, a transformer language model with an explicit two-dimensional spatial representation of model units. By combining a next-token prediction objective with a spatial smoothness loss, representations in this model assemble into clusters that correspond to semantically interpretable groupings of text and closely match the functional organization in the brain's language system. TopoLM successfully predicts the emergence of the spatio-functional organization of a cortical language system as well as the organization of functional clusters selective for fine-grained linguistic features empirically observed in human cortex. Our results suggest that the functional organization of the human language system is driven by a unified spatial objective, and provide a functionally and spatially aligned model of language processing in the brain.

While interacting in the world is a multi-sensory experience, many robots continue to predominantly rely on visual perception to map and navigate in their environments. In this work, we propose Audio-Visual-Language Maps (AVLMaps), a unified 3D spatial map representation for storing cross-modal information from audio, visual, and language cues. AVLMaps integrate the open-vocabulary capabilities of multimodal foundation models pre-trained on Internet-scale data by fusing their features into a centralized 3D voxel grid. In the context of navigation, we show that AVLMaps enable robot systems to index goals in the map based on multimodal queries, e.g., textual descriptions, images, or audio snippets of landmarks. In particular, the addition of audio information enables robots to more reliably disambiguate goal locations. Extensive experiments in simulation show that AVLMaps enable zero-shot multimodal goal navigation from multimodal prompts and provide 50% better recall in ambiguous scenarios. These capabilities extend to mobile robots in the real world - navigating to landmarks referring to visual, audio, and spatial concepts. Videos and code are available at: https://avlmaps.github.io.

Protein function prediction is a crucial task in bioinformatics, with significant implications for understanding biological processes and disease mechanisms. While the relationship between sequence and function has been extensively explored, translating protein structure to function continues to present substantial challenges. Various models, particularly, CNN and graph-based deep learning approaches that integrate structural and functional data, have been proposed to address these challenges. However, these methods often fall short in elucidating the functional significance of key residues essential for protein functionality, as they predominantly adopt a retrospective perspective, leading to suboptimal performance. Inspired by region proposal networks in computer vision, we introduce the Protein Region Proposal Network (ProteinRPN) for accurate protein function prediction. Specifically, the region proposal module component of ProteinRPN identifies potential functional regions (anchors) which are refined through the hierarchy-aware node drop pooling layer favoring nodes with defined secondary structures and spatial proximity. The representations of the predicted functional nodes are enriched using attention mechanisms and subsequently fed into a Graph Multiset Transformer, which is trained with supervised contrastive (SupCon) and InfoNCE losses on perturbed protein structures. Our model demonstrates significant improvements in predicting Gene Ontology (GO) terms, effectively localizing functional residues within protein structures. The proposed framework provides a robust, scalable solution for protein function annotation, advancing the understanding of protein structure-function relationships in computational biology.

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

Humans have a natural ability to perform semantic associations with the surrounding objects in the environment. This allows them to create a mental map of the environment, allowing them to navigate on-demand when given linguistic instructions. A natural goal in Vision Language Navigation (VLN) research is to impart autonomous agents with similar capabilities. Recent works take a step towards this goal by creating a semantic spatial map representation of the environment without any labeled data. However, their representations are limited for practical applicability as they do not distinguish between different instances of the same object. In this work, we address this limitation by integrating instance-level information into spatial map representation using a community detection algorithm and utilizing word ontology learned by large language models (LLMs) to perform open-set semantic associations in the mapping representation. The resulting map representation improves the navigation performance by two-fold (233%) on realistic language commands with instance-specific descriptions compared to the baseline. We validate the practicality and effectiveness of our approach through extensive qualitative and quantitative experiments.

We build upon vec2vec, a procedure designed to align text embedding spaces without parallel data. vec2vec finds a near-perfect alignment, but it is expensive and unstable. We present mini-vec2vec, a simple and efficient alternative that requires substantially lower computational cost and is highly robust. Moreover, the learned mapping is a linear transformation. Our method consists of three main stages: a tentative matching of pseudo-parallel embedding vectors, transformation fitting, and iterative refinement. Our linear alternative exceeds the original instantiation of vec2vec by orders of magnitude in efficiency, while matching or exceeding their results. The method's stability and interpretable algorithmic steps facilitate scaling and unlock new opportunities for adoption in new domains and fields.

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Semantic mapping based on the supervised object detectors is sensitive to image distribution. In real-world environments, the object detection and segmentation performance can lead to a major drop, preventing the use of semantic mapping in a wider domain. On the other hand, the development of vision-language foundation models demonstrates a strong zero-shot transferability across data distribution. It provides an opportunity to construct generalizable instance-aware semantic maps. Hence, this work explores how to boost instance-aware semantic mapping from object detection generated from foundation models. We propose a probabilistic label fusion method to predict close-set semantic classes from open-set label measurements. An instance refinement module merges the over-segmented instances caused by inconsistent segmentation. We integrate all the modules into a unified semantic mapping system. Reading a sequence of RGB-D input, our work incrementally reconstructs an instance-aware semantic map. We evaluate the zero-shot performance of our method in ScanNet and SceneNN datasets. Our method achieves 40.3 mean average precision (mAP) on the ScanNet semantic instance segmentation task. It outperforms the traditional semantic mapping method significantly.

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement higher-order functions. We present a set of primitive operators that serve as foundational building blocks for constructing several key types of functionals. For every introduced primitive operator, we derive and implement both linearization and transposition rules, aligning with JAX's internal protocols for forward and reverse mode automatic differentiation. This enhancement allows for functional differentiation in the same syntax traditionally use for functions. The resulting functional gradients are themselves functions ready to be invoked in python. We showcase this tool's efficacy and simplicity through applications where functional derivatives are indispensable. The source code of this work is released at https://github.com/sail-sg/autofd .

Understanding functionalities in 3D scenes involves interpreting natural language descriptions to locate functional interactive objects, such as handles and buttons, in a 3D environment. Functionality understanding is highly challenging, as it requires both world knowledge to interpret language and spatial perception to identify fine-grained objects. For example, given a task like 'turn on the ceiling light', an embodied AI agent must infer that it needs to locate the light switch, even though the switch is not explicitly mentioned in the task description. To date, no dedicated methods have been developed for this problem. In this paper, we introduce Fun3DU, the first approach designed for functionality understanding in 3D scenes. Fun3DU uses a language model to parse the task description through Chain-of-Thought reasoning in order to identify the object of interest. The identified object is segmented across multiple views of the captured scene by using a vision and language model. The segmentation results from each view are lifted in 3D and aggregated into the point cloud using geometric information. Fun3DU is training-free, relying entirely on pre-trained models. We evaluate Fun3DU on SceneFun3D, the most recent and only dataset to benchmark this task, which comprises over 3000 task descriptions on 230 scenes. Our method significantly outperforms state-of-the-art open-vocabulary 3D segmentation approaches. Project page: https://jcorsetti.github.io/fun3du

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

The massive interest in deep neural networks (DNNs) for both computer vision and natural language processing has been sparked by the growth in computational power. However, this led to an increase in the memory footprint, to a point where it can be challenging to simply load a model on commodity devices such as mobile phones. To address this limitation, quantization is a favored solution as it maps high precision tensors to a low precision, memory efficient format. In terms of memory footprint reduction, its most effective variants are based on codebooks. These methods, however, suffer from two limitations. First, they either define a single codebook for each tensor, or use a memory-expensive mapping to multiple codebooks. Second, gradient descent optimization of the mapping favors jumps toward extreme values, hence not defining a proximal search. In this work, we propose to address these two limitations. First, we initially group similarly distributed neurons and leverage the re-ordered structure to either apply different scale factors to the different groups, or map weights that fall in these groups to several codebooks, without any mapping overhead. Second, stemming from this initialization, we propose a joint learning of the codebook and weight mappings that bears similarities with recent gradient-based post-training quantization techniques. Third, drawing estimation from straight-through estimation techniques, we introduce a novel gradient update definition to enable a proximal search of the codebooks and their mappings. The proposed jointly learnable codebooks and mappings (JLCM) method allows a very efficient approximation of any DNN: as such, a Llama 7B can be compressed down to 2Go and loaded on 5-year-old smartphones.

We present Semantify: a self-supervised method that utilizes the semantic power of CLIP language-vision foundation model to simplify the control of 3D morphable models. Given a parametric model, training data is created by randomly sampling the model's parameters, creating various shapes and rendering them. The similarity between the output images and a set of word descriptors is calculated in CLIP's latent space. Our key idea is first to choose a small set of semantically meaningful and disentangled descriptors that characterize the 3DMM, and then learn a non-linear mapping from scores across this set to the parametric coefficients of the given 3DMM. The non-linear mapping is defined by training a neural network without a human-in-the-loop. We present results on numerous 3DMMs: body shape models, face shape and expression models, as well as animal shapes. We demonstrate how our method defines a simple slider interface for intuitive modeling, and show how the mapping can be used to instantly fit a 3D parametric body shape to in-the-wild images.

Attention Deficit Hyperactive Disorder (ADHD) is a common behavioral problem affecting children. In this work, we investigate the automatic classification of ADHD subjects using the resting state Functional Magnetic Resonance Imaging (fMRI) sequences of the brain. We show that the brain can be modeled as a functional network, and certain properties of the networks differ in ADHD subjects from control subjects. We compute the pairwise correlation of brain voxels' activity over the time frame of the experimental protocol which helps to model the function of a brain as a network. Different network features are computed for each of the voxels constructing the network. The concatenation of the network features of all the voxels in a brain serves as the feature vector. Feature vectors from a set of subjects are then used to train a PCA-LDA (principal component analysis-linear discriminant analysis) based classifier. We hypothesized that ADHD-related differences lie in some specific regions of the brain and using features only from those regions is sufficient to discriminate ADHD and control subjects. We propose a method to create a brain mask that includes the useful regions only and demonstrate that using the feature from the masked regions improves classification accuracy on the test data set. We train our classifier with 776 subjects and test on 171 subjects provided by The Neuro Bureau for the ADHD-200 challenge. We demonstrate the utility of graph-motif features, specifically the maps that represent the frequency of participation of voxels in network cycles of length 3. The best classification performance (69.59%) is achieved using 3-cycle map features with masking. Our proposed approach holds promise in being able to diagnose and understand the disorder.

Can we pre-train a generalist agent from a large amount of unlabeled offline trajectories such that it can be immediately adapted to any new downstream tasks in a zero-shot manner? In this work, we present a functional reward encoding (FRE) as a general, scalable solution to this zero-shot RL problem. Our main idea is to learn functional representations of any arbitrary tasks by encoding their state-reward samples using a transformer-based variational auto-encoder. This functional encoding not only enables the pre-training of an agent from a wide diversity of general unsupervised reward functions, but also provides a way to solve any new downstream tasks in a zero-shot manner, given a small number of reward-annotated samples. We empirically show that FRE agents trained on diverse random unsupervised reward functions can generalize to solve novel tasks in a range of simulated robotic benchmarks, often outperforming previous zero-shot RL and offline RL methods. Code for this project is provided at: https://github.com/kvfrans/fre

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

The concept of 3D scene graphs is increasingly recognized as a powerful semantic and hierarchical representation of the environment. Current approaches often address this at a coarse, object-level resolution. In contrast, our goal is to develop a representation that enables robots to directly interact with their environment by identifying both the location of functional interactive elements and how these can be used. To achieve this, we focus on detecting and storing objects at a finer resolution, focusing on affordance-relevant parts. The primary challenge lies in the scarcity of data that extends beyond instance-level detection and the inherent difficulty of capturing detailed object features using robotic sensors. We leverage currently available 3D resources to generate 2D data and train a detector, which is then used to augment the standard 3D scene graph generation pipeline. Through our experiments, we demonstrate that our approach achieves functional element segmentation comparable to state-of-the-art 3D models and that our augmentation enables task-driven affordance grounding with higher accuracy than the current solutions. See our project page at https://fungraph.github.io.

Many recent datasets contain a variety of different data modalities, for instance, image, question, and answer data in visual question answering (VQA). When training deep net classifiers on those multi-modal datasets, the modalities get exploited at different scales, i.e., some modalities can more easily contribute to the classification results than others. This is suboptimal because the classifier is inherently biased towards a subset of the modalities. To alleviate this shortcoming, we propose a novel regularization term based on the functional entropy. Intuitively, this term encourages to balance the contribution of each modality to the classification result. However, regularization with the functional entropy is challenging. To address this, we develop a method based on the log-Sobolev inequality, which bounds the functional entropy with the functional-Fisher-information. Intuitively, this maximizes the amount of information that the modalities contribute. On the two challenging multi-modal datasets VQA-CPv2 and SocialIQ, we obtain state-of-the-art results while more uniformly exploiting the modalities. In addition, we demonstrate the efficacy of our method on Colored MNIST.

Large language models (LLMs) have gained significant attention in chemistry. However, most existing datasets center on molecular-level property prediction and overlook the role of fine-grained functional group (FG) information. Incorporating FG-level data can provide valuable prior knowledge that links molecular structures with textual descriptions, which can be used to build more interpretable, structure-aware LLMs for reasoning on molecule-related tasks. Moreover, LLMs can learn from such fine-grained information to uncover hidden relationships between specific functional groups and molecular properties, thereby advancing molecular design and drug discovery. Here, we introduce FGBench, a dataset comprising 625K molecular property reasoning problems with functional group information. Functional groups are precisely annotated and localized within the molecule, which ensures the dataset's interoperability thereby facilitating further multimodal applications. FGBench includes both regression and classification tasks on 245 different functional groups across three categories for molecular property reasoning: (1) single functional group impacts, (2) multiple functional group interactions, and (3) direct molecular comparisons. In the benchmark of state-of-the-art LLMs on 7K curated data, the results indicate that current LLMs struggle with FG-level property reasoning, highlighting the need to enhance reasoning capabilities in LLMs for chemistry tasks. We anticipate that the methodology employed in FGBench to construct datasets with functional group-level information will serve as a foundational framework for generating new question-answer pairs, enabling LLMs to better understand fine-grained molecular structure-property relationships. The dataset and evaluation code are available at https://github.com/xuanliugit/FGBench.

Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While functional generative models are theoretically domain- and discretization-agnostic, current implementations heavily rely on the Fourier Neural Operator (FNO), limiting their applicability to regular grids and rectangular domains. To overcome these critical limitations, we introduce the Mesh-Informed Neural Operator (MINO). By leveraging graph neural operators and cross-attention mechanisms, MINO offers a principled, domain- and discretization-agnostic backbone for generative modeling in function spaces. This advancement significantly expands the scope of such models to more diverse applications in generative, inverse, and regression tasks. Furthermore, MINO provides a unified perspective on integrating neural operators with general advanced deep learning architectures. Finally, we introduce a suite of standardized evaluation metrics that enable objective comparison of functional generative models, addressing another critical gap in the field.

Open-set semantic mapping is crucial for open-world robots. Current mapping approaches either are limited by the depth range or only map beyond-range entities in constrained settings, where overall they fail to combine within-range and beyond-range observations. Furthermore, these methods make a trade-off between fine-grained semantics and efficiency. We introduce RayFronts, a unified representation that enables both dense and beyond-range efficient semantic mapping. RayFronts encodes task-agnostic open-set semantics to both in-range voxels and beyond-range rays encoded at map boundaries, empowering the robot to reduce search volumes significantly and make informed decisions both within & beyond sensory range, while running at 8.84 Hz on an Orin AGX. Benchmarking the within-range semantics shows that RayFronts's fine-grained image encoding provides 1.34x zero-shot 3D semantic segmentation performance while improving throughput by 16.5x. Traditionally, online mapping performance is entangled with other system components, complicating evaluation. We propose a planner-agnostic evaluation framework that captures the utility for online beyond-range search and exploration, and show RayFronts reduces search volume 2.2x more efficiently than the closest online baselines.

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring the formation of very high-dimensional matrices and tensors, and therefore being computationally infeasible. In this paper I show how a linear simplification of recursive neural tensor network models can be mapped directly onto the categorical approach, giving a way of computing the required matrices and tensors. This mapping suggests a number of lines of research for both categorical compositional vector space models of meaning and for recursive neural network models of compositionality.

Grounding language to the visual observations of a navigating agent can be performed using off-the-shelf visual-language models pretrained on Internet-scale data (e.g., image captions). While this is useful for matching images to natural language descriptions of object goals, it remains disjoint from the process of mapping the environment, so that it lacks the spatial precision of classic geometric maps. To address this problem, we propose VLMaps, a spatial map representation that directly fuses pretrained visual-language features with a 3D reconstruction of the physical world. VLMaps can be autonomously built from video feed on robots using standard exploration approaches and enables natural language indexing of the map without additional labeled data. Specifically, when combined with large language models (LLMs), VLMaps can be used to (i) translate natural language commands into a sequence of open-vocabulary navigation goals (which, beyond prior work, can be spatial by construction, e.g., "in between the sofa and TV" or "three meters to the right of the chair") directly localized in the map, and (ii) can be shared among multiple robots with different embodiments to generate new obstacle maps on-the-fly (by using a list of obstacle categories). Extensive experiments carried out in simulated and real world environments show that VLMaps enable navigation according to more complex language instructions than existing methods. Videos are available at https://vlmaps.github.io.

Building artificial intelligence (AI) systems on top of a set of foundation models (FMs) is becoming a new paradigm in AI research. Their representative and generative abilities learnt from vast amounts of data can be easily adapted and transferred to a wide range of downstream tasks without extra training from scratch. However, leveraging FMs in cross-modal generation remains under-researched when audio modality is involved. On the other hand, automatically generating semantically-relevant sound from visual input is an important problem in cross-modal generation studies. To solve this vision-to-audio (V2A) generation problem, existing methods tend to design and build complex systems from scratch using modestly sized datasets. In this paper, we propose a lightweight solution to this problem by leveraging foundation models, specifically CLIP, CLAP, and AudioLDM. We first investigate the domain gap between the latent space of the visual CLIP and the auditory CLAP models. Then we propose a simple yet effective mapper mechanism (V2A-Mapper) to bridge the domain gap by translating the visual input between CLIP and CLAP spaces. Conditioned on the translated CLAP embedding, pretrained audio generative FM AudioLDM is adopted to produce high-fidelity and visually-aligned sound. Compared to previous approaches, our method only requires a quick training of the V2A-Mapper. We further analyze and conduct extensive experiments on the choice of the V2A-Mapper and show that a generative mapper is better at fidelity and variability (FD) while a regression mapper is slightly better at relevance (CS). Both objective and subjective evaluation on two V2A datasets demonstrate the superiority of our proposed method compared to current state-of-the-art approaches - trained with 86% fewer parameters but achieving 53% and 19% improvement in FD and CS, respectively.

Advancements in LLMs have recently unveiled challenges tied to computational efficiency and continual scalability due to their requirements of huge parameters, making the applications and evolution of these models on devices with limited computation resources and scenarios requiring various abilities increasingly cumbersome. Inspired by modularity within the human brain, there is a growing tendency to decompose LLMs into numerous functional modules, allowing for inference with part of modules and dynamic assembly of modules to tackle complex tasks, such as mixture-of-experts. To highlight the inherent efficiency and composability of the modular approach, we coin the term brick to represent each functional module, designating the modularized structure as configurable foundation models. In this paper, we offer a comprehensive overview and investigation of the construction, utilization, and limitation of configurable foundation models. We first formalize modules into emergent bricks - functional neuron partitions that emerge during the pre-training phase, and customized bricks - bricks constructed via additional post-training to improve the capabilities and knowledge of LLMs. Based on diverse functional bricks, we further present four brick-oriented operations: retrieval and routing, merging, updating, and growing. These operations allow for dynamic configuration of LLMs based on instructions to handle complex tasks. To verify our perspective, we conduct an empirical analysis on widely-used LLMs. We find that the FFN layers follow modular patterns with functional specialization of neurons and functional neuron partitions. Finally, we highlight several open issues and directions for future research. Overall, this paper aims to offer a fresh modular perspective on existing LLM research and inspire the future creation of more efficient and scalable foundational models.

A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this new family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

Understanding how the brain represents visual information is a fundamental challenge in neuroscience and artificial intelligence. While AI-driven decoding of neural data has provided insights into the human visual system, integrating multimodal neuroimaging signals, such as EEG, MEG, and fMRI, remains a critical hurdle due to their inherent spatiotemporal misalignment. Current approaches often analyze these modalities in isolation, limiting a holistic view of neural representation. In this study, we introduce BrainFLORA, a unified framework for integrating cross-modal neuroimaging data to construct a shared neural representation. Our approach leverages multimodal large language models (MLLMs) augmented with modality-specific adapters and task decoders, achieving state-of-the-art performance in joint-subject visual retrieval task and has the potential to extend multitasking. Combining neuroimaging analysis methods, we further reveal how visual concept representations align across neural modalities and with real world object perception. We demonstrate that the brain's structured visual concept representations exhibit an implicit mapping to physical-world stimuli, bridging neuroscience and machine learning from different modalities of neural imaging. Beyond methodological advancements, BrainFLORA offers novel implications for cognitive neuroscience and brain-computer interfaces (BCIs). Our code is available at https://github.com/ncclab-sustech/BrainFLORA.

Reconstructing images seen by people from their fMRI brain recordings provides a non-invasive window into the human brain. Despite recent progress enabled by diffusion models, current methods often lack faithfulness to the actual seen images. We present "Brain-IT", a brain-inspired approach that addresses this challenge through a Brain Interaction Transformer (BIT), allowing effective interactions between clusters of functionally-similar brain-voxels. These functional-clusters are shared by all subjects, serving as building blocks for integrating information both within and across brains. All model components are shared by all clusters & subjects, allowing efficient training with a limited amount of data. To guide the image reconstruction, BIT predicts two complementary localized patch-level image features: (i)high-level semantic features which steer the diffusion model toward the correct semantic content of the image; and (ii)low-level structural features which help to initialize the diffusion process with the correct coarse layout of the image. BIT's design enables direct flow of information from brain-voxel clusters to localized image features. Through these principles, our method achieves image reconstructions from fMRI that faithfully reconstruct the seen images, and surpass current SotA approaches both visually and by standard objective metrics. Moreover, with only 1-hour of fMRI data from a new subject, we achieve results comparable to current methods trained on full 40-hour recordings.

LiDAR mapping is important yet challenging in self-driving and mobile robotics. To tackle such a global point cloud registration problem, DeepMapping converts the complex map estimation into a self-supervised training of simple deep networks. Despite its broad convergence range on small datasets, DeepMapping still cannot produce satisfactory results on large-scale datasets with thousands of frames. This is due to the lack of loop closures and exact cross-frame point correspondences, and the slow convergence of its global localization network. We propose DeepMapping2 by adding two novel techniques to address these issues: (1) organization of training batch based on map topology from loop closing, and (2) self-supervised local-to-global point consistency loss leveraging pairwise registration. Our experiments and ablation studies on public datasets (KITTI, NCLT, and Nebula) demonstrate the effectiveness of our method.

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper introduces a novel approach that bridges this gap by combining the interpretability of linear methods with the expressiveness of non-linear transformations. The proposed algorithm constructs a non-linear mapping between high-dimensional and low-dimensional spaces through a combination of linear transformations, each weighted by Gaussian functions. This architecture enables complex non-linear transformations while preserving the interpretability advantages of linear methods, as each transformation can be analyzed independently. The resulting model provides both powerful dimensionality reduction and transparent insights into the transformed space. Techniques for interpreting the learned transformations are presented, including methods for identifying suppressed dimensions and how space is expanded and contracted. These tools enable practitioners to understand how the algorithm preserves and modifies geometric relationships during dimensionality reduction. To ensure the practical utility of this algorithm, the creation of user-friendly software packages is emphasized, facilitating its adoption in both academia and industry.

Understanding how humans leverage semantic knowledge to navigate unfamiliar environments and decide where to explore next is pivotal for developing robots capable of human-like search behaviors. We introduce a zero-shot navigation approach, Vision-Language Frontier Maps (VLFM), which is inspired by human reasoning and designed to navigate towards unseen semantic objects in novel environments. VLFM builds occupancy maps from depth observations to identify frontiers, and leverages RGB observations and a pre-trained vision-language model to generate a language-grounded value map. VLFM then uses this map to identify the most promising frontier to explore for finding an instance of a given target object category. We evaluate VLFM in photo-realistic environments from the Gibson, Habitat-Matterport 3D (HM3D), and Matterport 3D (MP3D) datasets within the Habitat simulator. Remarkably, VLFM achieves state-of-the-art results on all three datasets as measured by success weighted by path length (SPL) for the Object Goal Navigation task. Furthermore, we show that VLFM's zero-shot nature enables it to be readily deployed on real-world robots such as the Boston Dynamics Spot mobile manipulation platform. We deploy VLFM on Spot and demonstrate its capability to efficiently navigate to target objects within an office building in the real world, without any prior knowledge of the environment. The accomplishments of VLFM underscore the promising potential of vision-language models in advancing the field of semantic navigation. Videos of real-world deployment can be viewed at naoki.io/vlfm.

Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit object-level reasoning and interconnectivity. In this paper, we propose a novel topological representation of an environment based on "image segments", which are semantically meaningful and open-vocabulary queryable, conferring several advantages over previous works based on pixel-level features. Unlike 3D scene graphs, we create a purely topological graph with segments as nodes, where edges are formed by a) associating segment-level descriptors between pairs of consecutive images and b) connecting neighboring segments within an image using their pixel centroids. This unveils a "continuous sense of a place", defined by inter-image persistence of segments along with their intra-image neighbours. It further enables us to represent and update segment-level descriptors through neighborhood aggregation using graph convolution layers, which improves robot localization based on segment-level retrieval. Using real-world data, we show how our proposed map representation can be used to i) generate navigation plans in the form of "hops over segments" and ii) search for target objects using natural language queries describing spatial relations of objects. Furthermore, we quantitatively analyze data association at the segment level, which underpins inter-image connectivity during mapping and segment-level localization when revisiting the same place. Finally, we show preliminary trials on segment-level `hopping' based zero-shot real-world navigation. Project page with supplementary details: oravus.github.io/RoboHop/

Large language models (LLMs) have demonstrated impressive capabilities in general scenarios, exhibiting a level of aptitude that approaches, in some aspects even surpasses, human-level intelligence. Among their numerous skills, the translation abilities of LLMs have received considerable attention. In contrast to traditional machine translation that focuses solely on source-target mapping, LLM-based translation can potentially mimic the human translation process that takes many preparatory steps to ensure high-quality translation. This work aims to explore this possibility by proposing the MAPS framework, which stands for Multi-Aspect Prompting and Selection. Specifically, we enable LLMs to first analyze the given source text and extract three aspects of translation-related knowledge: keywords, topics and relevant demonstrations to guide the translation process. To filter out the noisy and unhelpful knowledge, we employ a selection mechanism based on quality estimation. Experiments suggest that MAPS brings significant and consistent improvements over text-davinci-003 and Alpaca on eight translation directions from the latest WMT22 test sets. Our further analysis shows that the extracted knowledge is critical in resolving up to 59% of hallucination mistakes in translation. Code is available at https://github.com/zwhe99/MAPS-mt.

In this paper, we introduce MapBench-the first dataset specifically designed for human-readable, pixel-based map-based outdoor navigation, curated from complex path finding scenarios. MapBench comprises over 1600 pixel space map path finding problems from 100 diverse maps. In MapBench, LVLMs generate language-based navigation instructions given a map image and a query with beginning and end landmarks. For each map, MapBench provides Map Space Scene Graph (MSSG) as an indexing data structure to convert between natural language and evaluate LVLM-generated results. We demonstrate that MapBench significantly challenges state-of-the-art LVLMs both zero-shot prompting and a Chain-of-Thought (CoT) augmented reasoning framework that decomposes map navigation into sequential cognitive processes. Our evaluation of both open-source and closed-source LVLMs underscores the substantial difficulty posed by MapBench, revealing critical limitations in their spatial reasoning and structured decision-making capabilities. We release all the code and dataset in https://github.com/taco-group/MapBench.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

We introduce a new functional space U designed to contain all classical arithmetic functions (Mobius, von Mangoldt, Euler phi, divisor functions, Dirichlet characters, etc.). The norm of U combines a Hilbert-type component, based on square summability of Dirichlet coefficients for every s > 1, with a Banach component controlling logarithmic averages of partial sums. We prove that U is a complete Banach space which embeds continuously all standard Hilbert spaces of Dirichlet series and allows natural actions of Dirichlet convolution and shift operators. This framework provides a unified analytic setting for classical and modern problems in multiplicative number theory.

Maps are fundamental medium to visualize and represent the real word in a simple and 16 philosophical way. The emergence of the 3rd wave information has made a proportion of maps are available to be generated ubiquitously, which would significantly enrich the dimensions and perspectives to understand the characteristics of the real world. However, a majority of map dataset have never been discovered, acquired and effectively used, and the map data used in many applications might not be completely fitted for the authentic demands of these applications. This challenge is emerged due to the lack of numerous well-labelled benchmark datasets for implementing the deep learning approaches into identifying complicated map content. Thus, we develop a large-scale benchmark dataset that includes well-labelled dataset for map text annotation recognition, map scene classification, map super-resolution reconstruction, and map style transferring. Furthermore, these well-labelled datasets would facilitate the state-of-the-art machine intelligence technologies to conduct map feature detection, map pattern recognition and map content retrieval. We hope our efforts would be useful for AI-enhanced cartographical applications.

3D indoor scenes are widely used in computer graphics, with applications ranging from interior design to gaming to virtual and augmented reality. They also contain rich information, including room layout, as well as furniture type, geometry, and placement. High-quality 3D indoor scenes are highly demanded while it requires expertise and is time-consuming to design high-quality 3D indoor scenes manually. Existing research only addresses partial problems: some works learn to generate room layout, and other works focus on generating detailed structure and geometry of individual furniture objects. However, these partial steps are related and should be addressed together for optimal synthesis. We propose SCENEHGN, a hierarchical graph network for 3D indoor scenes that takes into account the full hierarchy from the room level to the object level, then finally to the object part level. Therefore for the first time, our method is able to directly generate plausible 3D room content, including furniture objects with fine-grained geometry, and their layout. To address the challenge, we introduce functional regions as intermediate proxies between the room and object levels to make learning more manageable. To ensure plausibility, our graph-based representation incorporates both vertical edges connecting child nodes with parent nodes from different levels, and horizontal edges encoding relationships between nodes at the same level. Extensive experiments demonstrate that our method produces superior generation results, even when comparing results of partial steps with alternative methods that can only achieve these. We also demonstrate that our method is effective for various applications such as part-level room editing, room interpolation, and room generation by arbitrary room boundaries.

Multimodal Large Language Models (MLLMs) have shown significant potential in medical image analysis. However, their capabilities in interpreting fundus images, a critical skill for ophthalmology, remain under-evaluated. Existing benchmarks lack fine-grained task divisions and fail to provide modular analysis of its two key modules, i.e., large language model (LLM) and vision encoder (VE). This paper introduces FunBench, a novel visual question answering (VQA) benchmark designed to comprehensively evaluate MLLMs' fundus reading skills. FunBench features a hierarchical task organization across four levels (modality perception, anatomy perception, lesion analysis, and disease diagnosis). It also offers three targeted evaluation modes: linear-probe based VE evaluation, knowledge-prompted LLM evaluation, and holistic evaluation. Experiments on nine open-source MLLMs plus GPT-4o reveal significant deficiencies in fundus reading skills, particularly in basic tasks such as laterality recognition. The results highlight the limitations of current MLLMs and emphasize the need for domain-specific training and improved LLMs and VEs.

Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs, scientists search for models that best explain data, etc. The goal of search algorithms has traditionally been to return the single highest-performing solution in a search space. Here we describe a new, fundamentally different type of algorithm that is more useful because it provides a holistic view of how high-performing solutions are distributed throughout a search space. It creates a map of high-performing solutions at each point in a space defined by dimensions of variation that a user gets to choose. This Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm illuminates search spaces, allowing researchers to understand how interesting attributes of solutions combine to affect performance, either positively or, equally of interest, negatively. For example, a drug company may wish to understand how performance changes as the size of molecules and their cost-to-produce vary. MAP-Elites produces a large diversity of high-performing, yet qualitatively different solutions, which can be more helpful than a single, high-performing solution. Interestingly, because MAP-Elites explores more of the search space, it also tends to find a better overall solution than state-of-the-art search algorithms. We demonstrate the benefits of this new algorithm in three different problem domains ranging from producing modular neural networks to designing simulated and real soft robots. Because MAP- Elites (1) illuminates the relationship between performance and dimensions of interest in solutions, (2) returns a set of high-performing, yet diverse solutions, and (3) improves finding a single, best solution, it will advance science and engineering.

Object goal navigation aims to navigate an agent to locations of a given object category in unseen environments. Classical methods explicitly build maps of environments and require extensive engineering while lacking semantic information for object-oriented exploration. On the other hand, end-to-end learning methods alleviate manual map design and predict actions using implicit representations. Such methods, however, lack an explicit notion of geometry and may have limited ability to encode navigation history. In this work, we propose an implicit spatial map for object goal navigation. Our implicit map is recursively updated with new observations at each step using a transformer. To encourage spatial reasoning, we introduce auxiliary tasks and train our model to reconstruct explicit maps as well as to predict visual features, semantic labels and actions. Our method significantly outperforms the state of the art on the challenging MP3D dataset and generalizes well to the HM3D dataset. We successfully deploy our model on a real robot and achieve encouraging object goal navigation results in real scenes using only a few real-world demonstrations. Code, trained models and videos are available at https://www.di.ens.fr/willow/research/onav_rim/.

Recent works successfully leveraged Large Language Models' (LLM) abilities to capture abstract knowledge about world's physics to solve decision-making problems. Yet, the alignment between LLMs' knowledge and the environment can be wrong and limit functional competence due to lack of grounding. In this paper, we study an approach (named GLAM) to achieve this alignment through functional grounding: we consider an agent using an LLM as a policy that is progressively updated as the agent interacts with the environment, leveraging online Reinforcement Learning to improve its performance to solve goals. Using an interactive textual environment designed to study higher-level forms of functional grounding, and a set of spatial and navigation tasks, we study several scientific questions: 1) Can LLMs boost sample efficiency for online learning of various RL tasks? 2) How can it boost different forms of generalization? 3) What is the impact of online learning? We study these questions by functionally grounding several variants (size, architecture) of FLAN-T5.

Model merging has emerged as an effective approach to combine multiple single-task models into a multitask model. This process typically involves computing a weighted average of the model parameters without any additional training. Existing model-merging methods focus on enhancing average task accuracy. However, interference and conflicts between the objectives of different tasks can lead to trade-offs during the merging process. In real-world applications, a set of solutions with various trade-offs can be more informative, helping practitioners make decisions based on diverse preferences. In this paper, we introduce a novel and low-compute algorithm, Model Merging with Amortized Pareto Front (MAP). MAP efficiently identifies a Pareto set of scaling coefficients for merging multiple models, reflecting the trade-offs involved. It amortizes the substantial computational cost of evaluations needed to estimate the Pareto front by using quadratic approximation surrogate models derived from a pre-selected set of scaling coefficients. Experimental results on vision and natural language processing tasks demonstrate that MAP can accurately identify the Pareto front, providing practitioners with flexible solutions to balance competing task objectives. We also introduce Bayesian MAP for scenarios with a relatively low number of tasks and Nested MAP for situations with a high number of tasks, further reducing the computational cost of evaluation.

Autonomous driving systems require High-Definition (HD) semantic maps to navigate around urban roads. Existing solutions approach the semantic mapping problem by offline manual annotation, which suffers from serious scalability issues. Recent learning-based methods produce dense rasterized segmentation predictions to construct maps. However, these predictions do not include instance information of individual map elements and require heuristic post-processing to obtain vectorized maps. To tackle these challenges, we introduce an end-to-end vectorized HD map learning pipeline, termed VectorMapNet. VectorMapNet takes onboard sensor observations and predicts a sparse set of polylines in the bird's-eye view. This pipeline can explicitly model the spatial relation between map elements and generate vectorized maps that are friendly to downstream autonomous driving tasks. Extensive experiments show that VectorMapNet achieve strong map learning performance on both nuScenes and Argoverse2 dataset, surpassing previous state-of-the-art methods by 14.2 mAP and 14.6mAP. Qualitatively, VectorMapNet is capable of generating comprehensive maps and capturing fine-grained details of road geometry. To the best of our knowledge, VectorMapNet is the first work designed towards end-to-end vectorized map learning from onboard observations. Our project website is available at https://tsinghua-mars-lab.github.io/vectormapnet/.

Recent advancements in Large Language Models (LLMs) have set themselves apart with their exceptional performance in complex language modelling tasks. However, these models are also known for their significant computational and storage requirements, primarily due to the quadratic computation complexity of softmax attention. To mitigate this issue, linear attention has been designed to reduce the quadratic space-time complexity that is inherent in standard transformers. In this work, we embarked on a comprehensive exploration of three key components that substantially impact the performance of the Gated Linear Attention module: feature maps, normalization, and the gating mechanism. We developed a feature mapping function to address some crucial issues that previous suggestions overlooked. Then we offered further rationale for the integration of normalization layers to stabilize the training process. Moreover, we explored the saturation phenomenon of the gating mechanism and augmented it with a refining module. We conducted extensive experiments and showed our architecture outperforms previous Gated Linear Attention mechanisms in extensive tasks including training from scratch and post-linearization with continual pre-training.

Understanding the hidden mechanisms behind human's visual perception is a fundamental question in neuroscience. To that end, investigating into the neural responses of human mind activities, such as functional Magnetic Resonance Imaging (fMRI), has been a significant research vehicle. However, analyzing fMRI signals is challenging, costly, daunting, and demanding for professional training. Despite remarkable progress in fMRI analysis, existing approaches are limited to generating 2D images and far away from being biologically meaningful and practically useful. Under this insight, we propose to generate visually plausible and functionally more comprehensive 3D outputs decoded from brain signals, enabling more sophisticated modeling of fMRI data. Conceptually, we reformulate this task as a {\em fMRI conditioned 3D object generation} problem. We design a novel 3D object representation learning method, Brain3D, that takes as input the fMRI data of a subject who was presented with a 2D image, and yields as output the corresponding 3D object images. The key capabilities of this model include tackling the noises with high-level semantic signals and a two-stage architecture design for progressive high-level information integration. Extensive experiments validate the superior capability of our model over previous state-of-the-art 3D object generation methods. Importantly, we show that our model captures the distinct functionalities of each region of human vision system as well as their intricate interplay relationships, aligning remarkably with the established discoveries in neuroscience. Further, preliminary evaluations indicate that Brain3D can successfully identify the disordered brain regions in simulated scenarios, such as V1, V2, V3, V4, and the medial temporal lobe (MTL) within the human visual system. Our data and code will be available at https://brain-3d.github.io/.

Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of relevant features to the functional entropy of the network with respect to the input. We rely on the log-Sobolev inequality that bounds the functional entropy by the functional Fisher information with respect to the covariance of the data. This provides a principled way to measure the amount of information contribution of a subset of features to the decision function. Through extensive experiments, we show that our method surpasses existing interpretability sampling-based methods on various data signals such as image, text, and audio.

Not yet. We present SPACE, a benchmark that systematically evaluates spatial cognition in frontier models. Our benchmark builds on decades of research in cognitive science. It evaluates large-scale mapping abilities that are brought to bear when an organism traverses physical environments, smaller-scale reasoning about object shapes and layouts, and cognitive infrastructure such as spatial attention and memory. For many tasks, we instantiate parallel presentations via text and images, allowing us to benchmark both large language models and large multimodal models. Results suggest that contemporary frontier models fall short of the spatial intelligence of animals, performing near chance level on a number of classic tests of animal cognition.

Depth maps are widely used in feed-forward 3D Gaussian Splatting (3DGS) pipelines by unprojecting them into 3D point clouds for novel view synthesis. This approach offers advantages such as efficient training, the use of known camera poses, and accurate geometry estimation. However, depth discontinuities at object boundaries often lead to fragmented or sparse point clouds, degrading rendering quality -- a well-known limitation of depth-based representations. To tackle this issue, we introduce PM-Loss, a novel regularization loss based on a pointmap predicted by a pre-trained transformer. Although the pointmap itself may be less accurate than the depth map, it effectively enforces geometric smoothness, especially around object boundaries. With the improved depth map, our method significantly improves the feed-forward 3DGS across various architectures and scenes, delivering consistently better rendering results. Our project page: https://aim-uofa.github.io/PMLoss

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

A fuzzy theoretic analytical approach was recently introduced that leads to efficient and robust models while addressing automatically the typical issues associated to parametric deep models. However, a formal conceptualization of the fuzzy theoretic analytical deep models is still not available. This paper introduces using measure theoretic basis the notion of membership-mapping for representing data points through attribute values (motivated by fuzzy theory). A property of the membership-mapping, that can be exploited for data representation learning, is of providing an interpolation on the given data points in the data space. An analytical approach to the variational learning of a membership-mappings based data representation model is considered.

Brain MRI scans are often found in four modalities, consisting of T1-weighted with and without contrast enhancement (T1ce and T1w), T2-weighted imaging (T2w), and Flair. Leveraging complementary information from these different modalities enables models to learn richer, more discriminative features for understanding brain anatomy, which could be used in downstream tasks such as anomaly detection. However, in clinical practice, not all MRI modalities are always available due to various reasons. This makes missing modality generation a critical challenge in medical image analysis. In this paper, we propose SLaM-DiMM, a novel missing modality generation framework that harnesses the power of diffusion models to synthesize any of the four target MRI modalities from other available modalities. Our approach not only generates high-fidelity images but also ensures structural coherence across the depth of the volume through a dedicated coherence enhancement mechanism. Qualitative and quantitative evaluations on the BraTS-Lighthouse-2025 Challenge dataset demonstrate the effectiveness of the proposed approach in synthesizing anatomically plausible and structurally consistent results. Code is available at https://github.com/BheeshmSharma/SLaM-DiMM-MICCAI-BraTS-Challenge-2025.

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The exact definitions of maps, however, are often application-specific and hand-crafted for different scenarios (e.g. 3D landmarks, lines, planes, bags of visual words). We propose to represent maps as a deep neural net called MapNet, which enables learning a data-driven map representation. Unlike prior work on learning maps, MapNet exploits cheap and ubiquitous sensory inputs like visual odometry and GPS in addition to images and fuses them together for camera localization. Geometric constraints expressed by these inputs, which have traditionally been used in bundle adjustment or pose-graph optimization, are formulated as loss terms in MapNet training and also used during inference. In addition to directly improving localization accuracy, this allows us to update the MapNet (i.e., maps) in a self-supervised manner using additional unlabeled video sequences from the scene. We also propose a novel parameterization for camera rotation which is better suited for deep-learning based camera pose regression. Experimental results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar dataset show significant performance improvement over prior work. The MapNet project webpage is https://goo.gl/mRB3Au.

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

Foundation models have triggered a paradigm shift in computer vision and are increasingly being adopted in remote sensing, particularly for multispectral imagery. Yet, their potential in hyperspectral imaging (HSI) remains untapped due to the absence of comprehensive and globally representative hyperspectral datasets. To close this gap, we introduce SpectralEarth, a large-scale multi-temporal dataset designed to pretrain hyperspectral foundation models leveraging data from the Environmental Mapping and Analysis Program (EnMAP). SpectralEarth comprises 538,974 image patches covering 415,153 unique locations from more than 11,636 globally distributed EnMAP scenes spanning two years of archive. Additionally, 17.5% of these locations include multiple timestamps, enabling multi-temporal HSI analysis. Utilizing state-of-the-art self-supervised learning (SSL) algorithms, we pretrain a series of foundation models on SpectralEarth. We integrate a spectral adapter into classical vision backbones to accommodate the unique characteristics of HSI. In tandem, we construct four downstream datasets for land-cover and crop-type mapping, providing benchmarks for model evaluation. Experimental results support the versatility of our models, showcasing their generalizability across different tasks and sensors. We also highlight computational efficiency during model fine-tuning. The dataset, models, and source code will be made publicly available.

The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However, finding the right permutation is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to sub-optimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature, under several conditions for both optimal transport finding and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with state-of-art results from the literature.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

A major goal of neuroscience is to understand brain computations during visual processing in naturalistic settings. A dominant approach is to use image-computable deep neural networks trained with different task objectives as a basis for linear encoding models. However, in addition to requiring tuning a large number of parameters, the linear encoding approach ignores the structure of the feature maps both in the brain and the models. Recently proposed alternatives have focused on decomposing the linear mapping to spatial and feature components but focus on finding static receptive fields for units that are applicable only in early visual areas. In this work, we employ the attention mechanism used in the transformer architecture to study how retinotopic visual features can be dynamically routed to category-selective areas in high-level visual processing. We show that this computational motif is significantly more powerful than alternative methods in predicting brain activity during natural scene viewing, across different feature basis models and modalities. We also show that this approach is inherently more interpretable, without the need to create importance maps, by interpreting the attention routing signal for different high-level categorical areas. Our approach proposes a mechanistic model of how visual information from retinotopic maps can be routed based on the relevance of the input content to different category-selective regions.

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and inverse problems like geometric design. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

Training a Large Visual Language Model (LVLM) from scratch, like GPT-4, is resource-intensive. Our paper presents a play-and-plug module for Large Language Models (LLMs), namely Interactive Perception Network (IPN), aiming to achieve a LVLM by incorporating the image understanding capability into LLMs. Previous methods incorporate visual information into LLMs with a simple visual mapping network, where the image feature is projected into the embedding space of LLMs via a linear layer. Such mapping network projects the image feature once yet does not consider the interaction between the image and the human input query. Hence, the obtained visual information with no connections with human intention may be inadequate for LLMs to make intention-following responses, which we term as static visual information. IPN addresses this issue by allowing the LLM to request the desired visual information aligned with various human instructions, which we term as the dynamic interaction between the LLM and visual information. Specifically, IPN consists of a simple visual mapping network to provide the basic perception of an image for LLMs. It also contains additional modules responsible for acquiring requests from LLMs, performing request-based visual information interaction, and transmitting the resulting interacted visual information to LLMs, respectively. In this way, LLMs act to understand the human query, deliver the corresponding request to the request-based visual information interaction module, and generate the response based on the interleaved multimodal information. We evaluate IPN through extensive experiments on multimodal question answering, reasoning, and so on, demonstrating that it significantly improves the zero-shot performance of LVLMs on various multimodal tasks compared to previous methods.

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

A heuristic extending the Squarified Treemap technique for the representation of hierarchical information as treemaps is presented. The original technique gives high quality treemap views, since items are laid out with rectangles that approximate squares, allowing easy comparison and selection operations. New key steps, with a low computational impact, have been introduced to yield treemaps with even better aspect ratios and higher homogeneity among items.

Automated Theorem Proving (ATP) faces challenges due to its complexity and computational demands. Recent work has explored using Large Language Models (LLMs) for ATP action selection, but these methods can be resource-intensive. This study introduces FEAS, an agent that enhances the COPRA in-context learning framework within Lean. FEAS refines prompt generation, response parsing, and incorporates domain-specific heuristics for functional equations. It introduces FunEq, a curated dataset of functional equation problems with varying difficulty. FEAS outperforms baselines on FunEq, particularly with the integration of domain-specific heuristics. The results demonstrate FEAS's effectiveness in generating and formalizing high-level proof strategies into Lean proofs, showcasing the potential of tailored approaches for specific ATP challenges.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF) which are maps parameterized with deep neural networks trained to push a reference distribution towards a target. NF-enhanced samplers recently proposed blend (Markov chain) Monte Carlo methods with either (i) proposal draws from the flow or (ii) a flow-based reparametrization. In both cases, the quality of the learned transport conditions performance. The present work clarifies for the first time the relative strengths and weaknesses of these two approaches. Our study concludes that multimodal targets can be reliably handled with flow-based proposals up to moderately high dimensions. In contrast, methods relying on reparametrization struggle with multimodality but are more robust otherwise in high-dimensional settings and under poor training. To further illustrate the influence of target-proposal adequacy, we also derive a new quantitative bound for the mixing time of the Independent Metropolis-Hastings sampler.

To represent the biological variability of clinical neuroimaging populations, it is vital to be able to combine data across scanners and studies. However, different MRI scanners produce images with different characteristics, resulting in a domain shift known as the `harmonisation problem'. Additionally, neuroimaging data is inherently personal in nature, leading to data privacy concerns when sharing the data. To overcome these barriers, we propose an Unsupervised Source-Free Domain Adaptation (SFDA) method, SFHarmony. Through modelling the imaging features as a Gaussian Mixture Model and minimising an adapted Bhattacharyya distance between the source and target features, we can create a model that performs well for the target data whilst having a shared feature representation across the data domains, without needing access to the source data for adaptation or target labels. We demonstrate the performance of our method on simulated and real domain shifts, showing that the approach is applicable to classification, segmentation and regression tasks, requiring no changes to the algorithm. Our method outperforms existing SFDA approaches across a range of realistic data scenarios, demonstrating the potential utility of our approach for MRI harmonisation and general SFDA problems. Our code is available at https://github.com/nkdinsdale/SFHarmony.

Image-to-image translation is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image using a training set of aligned image pairs. However, for many tasks, paired training data will not be available. We present an approach for learning to translate an image from a source domain X to a target domain Y in the absence of paired examples. Our goal is to learn a mapping G: X rightarrow Y such that the distribution of images from G(X) is indistinguishable from the distribution Y using an adversarial loss. Because this mapping is highly under-constrained, we couple it with an inverse mapping F: Y rightarrow X and introduce a cycle consistency loss to push F(G(X)) approx X (and vice versa). Qualitative results are presented on several tasks where paired training data does not exist, including collection style transfer, object transfiguration, season transfer, photo enhancement, etc. Quantitative comparisons against several prior methods demonstrate the superiority of our approach.

Despite recent progress made by large language models in code generation, they still struggle with programs that meet complex requirements. Recent work utilizes plan-and-solve decomposition to decrease the complexity and leverage self-tests to refine the generated program. Yet, planning deep-inside requirements in advance can be challenging, and the tests need to be accurate to accomplish self-improvement. To this end, we propose FunCoder, a code generation framework incorporating the divide-and-conquer strategy with functional consensus. Specifically, FunCoder recursively branches off sub-functions as smaller goals during code generation, represented by a tree hierarchy. These sub-functions are then composited to attain more complex objectives. Additionally, we designate functions via a consensus formed by identifying similarities in program behavior, mitigating error propagation. FunCoder outperforms state-of-the-art methods by +9.8% on average in HumanEval, MBPP, xCodeEval and MATH with GPT-3.5 and GPT-4. Moreover, our method demonstrates superiority on smaller models: With FunCoder, StableCode-3b surpasses GPT-3.5 by +18.6% and achieves 97.7% of GPT-4's performance on HumanEval. Further analysis reveals that our proposed dynamic function decomposition is capable of handling complex requirements, and the functional consensus prevails over self-testing in correctness evaluation.

Foundational mapping remains a challenge in many parts of the world, particularly in dynamic scenarios such as natural disasters when timely updates are critical. Updating maps is currently a highly manual process requiring a large number of human labelers to either create features or rigorously validate automated outputs. We propose that the frequent revisits of earth imaging satellite constellations may accelerate existing efforts to quickly update foundational maps when combined with advanced machine learning techniques. Accordingly, the SpaceNet partners (CosmiQ Works, Radiant Solutions, and NVIDIA), released a large corpus of labeled satellite imagery on Amazon Web Services (AWS) called SpaceNet. The SpaceNet partners also launched a series of public prize competitions to encourage improvement of remote sensing machine learning algorithms. The first two of these competitions focused on automated building footprint extraction, and the most recent challenge focused on road network extraction. In this paper we discuss the SpaceNet imagery, labels, evaluation metrics, prize challenge results to date, and future plans for the SpaceNet challenge series.

Graph Transformers have recently been successful in various graph representation learning tasks, providing a number of advantages over message-passing Graph Neural Networks. Utilizing Graph Transformers for learning the representation of the brain functional connectivity network is also gaining interest. However, studies to date have underlooked the temporal dynamics of functional connectivity, which fluctuates over time. Here, we propose a method for learning the representation of dynamic functional connectivity with Graph Transformers. Specifically, we define the connectome embedding, which holds the position, structure, and time information of the functional connectivity graph, and use Transformers to learn its representation across time. We perform experiments with over 50,000 resting-state fMRI samples obtained from three datasets, which is the largest number of fMRI data used in studies by far. The experimental results show that our proposed method outperforms other competitive baselines in gender classification and age regression tasks based on the functional connectivity extracted from the fMRI data.

Zero-Shot Learning (ZSL) promises to scale visual recognition by bypassing the conventional model training requirement of annotated examples for every category. This is achieved by establishing a mapping connecting low-level features and a semantic description of the label space, referred as visual-semantic mapping, on auxiliary data. Reusing the learned mapping to project target videos into an embedding space thus allows novel-classes to be recognised by nearest neighbour inference. However, existing ZSL methods suffer from auxiliary-target domain shift intrinsically induced by assuming the same mapping for the disjoint auxiliary and target classes. This compromises the generalisation accuracy of ZSL recognition on the target data. In this work, we improve the ability of ZSL to generalise across this domain shift in both model- and data-centric ways by formulating a visual-semantic mapping with better generalisation properties and a dynamic data re-weighting method to prioritise auxiliary data that are relevant to the target classes. Specifically: (1) We introduce a multi-task visual-semantic mapping to improve generalisation by constraining the semantic mapping parameters to lie on a low-dimensional manifold, (2) We explore prioritised data augmentation by expanding the pool of auxiliary data with additional instances weighted by relevance to the target domain. The proposed new model is applied to the challenging zero-shot action recognition problem to demonstrate its advantages over existing ZSL models.

Objective: fMRI and derived measures such as functional connectivity (FC) have been used to predict brain age, general fluid intelligence, psychiatric disease status, and preclinical neurodegenerative disease. However, it is not always clear that all demographic confounds, such as age, sex, and race, have been removed from fMRI data. Additionally, many fMRI datasets are restricted to authorized researchers, making dissemination of these valuable data sources challenging. Methods: We create a variational autoencoder (VAE)-based model, DemoVAE, to decorrelate fMRI features from demographics and generate high-quality synthetic fMRI data based on user-supplied demographics. We train and validate our model using two large, widely used datasets, the Philadelphia Neurodevelopmental Cohort (PNC) and Bipolar and Schizophrenia Network for Intermediate Phenotypes (BSNIP). Results: We find that DemoVAE recapitulates group differences in fMRI data while capturing the full breadth of individual variations. Significantly, we also find that most clinical and computerized battery fields that are correlated with fMRI data are not correlated with DemoVAE latents. An exception are several fields related to schizophrenia medication and symptom severity. Conclusion: Our model generates fMRI data that captures the full distribution of FC better than traditional VAE or GAN models. We also find that most prediction using fMRI data is dependent on correlation with, and prediction of, demographics. Significance: Our DemoVAE model allows for generation of high quality synthetic data conditioned on subject demographics as well as the removal of the confounding effects of demographics. We identify that FC-based prediction tasks are highly influenced by demographic confounds.

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

Magnetic resonance imaging (MRI) is the standard modality to understand human brain structure and function in vivo (antemortem). Decades of research in human neuroimaging has led to the widespread development of methods and tools to provide automated volume-based segmentations and surface-based parcellations which help localize brain functions to specialized anatomical regions. Recently ex vivo (postmortem) imaging of the brain has opened-up avenues to study brain structure at sub-millimeter ultra high-resolution revealing details not possible to observe with in vivo MRI. Unfortunately, there has been limited methodological development in ex vivo MRI primarily due to lack of datasets and limited centers with such imaging resources. Therefore, in this work, we present one-of-its-kind dataset of 82 ex vivo T2w whole brain hemispheres MRI at 0.3 mm isotropic resolution spanning Alzheimer's disease and related dementias. We adapted and developed a fast and easy-to-use automated surface-based pipeline to parcellate, for the first time, ultra high-resolution ex vivo brain tissue at the native subject space resolution using the Desikan-Killiany-Tourville (DKT) brain atlas. This allows us to perform vertex-wise analysis in the template space and thereby link morphometry measures with pathology measurements derived from histology. We will open-source our dataset docker container, Jupyter notebooks for ready-to-use out-of-the-box set of tools and command line options to advance ex vivo MRI clinical brain imaging research on the project webpage.

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable functional regression at new points with mean and density estimation. Our method outperforms state-of-the-art models in stochastic process learning, functional regression, and prior learning.

Electronic maps consist of diverse entities, such as points of interest (POIs), road networks, and land parcels, playing a vital role in applications like ITS and LBS. Map entity representation learning (MapRL) generates versatile and reusable data representations, providing essential tools for efficiently managing and utilizing map entity data. Despite the progress in MapRL, two key challenges constrain further development. First, existing research is fragmented, with models classified by the type of map entity, limiting the reusability of techniques across different tasks. Second, the lack of unified benchmarks makes systematic evaluation and comparison of models difficult. To address these challenges, we propose a novel taxonomy for MapRL that organizes models based on functional module-such as encoders, pre-training tasks, and downstream tasks-rather than by entity type. Building on this taxonomy, we present a taxonomy-driven library, VecCity, which offers easy-to-use interfaces for encoding, pre-training, fine-tuning, and evaluation. The library integrates datasets from nine cities and reproduces 21 mainstream MapRL models, establishing the first standardized benchmarks for the field. VecCity also allows users to modify and extend models through modular components, facilitating seamless experimentation. Our comprehensive experiments cover multiple types of map entities and evaluate 21 VecCity pre-built models across various downstream tasks. Experimental results demonstrate the effectiveness of VecCity in streamlining model development and provide insights into the impact of various components on performance. By promoting modular design and reusability, VecCity offers a unified framework to advance research and innovation in MapRL. The code is available at https://github.com/Bigscity-VecCity/VecCity.

The human brain is a complex, dynamic network, which is commonly studied using functional magnetic resonance imaging (fMRI) and modeled as network of Regions of interest (ROIs) for understanding various brain functions. Recent studies utilize deep learning approaches to learn the brain network representation based on functional connectivity (FC) profile, broadly falling into two main categories. The Fixed-FC approaches, utilizing the FC profile which represents the linear temporal relation within the brain network, are limited by failing to capture informative brain temporal dynamics. On the other hand, the Dynamic-FC approaches, modeling the evolving FC profile over time, often exhibit less satisfactory performance due to challenges in handling the inherent noisy nature of fMRI data. To address these challenges, we propose Brain Masked Auto-Encoder (BrainMAE) for learning representations directly from fMRI time-series data. Our approach incorporates two essential components: a region-aware graph attention mechanism designed to capture the relationships between different brain ROIs, and a novel self-supervised masked autoencoding framework for effective model pre-training. These components enable the model to capture rich temporal dynamics of brain activity while maintaining resilience to inherent noise in fMRI data. Our experiments demonstrate that BrainMAE consistently outperforms established baseline methods by significant margins in four distinct downstream tasks. Finally, leveraging the model's inherent interpretability, our analysis of model-generated representations reveals findings that resonate with ongoing research in the field of neuroscience.

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

We address prevailing challenges of the brain-powered research, departing from the observation that the literature hardly recover accurate spatial information and require subject-specific models. To address these challenges, we propose UMBRAE, a unified multimodal decoding of brain signals. First, to extract instance-level conceptual and spatial details from neural signals, we introduce an efficient universal brain encoder for multimodal-brain alignment and recover object descriptions at multiple levels of granularity from subsequent multimodal large language model (MLLM). Second, we introduce a cross-subject training strategy mapping subject-specific features to a common feature space. This allows a model to be trained on multiple subjects without extra resources, even yielding superior results compared to subject-specific models. Further, we demonstrate this supports weakly-supervised adaptation to new subjects, with only a fraction of the total training data. Experiments demonstrate that UMBRAE not only achieves superior results in the newly introduced tasks but also outperforms methods in well established tasks. To assess our method, we construct and share with the community a comprehensive brain understanding benchmark BrainHub. Our code and benchmark are available at https://weihaox.github.io/UMBRAE.

In this work, we present a network-specific approach for predicting brain responses to complex multimodal movies, leveraging the Yeo 7-network parcellation of the Schaefer atlas. Rather than treating the brain as a homogeneous system, we grouped the seven functional networks into four clusters and trained separate multi-subject, multi-layer perceptron (MLP) models for each. This architecture supports cluster-specific optimization and adaptive memory modeling, allowing each model to adjust temporal dynamics and modality weighting based on the functional role of its target network. Our results demonstrate that this clustered strategy significantly enhances prediction accuracy across the 1,000 cortical regions of the Schaefer atlas. The final model achieved an eighth-place ranking in the Algonauts Project 2025 Challenge, with out-of-distribution (OOD) correlation scores nearly double those of the baseline model used in the selection phase. Code is available at https://github.com/Corsi01/algo2025.

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional interactions can change over time. To model dynamically changing functional interactions, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional interactions are shaped and confined by the underlying anatomical connectome. Here, we propose a novel prior-informed state-switching GLM. We introduce both a Gaussian prior and a one-hot prior over the GLM in each state. The priors are learnable. We will show that the learned prior should capture the state-constant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood with real neural datasets, and render interaction structures and hidden states more interpretable when applied to real neural data.

We report the presence of a simple neural mechanism that represents an input-output function as a vector within autoregressive transformer language models (LMs). Using causal mediation analysis on a diverse range of in-context-learning (ICL) tasks, we find that a small number attention heads transport a compact representation of the demonstrated task, which we call a function vector (FV). FVs are robust to changes in context, i.e., they trigger execution of the task on inputs such as zero-shot and natural text settings that do not resemble the ICL contexts from which they are collected. We test FVs across a range of tasks, models, and layers and find strong causal effects across settings in middle layers. We investigate the internal structure of FVs and find while that they often contain information that encodes the output space of the function, this information alone is not sufficient to reconstruct an FV. Finally, we test semantic vector composition in FVs, and find that to some extent they can be summed to create vectors that trigger new complex tasks. Taken together, our findings suggest that LLMs contain internal abstractions of general-purpose functions that can be invoked in a variety of contexts.

The goal of product mapping is to decide, whether two listings from two different e-shops describe the same products. Existing datasets of matching and non-matching pairs of products, however, often suffer from incomplete product information or contain only very distant non-matching products. Therefore, while predictive models trained on these datasets achieve good results on them, in practice, they are unusable as they cannot distinguish very similar but non-matching pairs of products. This paper introduces two new datasets for product mapping: ProMapCz consisting of 1,495 Czech product pairs and ProMapEn consisting of 1,555 English product pairs of matching and non-matching products manually scraped from two pairs of e-shops. The datasets contain both images and textual descriptions of the products, including their specifications, making them one of the most complete datasets for product mapping. Additionally, the non-matching products were selected in two phases, creating two types of non-matches -- close non-matches and medium non-matches. Even the medium non-matches are pairs of products that are much more similar than non-matches in other datasets -- for example, they still need to have the same brand and similar name and price. After simple data preprocessing, several machine learning algorithms were trained on these and two the other datasets to demonstrate the complexity and completeness of ProMap datasets. ProMap datasets are presented as a golden standard for further research of product mapping filling the gaps in existing ones.

Identifying cell types and understanding their functional properties is crucial for unraveling the mechanisms underlying perception and cognition. In the retina, functional types can be identified by carefully selected stimuli, but this requires expert domain knowledge and biases the procedure towards previously known cell types. In the visual cortex, it is still unknown what functional types exist and how to identify them. Thus, for unbiased identification of the functional cell types in retina and visual cortex, new approaches are needed. Here we propose an optimization-based clustering approach using deep predictive models to obtain functional clusters of neurons using Most Discriminative Stimuli (MDS). Our approach alternates between stimulus optimization with cluster reassignment akin to an expectation-maximization algorithm. The algorithm recovers functional clusters in mouse retina, marmoset retina and macaque visual area V4. This demonstrates that our approach can successfully find discriminative stimuli across species, stages of the visual system and recording techniques. The resulting most discriminative stimuli can be used to assign functional cell types fast and on the fly, without the need to train complex predictive models or show a large natural scene dataset, paving the way for experiments that were previously limited by experimental time. Crucially, MDS are interpretable: they visualize the distinctive stimulus patterns that most unambiguously identify a specific type of neuron.

Existing evaluation benchmarks of language models of code (code LMs) focus almost exclusively on whether the LMs can generate functionally-correct code. In real-world software engineering, developers think beyond functional correctness. They have requirements on "how" a functionality should be implemented to meet overall system design objectives like efficiency, security, and maintainability. They would also trust the code LMs more if the LMs demonstrate robust understanding of requirements and code semantics. We propose a new benchmark NoFunEval to evaluate code LMs on non-functional requirements and simple classification instances for both functional and non-functional requirements. We propose a prompting method, Coding Concepts (CoCo), as a way for a developer to communicate the domain knowledge to the LMs. We conduct an extensive evaluation of twenty-two code LMs. Our finding is that they generally falter when tested on our benchmark, hinting at fundamental blindspots in their training setups. Surprisingly, even the classification accuracy on functional-correctness instances derived from the popular HumanEval benchmark is low, calling in question the depth of their comprehension and the source of their success in generating functionally-correct code in the first place. We will release our benchmark and evaluation scripts publicly at https://aka.ms/NoFunEval.

As deep learning continues to advance, the transparency of neural network decision-making remains a critical challenge, limiting trust and applicability in high-stakes domains. Class Activation Mapping (CAM) techniques have emerged as a key approach toward visualizing model decisions, yet existing methods face inherent trade-offs. Gradient-based CAM variants suffer from sensitivity to gradient perturbations due to gradient noise, leading to unstable and unreliable explanations. Conversely, gradient-free approaches mitigate gradient instability but incur significant computational overhead and inference latency. To address these limitations, we propose a Cluster Filter Class Activation Map (CF-CAM) technique, a novel framework that reintroduces gradient-based weighting while enhancing robustness against gradient noise. CF-CAM utilizes hierarchical importance weighting strategy to balance discriminative feature preservation and noise elimination. A density-aware channel clustering method via Density-Based Spatial Clustering of Applications with Noise (DBSCAN) groups semantically relevant feature channels and discard noise-prone activations. Additionally, cluster-conditioned gradient filtering leverages Gaussian filters to refine gradient signals, preserving edge-aware localization while suppressing noise impact. Experiment results demonstrate that CF-CAM achieves superior interpretability performance while enhancing computational efficiency, outperforming state-of-the-art CAM methods in faithfulness and robustness. By effectively mitigating gradient instability without excessive computational cost, CF-CAM provides a competitive solution for enhancing the interpretability of deep neural networks in critical applications such as autonomous driving and medical diagnosis.

Vision-and-language navigation (VLN) enables the agent to navigate to a remote location following the natural language instruction in 3D environments. To represent the previously visited environment, most approaches for VLN implement memory using recurrent states, topological maps, or top-down semantic maps. In contrast to these approaches, we build the top-down egocentric and dynamically growing Grid Memory Map (i.e., GridMM) to structure the visited environment. From a global perspective, historical observations are projected into a unified grid map in a top-down view, which can better represent the spatial relations of the environment. From a local perspective, we further propose an instruction relevance aggregation method to capture fine-grained visual clues in each grid region. Extensive experiments are conducted on both the REVERIE, R2R, SOON datasets in the discrete environments, and the R2R-CE dataset in the continuous environments, showing the superiority of our proposed method.

Electronic health record (EHR) systems are used extensively throughout the healthcare domain. However, data interchangeability between EHR systems is limited due to the use of different coding standards across systems. Existing methods of mapping coding standards based on manual human experts mapping, dictionary mapping, symbolic NLP and classification are unscalable and cannot accommodate large scale EHR datasets. In this work, we present Text2Node, a cross-domain mapping system capable of mapping medical phrases to concepts in a large taxonomy (such as SNOMED CT). The system is designed to generalize from a limited set of training samples and map phrases to elements of the taxonomy that are not covered by training data. As a result, our system is scalable, robust to wording variants between coding systems and can output highly relevant concepts when no exact concept exists in the target taxonomy. Text2Node operates in three main stages: first, the lexicon is mapped to word embeddings; second, the taxonomy is vectorized using node embeddings; and finally, the mapping function is trained to connect the two embedding spaces. We compared multiple algorithms and architectures for each stage of the training, including GloVe and FastText word embeddings, CNN and Bi-LSTM mapping functions, and node2vec for node embeddings. We confirmed the robustness and generalisation properties of Text2Node by mapping ICD-9-CM Diagnosis phrases to SNOMED CT and by zero-shot training at comparable accuracy. This system is a novel methodological contribution to the task of normalizing and linking phrases to a taxonomy, advancing data interchangeability in healthcare. When applied, the system can use electronic health records to generate an embedding that incorporates taxonomical medical knowledge to improve clinical predictive models.

Denoising diffusion models have enabled high-quality image generation and editing. We present a method to localize the desired edit region implicit in a text instruction. We leverage InstructPix2Pix (IP2P) and identify the discrepancy between IP2P predictions with and without the instruction. This discrepancy is referred to as the relevance map. The relevance map conveys the importance of changing each pixel to achieve the edits, and is used to to guide the modifications. This guidance ensures that the irrelevant pixels remain unchanged. Relevance maps are further used to enhance the quality of text-guided editing of 3D scenes in the form of neural radiance fields. A field is trained on relevance maps of training views, denoted as the relevance field, defining the 3D region within which modifications should be made. We perform iterative updates on the training views guided by rendered relevance maps from the relevance field. Our method achieves state-of-the-art performance on both image and NeRF editing tasks. Project page: https://ashmrz.github.io/WatchYourSteps/

We propose a method to fuse frozen text-only large language models (LLMs) with pre-trained image encoder and decoder models, by mapping between their embedding spaces. Our model demonstrates a wide suite of multimodal capabilities: image retrieval, novel image generation, and multimodal dialogue. Ours is the first approach capable of conditioning on arbitrarily interleaved image and text inputs to generate coherent image (and text) outputs. To achieve strong performance on image generation, we propose an efficient mapping network to ground the LLM to an off-the-shelf text-to-image generation model. This mapping network translates hidden representations of text into the embedding space of the visual models, enabling us to leverage the strong text representations of the LLM for visual outputs. Our approach outperforms baseline generation models on tasks with longer and more complex language. In addition to novel image generation, our model is also capable of image retrieval from a prespecified dataset, and decides whether to retrieve or generate at inference time. This is done with a learnt decision module which conditions on the hidden representations of the LLM. Our model exhibits a wider range of capabilities compared to prior multimodal language models. It can process image-and-text inputs, and produce retrieved images, generated images, and generated text -- outperforming non-LLM based generation models across several text-to-image tasks that measure context dependence.

Generalizable active mapping in complex unknown environments remains a critical challenge for mobile robots. Existing methods, constrained by insufficient training data and conservative exploration strategies, exhibit limited generalizability across scenes with diverse layouts and complex connectivity. To enable scalable training and reliable evaluation, we introduce GLEAM-Bench, the first large-scale benchmark designed for generalizable active mapping with 1,152 diverse 3D scenes from synthetic and real-scan datasets. Building upon this foundation, we propose GLEAM, a unified generalizable exploration policy for active mapping. Its superior generalizability comes mainly from our semantic representations, long-term navigable goals, and randomized strategies. It significantly outperforms state-of-the-art methods, achieving 66.50% coverage (+9.49%) with efficient trajectories and improved mapping accuracy on 128 unseen complex scenes. Project page: https://xiao-chen.tech/gleam/.

Autonomous driving for urban and highway driving applications often requires High Definition (HD) maps to generate a navigation plan. Nevertheless, various challenges arise when generating and maintaining HD maps at scale. While recent online mapping methods have started to emerge, their performance especially for longer ranges is limited by heavy occlusion in dynamic environments. With these considerations in mind, our work focuses on leveraging lightweight and scalable priors-Standard Definition (SD) maps-in the development of online vectorized HD map representations. We first examine the integration of prototypical rasterized SD map representations into various online mapping architectures. Furthermore, to identify lightweight strategies, we extend the OpenLane-V2 dataset with OpenStreetMaps and evaluate the benefits of graphical SD map representations. A key finding from designing SD map integration components is that SD map encoders are model agnostic and can be quickly adapted to new architectures that utilize bird's eye view (BEV) encoders. Our results show that making use of SD maps as priors for the online mapping task can significantly speed up convergence and boost the performance of the online centerline perception task by 30% (mAP). Furthermore, we show that the introduction of the SD maps leads to a reduction of the number of parameters in the perception and reasoning task by leveraging SD map graphs while improving the overall performance. Project Page: https://henryzhangzhy.github.io/sdhdmap/.

We present vMAP, an object-level dense SLAM system using neural field representations. Each object is represented by a small MLP, enabling efficient, watertight object modelling without the need for 3D priors. As an RGB-D camera browses a scene with no prior information, vMAP detects object instances on-the-fly, and dynamically adds them to its map. Specifically, thanks to the power of vectorised training, vMAP can optimise as many as 50 individual objects in a single scene, with an extremely efficient training speed of 5Hz map update. We experimentally demonstrate significantly improved scene-level and object-level reconstruction quality compared to prior neural field SLAM systems. Project page: https://kxhit.github.io/vMAP.

Sound designers and Foley artists usually sonorize a scene, such as from a movie or video game, by manually annotating and sonorizing each action of interest in the video. In our case, the intent is to leave full creative control to sound designers with a tool that allows them to bypass the more repetitive parts of their work, thus being able to focus on the creative aspects of sound production. We achieve this presenting Stable-V2A, a two-stage model consisting of: an RMS-Mapper that estimates an envelope representative of the audio characteristics associated with the input video; and Stable-Foley, a diffusion model based on Stable Audio Open that generates audio semantically and temporally aligned with the target video. Temporal alignment is guaranteed by the use of the envelope as a ControlNet input, while semantic alignment is achieved through the use of sound representations chosen by the designer as cross-attention conditioning of the diffusion process. We train and test our model on Greatest Hits, a dataset commonly used to evaluate V2A models. In addition, to test our model on a case study of interest, we introduce Walking The Maps, a dataset of videos extracted from video games depicting animated characters walking in different locations. Samples and code available on our demo page at https://ispamm.github.io/Stable-V2A.