Daily Papers

The rapid rise of large language models (LLMs) has unlocked many applications but also underscores the challenge of aligning them with diverse values and preferences. Direct Preference Optimization (DPO) is central to alignment but constrained by fixed divergences and limited feature transformations. We propose DPO-Kernels, which integrates kernel methods to address these issues through four key contributions: (i) Kernelized Representations with polynomial, RBF, Mahalanobis, and spectral kernels for richer transformations, plus a hybrid loss combining embedding-based and probability-based objectives; (ii) Divergence Alternatives (Jensen-Shannon, Hellinger, Renyi, Bhattacharyya, Wasserstein, and f-divergences) for greater stability; (iii) Data-Driven Selection metrics that automatically choose the best kernel-divergence pair; and (iv) a Hierarchical Mixture of Kernels for both local precision and global modeling. Evaluations on 12 datasets demonstrate state-of-the-art performance in factuality, safety, reasoning, and instruction following. Grounded in Heavy-Tailed Self-Regularization, DPO-Kernels maintains robust generalization for LLMs, offering a comprehensive resource for further alignment research.

The size and compute characteristics of modern large language models have led to an increased interest in developing specialized kernels tailored for training and inference. Existing kernels primarily optimize for compute utilization, targeting the large-batch training and inference settings. However, low-batch inference, where memory bandwidth and kernel launch overheads contribute are significant factors, remains important for many applications of interest such as in edge deployment and latency-sensitive applications. This paper describes FlashFormer, a proof-of-concept kernel for accelerating single-batch inference for transformer-based large language models. Across various model sizes and quantizations settings, we observe nontrivial speedups compared to existing state-of-the-art inference kernels.

Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the quantum feature map. However, the challenge of designing effective quantum feature maps for real-world datasets, particularly in the absence of sufficient prior information, remains a significant obstacle. In this study, we present a data-driven approach that automates the design of problem-specific quantum feature maps. Our approach leverages feature-selection techniques to handle high-dimensional data on near-term quantum machines with limited qubits, and incorporates a deep neural predictor to efficiently evaluate the performance of various candidate quantum kernels. Through extensive numerical simulations on different datasets, we demonstrate the superiority of our proposal over prior methods, especially for the capability of eliminating the kernel concentration issue and identifying the feature map with prediction advantages. Our work not only unlocks the potential of quantum kernels for enhancing real-world tasks but also highlights the substantial role of deep learning in advancing quantum machine learning.

It is well established that the spectral analysis of canonically quantized four-dimensional Seiberg-Witten curves can be systematically studied via the Nekrasov-Shatashvili functions. In this paper, we explore another aspect of the relation between N=2 supersymmetric gauge theories in four dimensions and operator theory. Specifically, we study an example of an integral operator associated with Painlev\'e equations and whose spectral traces are related to correlation functions of the 2d Ising model. This operator does not correspond to a canonically quantized Seiberg-Witten curve, but its kernel can nevertheless be interpreted as the density matrix of an ideal Fermi gas. Adopting the approach of Tracy and Widom, we provide an explicit expression for its eigenfunctions via an O(2) matrix model. We then show that these eigenfunctions are computed by surface defects in SU(2) super Yang-Mills in the self-dual phase of the Omega-background. Our result also yields a strong coupling expression for such defects which resums the instanton expansion. Even though we focus on one concrete example, we expect these results to hold for a larger class of operators arising in the context of isomonodromic deformation equations.

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to computational hardness assumptions, cannot be computed classically. It is an important challenge to find quantum kernels that provide an advantage in the classification of real-world data. We introduce a class of quantum kernels that can be used for data with a group structure. The kernel is defined in terms of a unitary representation of the group and a fiducial state that can be optimized using a technique called kernel alignment. We apply this method to a learning problem on a coset-space that embodies the structure of many essential learning problems on groups. We implement the learning algorithm with 27 qubits on a superconducting processor.

The segmentation of cell nuclei in tissue images stained with the blood dye hematoxylin and eosin (H&E) is essential for various clinical applications and analyses. Due to the complex characteristics of cellular morphology, a large receptive field is considered crucial for generating high-quality segmentation. However, previous methods face challenges in achieving a balance between the receptive field and computational burden. To address this issue, we propose LKCell, a high-accuracy and efficient cell segmentation method. Its core insight lies in unleashing the potential of large convolution kernels to achieve computationally efficient large receptive fields. Specifically, (1) We transfer pre-trained large convolution kernel models to the medical domain for the first time, demonstrating their effectiveness in cell segmentation. (2) We analyze the redundancy of previous methods and design a new segmentation decoder based on large convolution kernels. It achieves higher performance while significantly reducing the number of parameters. We evaluate our method on the most challenging benchmark and achieve state-of-the-art results (0.5080 mPQ) in cell nuclei instance segmentation with only 21.6% FLOPs compared with the previous leading method. Our source code and models are available at https://github.com/hustvl/LKCell.

This paper proposes the paradigm of large convolutional kernels in designing modern Convolutional Neural Networks (ConvNets). We establish that employing a few large kernels, instead of stacking multiple smaller ones, can be a superior design strategy. Our work introduces a set of architecture design guidelines for large-kernel ConvNets that optimize their efficiency and performance. We propose the UniRepLKNet architecture, which offers systematical architecture design principles specifically crafted for large-kernel ConvNets, emphasizing their unique ability to capture extensive spatial information without deep layer stacking. This results in a model that not only surpasses its predecessors with an ImageNet accuracy of 88.0%, an ADE20K mIoU of 55.6%, and a COCO box AP of 56.4% but also demonstrates impressive scalability and performance on various modalities such as time-series forecasting, audio, point cloud, and video recognition. These results indicate the universal modeling abilities of large-kernel ConvNets with faster inference speed compared with vision transformers. Our findings reveal that large-kernel ConvNets possess larger effective receptive fields and a higher shape bias, moving away from the texture bias typical of smaller-kernel CNNs. All codes and models are publicly available at https://github.com/AILab-CVC/UniRepLKNet promoting further research and development in the community.

Efficient GPU kernels are crucial for building performant machine learning architectures, but writing them is a time-consuming challenge that requires significant expertise; therefore, we explore using language models (LMs) to automate kernel generation. We introduce KernelBench, an open-source framework for evaluating LMs' ability to write fast and correct kernels on a suite of 250 carefully selected PyTorch ML workloads. KernelBench represents a real-world engineering environment and making progress on the introduced benchmark directly translates to faster practical kernels. We introduce a new evaluation metric fast_p, which measures the percentage of generated kernels that are functionally correct and offer a speedup greater than an adjustable threshold p over baseline. Our experiments across various state-of-the-art models and test-time methods show that frontier reasoning models perform the best out of the box but still fall short overall, matching the PyTorch baseline in less than 20% of the cases. While we show that results can improve by leveraging execution and profiling feedback during iterative refinement, KernelBench remains a challenging benchmark, with its difficulty increasing as we raise speedup threshold p.

Training Large Language Models (LLMs) efficiently at scale presents a formidable challenge, driven by their ever-increasing computational demands and the need for enhanced performance. In this work, we introduce Liger-Kernel, an open-sourced set of Triton kernels developed specifically for LLM training. With kernel optimization techniques like kernel operation fusing and input chunking, our kernels achieve on average a 20% increase in training throughput and a 60% reduction in GPU memory usage for popular LLMs compared to HuggingFace implementations. In addition, Liger-Kernel is designed with modularity, accessibility, and adaptability in mind, catering to both casual and expert users. Comprehensive benchmarks and integration tests are built in to ensure compatibility, performance, correctness, and convergence across diverse computing environments and model architectures. The source code is available under a permissive license at: github.com/linkedin/Liger-Kernel.

Motivated by the paradigm of reservoir computing, we consider randomly initialized controlled ResNets defined as Euler-discretizations of neural controlled differential equations (Neural CDEs), a unified architecture which enconpasses both RNNs and ResNets. We show that in the infinite-width-depth limit and under proper scaling, these architectures converge weakly to Gaussian processes indexed on some spaces of continuous paths and with kernels satisfying certain partial differential equations (PDEs) varying according to the choice of activation function, extending the results of Hayou (2022); Hayou & Yang (2023) to the controlled and homogeneous case. In the special, homogeneous, case where the activation is the identity, we show that the equation reduces to a linear PDE and the limiting kernel agrees with the signature kernel of Salvi et al. (2021a). We name this new family of limiting kernels neural signature kernels. Finally, we show that in the infinite-depth regime, finite-width controlled ResNets converge in distribution to Neural CDEs with random vector fields which, depending on whether the weights are shared across layers, are either time-independent and Gaussian or behave like a matrix-valued Brownian motion.

Recent advances have discussed cell complexes as ideal learning representations. However, there is a lack of available machine learning methods suitable for learning on CW complexes. In this paper, we derive an explicit expression for the Wasserstein distance between cell complex signal distributions in terms of a Hodge-Laplacian matrix. This leads to a structurally meaningful measure to compare CW complexes and define the optimal transportation map. In order to simultaneously include both feature and structure information, we extend the Fused Gromov-Wasserstein distance to CW complexes. Finally, we introduce novel kernels over the space of probability measures on CW complexes based on the dual formulation of optimal transport.

Recent advances in depthwise-separable convolutional neural networks (DS-CNNs) have led to novel architectures, that surpass the performance of classical CNNs, by a considerable scalability and accuracy margin. This paper reveals another striking property of DS-CNN architectures: discernible and explainable patterns emerge in their trained depthwise convolutional kernels in all layers. Through an extensive analysis of millions of trained filters, with different sizes and from various models, we employed unsupervised clustering with autoencoders, to categorize these filters. Astonishingly, the patterns converged into a few main clusters, each resembling the difference of Gaussian (DoG) functions, and their first and second-order derivatives. Notably, we were able to classify over 95\% and 90\% of the filters from state-of-the-art ConvNextV2 and ConvNeXt models, respectively. This finding is not merely a technological curiosity; it echoes the foundational models neuroscientists have long proposed for the vision systems of mammals. Our results thus deepen our understanding of the emergent properties of trained DS-CNNs and provide a bridge between artificial and biological visual processing systems. More broadly, they pave the way for more interpretable and biologically-inspired neural network designs in the future.

We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks, that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ell_2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

We revisit large kernel design in modern convolutional neural networks (CNNs). Inspired by recent advances in vision transformers (ViTs), in this paper, we demonstrate that using a few large convolutional kernels instead of a stack of small kernels could be a more powerful paradigm. We suggested five guidelines, e.g., applying re-parameterized large depth-wise convolutions, to design efficient high-performance large-kernel CNNs. Following the guidelines, we propose RepLKNet, a pure CNN architecture whose kernel size is as large as 31x31, in contrast to commonly used 3x3. RepLKNet greatly closes the performance gap between CNNs and ViTs, e.g., achieving comparable or superior results than Swin Transformer on ImageNet and a few typical downstream tasks, with lower latency. RepLKNet also shows nice scalability to big data and large models, obtaining 87.8% top-1 accuracy on ImageNet and 56.0% mIoU on ADE20K, which is very competitive among the state-of-the-arts with similar model sizes. Our study further reveals that, in contrast to small-kernel CNNs, large-kernel CNNs have much larger effective receptive fields and higher shape bias rather than texture bias. Code & models at https://github.com/megvii-research/RepLKNet.

Depthwise convolution is becoming increasingly popular in modern efficient ConvNets, but its kernel size is often overlooked. In this paper, we systematically study the impact of different kernel sizes, and observe that combining the benefits of multiple kernel sizes can lead to better accuracy and efficiency. Based on this observation, we propose a new mixed depthwise convolution (MixConv), which naturally mixes up multiple kernel sizes in a single convolution. As a simple drop-in replacement of vanilla depthwise convolution, our MixConv improves the accuracy and efficiency for existing MobileNets on both ImageNet classification and COCO object detection. To demonstrate the effectiveness of MixConv, we integrate it into AutoML search space and develop a new family of models, named as MixNets, which outperform previous mobile models including MobileNetV2 [20] (ImageNet top-1 accuracy +4.2%), ShuffleNetV2 [16] (+3.5%), MnasNet [26] (+1.3%), ProxylessNAS [2] (+2.2%), and FBNet [27] (+2.0%). In particular, our MixNet-L achieves a new state-of-the-art 78.9% ImageNet top-1 accuracy under typical mobile settings (<600M FLOPS). Code is at https://github.com/ tensorflow/tpu/tree/master/models/official/mnasnet/mixnet

One of the most important problems in audio event detection research is absence of benchmark results for comparison with any proposed method. Different works consider different sets of events and datasets which makes it difficult to comprehensively analyze any novel method with an existing one. In this paper we propose to establish results for audio event recognition on two recent publicly-available datasets. In particular we use Gaussian Mixture model based feature representation and combine them with linear as well as non-linear kernel Support Vector Machines.

Large Language Models (LLMs) have demonstrated strong capabilities in general-purpose code generation. However, generating the code which is deeply hardware-specific, architecture-aware, and performance-critical, especially for massively parallel GPUs, remains a complex challenge. In this work, we explore the use of LLMs for the automated generation and optimization of CUDA programs, with the goal of producing high-performance GPU kernels that fully exploit the underlying hardware. To address this challenge, we propose a novel framework called Feature Search and Reinforcement (FSR). FSR jointly optimizes compilation and functional correctness, as well as the runtime performance, which are validated through extensive and diverse test cases, and measured by actual kernel execution latency on the target GPU, respectively. This approach enables LLMs not only to generate syntactically and semantically correct CUDA code but also to iteratively refine it for efficiency, tailored to the characteristics of the GPU architecture. We evaluate FSR on representative CUDA kernels, covering AI workloads and computational intensive algorithms. Our results show that LLMs augmented with FSR consistently guarantee correctness rates. Meanwhile, the automatically generated kernels can outperform general human-written code by a factor of up to 179times in execution speeds. These findings highlight the potential of combining LLMs with performance reinforcement to automate GPU programming for hardware-specific, architecture-sensitive, and performance-critical applications.

The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|^r, r in (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N^2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

We generalise an existing construction of Bayesian Lenses to admit lenses between pairs of objects where the backwards object is dependent on states on the forwards object (interpreted as probability distributions). This gives a natural setting for studying stochastic maps with Bayesian inverses restricted to the points supported by a given prior. In order to state this formally we develop a proposed definition by Fritz of a support object in a Markov category and show that these give rise to a section into the category of dependent Bayesian lenses encoding a more canonical notion of Bayesian inversion.

Optical flow estimation is a classical yet challenging task in computer vision. One of the essential factors in accurately predicting optical flow is to alleviate occlusions between frames. However, it is still a thorny problem for current top-performing optical flow estimation methods due to insufficient local evidence to model occluded areas. In this paper, we propose the Super Kernel Flow Network (SKFlow), a CNN architecture to ameliorate the impacts of occlusions on optical flow estimation. SKFlow benefits from the super kernels which bring enlarged receptive fields to complement the absent matching information and recover the occluded motions. We present efficient super kernel designs by utilizing conical connections and hybrid depth-wise convolutions. Extensive experiments demonstrate the effectiveness of SKFlow on multiple benchmarks, especially in the occluded areas. Without pre-trained backbones on ImageNet and with a modest increase in computation, SKFlow achieves compelling performance and ranks 1st among currently published methods on the Sintel benchmark. On the challenging Sintel clean and final passes (test), SKFlow surpasses the best-published result in the unmatched areas (7.96 and 12.50) by 9.09% and 7.92%. The code is available at https://github.com/littlespray/SKFlow{https://github.com/littlespray/SKFlow}.

Most methods for time series classification that attain state-of-the-art accuracy have high computational complexity, requiring significant training time even for smaller datasets, and are intractable for larger datasets. Additionally, many existing methods focus on a single type of feature such as shape or frequency. Building on the recent success of convolutional neural networks for time series classification, we show that simple linear classifiers using random convolutional kernels achieve state-of-the-art accuracy with a fraction of the computational expense of existing methods.

We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher--Neyman, Basu, and Bahadur. Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.

We derive a Fast Multipole Method (FMM) where a low-rank approximation of the kernel is obtained using the Empirical Interpolation Method (EIM). Contrary to classical interpolation-based FMM, where the interpolation points and basis are fixed beforehand, the EIM is a nonlinear approximation method which constructs interpolation points and basis which are adapted to the kernel under consideration. The basis functions are obtained using evaluations of the kernel itself. We restrict ourselves to translation-invariant kernels, for which a modified version of the EIM approximation can be used in a multilevel FMM context; we call the obtained algorithm Empirical Interpolation Fast Multipole Method (EIFMM). An important feature of the EIFMM is a built-in error estimation of the interpolation error made by the low-rank approximation of the far-field behavior of the kernel: the algorithm selects the optimal number of interpolation points required to ensure a given accuracy for the result, leading to important gains for inhomogeneous kernels.

The challenge of mapping AI architectures to GPU hardware is creating a critical bottleneck in AI progress. Despite substantial efforts, hand-written custom kernels fail to meet their theoretical performance thresholds, even on well-established operations like linear attention. The diverse hardware capabilities of GPUs might suggest that we need a wide variety of techniques to achieve high performance. However, our work explores whether a small number of key abstractions can drastically simplify the process. We present ThunderKittens (TK), a framework for writing performant AI kernels while remaining easy to use and maintain. Our abstractions map to the three levels of the GPU hierarchy: (1) at the warp-level, we provide 16x16 matrix tiles as basic data structures and PyTorch-like parallel compute operations over tiles, (2) at the thread-block level, we provide a template for overlapping asynchronous operations across parallel warps, and (3) at the grid-level, we provide support to help hide the block launch and tear-down, and memory costs. We show the value of TK by providing kernels that match or outperform prior kernels for a range of AI operations. We match CuBLAS and FlashAttention-3 on GEMM and attention inference performance and outperform the strongest baselines by 10-40% on attention backwards, 8times on state space models, and 14times on linear attention.

Over the past 7 years, attention has become one of the most important primitives in deep learning. The primary approach to optimize attention is FlashAttention, which fuses the operation together, drastically improving both the runtime and the memory consumption. However, the importance of FlashAttention combined with its monolithic nature poses a problem for researchers aiming to try new attention variants -- a "software lottery". This problem is exacerbated by the difficulty of writing efficient fused attention kernels, resisting traditional compiler-based approaches. We introduce FlexAttention, a novel compiler-driven programming model that allows implementing the majority of attention variants in a few lines of idiomatic PyTorch code. We demonstrate that many existing attention variants (e.g. Alibi, Document Masking, PagedAttention, etc.) can be implemented via FlexAttention, and that we achieve competitive performance compared to these handwritten kernels. Finally, we demonstrate how FlexAttention allows for easy composition of attention variants, solving the combinatorial explosion of attention variants.

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based optimizers. Despite the existing empirical and theoretical investigations, the convergence of QNN training is not fully understood. Inspired by the success of the neural tangent kernels (NTKs) in probing into the dynamics of classical neural networks, a recent line of works proposes to study over-parameterized QNNs by examining a quantum version of tangent kernels. In this work, we study the dynamics of QNNs and show that contrary to popular belief it is qualitatively different from that of any kernel regression: due to the unitarity of quantum operations, there is a non-negligible deviation from the tangent kernel regression derived at the random initialization. As a result of the deviation, we prove the at-most sublinear convergence for QNNs with Pauli measurements, which is beyond the explanatory power of any kernel regression dynamics. We then present the actual dynamics of QNNs in the limit of over-parameterization. The new dynamics capture the change of convergence rate during training and implies that the range of measurements is crucial to the fast QNN convergence.

Current neural architecture search (NAS) strategies focus only on finding a single, good, architecture. They offer little insight into why a specific network is performing well, or how we should modify the architecture if we want further improvements. We propose a Bayesian optimisation (BO) approach for NAS that combines the Weisfeiler-Lehman graph kernel with a Gaussian process surrogate. Our method optimises the architecture in a highly data-efficient manner: it is capable of capturing the topological structures of the architectures and is scalable to large graphs, thus making the high-dimensional and graph-like search spaces amenable to BO. More importantly, our method affords interpretability by discovering useful network features and their corresponding impact on the network performance. Indeed, we demonstrate empirically that our surrogate model is capable of identifying useful motifs which can guide the generation of new architectures. We finally show that our method outperforms existing NAS approaches to achieve the state of the art on both closed- and open-domain search spaces.

Top-down attention plays a crucial role in the human vision system, wherein the brain initially obtains a rough overview of a scene to discover salient cues (i.e., overview first), followed by a more careful finer-grained examination (i.e., look closely next). However, modern ConvNets remain confined to a pyramid structure that successively downsamples the feature map for receptive field expansion, neglecting this crucial biomimetic principle. We present OverLoCK, the first pure ConvNet backbone architecture that explicitly incorporates a top-down attention mechanism. Unlike pyramid backbone networks, our design features a branched architecture with three synergistic sub-networks: 1) a Base-Net that encodes low/mid-level features; 2) a lightweight Overview-Net that generates dynamic top-down attention through coarse global context modeling (i.e., overview first); and 3) a robust Focus-Net that performs finer-grained perception guided by top-down attention (i.e., look closely next). To fully unleash the power of top-down attention, we further propose a novel context-mixing dynamic convolution (ContMix) that effectively models long-range dependencies while preserving inherent local inductive biases even when the input resolution increases, addressing critical limitations in existing convolutions. Our OverLoCK exhibits a notable performance improvement over existing methods. For instance, OverLoCK-T achieves a Top-1 accuracy of 84.2%, significantly surpassing ConvNeXt-B while using only around one-third of the FLOPs/parameters. On object detection, our OverLoCK-S clearly surpasses MogaNet-B by 1% in AP^b. On semantic segmentation, our OverLoCK-T remarkably improves UniRepLKNet-T by 1.7% in mIoU. Code is publicly available at https://github.com/LMMMEng/OverLoCK.

Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).