You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
This paper proposes a novel method for factorising the information in the latent space of an autoencoder (AE), to improve the interpretability of the latent space and facilitate controlled generation. When trained on a dataset with labelled attributes we can produce a latent vector which separates information encoding the attributes from other characteristic information, and also disentangles the attribute information. This then allows us to manipulate each attribute of the latent representation individually without affecting others. Our method, matrix subspace projection, is simpler than the state of the art adversarial network approaches to latent space factorisation. We demonstrate the utility of the method for attribute manipulation tasks on the CelebA image dataset and the E2E text corpus.

Cited Abstract(s):
[1]: This paper investigates a novel problem of generating images from visual attributes. We model the image as a composite of foreground and background and develop a layered generative model with disentangled latent variables that can be learned end-to-end using a variational auto-encoder. We experiment with natural images of faces and birds and demonstrate that the proposed models are capable of generating realistic and diverse samples with disentangled latent representations. We use a general energy minimization algorithm for posterior inference of latent variables given novel images. Therefore, the learned generative models show excellent quantitative and visual results in the tasks of attribute-conditioned image reconstruction and completion.

[2]: The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.

[3]: We present variational generative adversarial networks, a general learning framework that combines a variational auto-encoder with a generative adversarial network, for synthesizing images in fine-grained categories, such as faces of a specific person or objects in a category. Our approach models an image as a composition of label and latent attributes in a probabilistic model. By varying the fine-grained category label fed into the resulting generative model, we can generate images in a specific category with randomly drawn values on a latent attribute vector. Our approach has two novel aspects. First, we adopt a cross entropy loss for the discriminative and classifier network, but a mean discrepancy objective for the generative network. This kind of asymmetric loss function makes the GAN training more stable. Second, we adopt an encoder network to learn the relationship between the latent space and the real image space, and use pairwise feature matching to keep the structure of generated images. We experiment with natural images of faces, flowers, and birds, and demonstrate that the proposed models are capable of generating realistic and diverse samples with fine-grained category labels. We further show that our models can be applied to other tasks, such as image inpainting, super-resolution, and data augmentation for training better face recognition models.

[4]: Supervised deep learning has been successfully applied to many recognition problems. Although it can approximate a complex many-to-one function well when a large amount of training data is provided, it is still challenging to model complex structured output representations that effectively perform probabilistic inference and make diverse predictions. In this work, we develop a deep conditional generative model for structured output prediction using Gaussian latent variables. The model is trained efficiently in the framework of stochastic gradient variational Bayes, and allows for fast prediction using stochastic feed-forward inference. In addition, we provide novel strategies to build robust structured prediction algorithms, such as input noise-injection and multi-scale prediction objective at training. In experiments, we demonstrate the effectiveness of our proposed algorithm in comparison to the deterministic deep neural network counterparts in generating diverse but realistic structured output predictions using stochastic inference. Furthermore, the proposed training methods are complimentary, which leads to strong pixel-level object segmentation and semantic labeling performance on Caltech-UCSD Birds 200 and the subset of Labeled Faces in the Wild dataset.
The problem of control of generation by attributes is somewhat different to the problem of generating specified individuals (or fine-grained categories) tackled by [3] , because individuals are mutually exclusive in the training data and do not need to be produced in combinations. We focus here on control of generation by attributes. The first approaches to this problem (conditional VAEs [2] [4] [1] ) added attribute label information as an extra input to the encoder and the decoder. These approaches generate using a latent @math vector and also a label @math , where the @math vector often conflicts with the label. The @math vector has not been separated into components correlated with @math and components uncorrelated with @math , to remove any information that might conflict with @math . With conflicting inputs the best the VAE can do is to produce a blurry image.