Autoencoders and their variations provide unsupervised models for learning low-dimensional representations for downstream tasks. Without proper regularization, autoencoder models are susceptible to the overfitting problem and the so-called posterior collapse phenomenon. In this paper, we introduce a quantization-based regularizer in the bottleneck stage of autoencoder models to learn meaningful latent representations. We combine both perspectives of Vector Quantized-Variational AutoEncoders (VQ-VAE) and classical denoising regularization schemes of neural networks. We interpret quantizers as regularizers that constrain latent representations while fostering a similarity mapping at the encoder. Before quantization, we impose noise on the latent variables and use a Bayesian estimator to optimize the quantizer-based representation. The introduced bottleneck Bayesian estimator outputs the posterior mean of the centroids to the decoder, and thus, is performing soft quantization of the latent variables. We show that our proposed regularization method results in improved latent representations for both supervised learning and clustering downstream tasks when compared to autoencoders using other bottleneck structures.
Various techniques for regularizing the autoencoders have been proposed recently. @cite_5 proposes an adversarial regularizer which encourages interpolation in the outputs and also improves the learned representation. @cite_29 interprets the VAEs as a amortized inference algorithm and proposed a procedure to constrain the expressiveness of the encoder. In addition, there is a increasing popularity of using information-theoretic principles to improve autoencoders. @cite_10 @cite_12 use the information bottleneck principle @cite_15 to recover the objective of @math -VAE and show that the KL divergence term in ELBO is an upper bound on the information rate between input and prior. @cite_2 is also inspired by the information bottleneck principle and introduces the information dropout method to penalize the transfer of information from data to the latents. @cite_24 proposes to use encoder-decoder structures to simulate the binary symmetric channel (BSC) to solve the joint source-channel coding problem while at the same time learn robust representations.
@cite_29 @cite_24 @cite_2 @cite_5 @cite_15 @cite_10 @cite_12
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The variational autoencoder (VAE) is a popular model for density estimation and representation learning. Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is accurate. However, it is often overlooked that an overly-expressive inference model can be detrimental to the test set performance of both the amortized posterior approximator and, more importantly, the generative density estimator. In this paper, we leverage the fact that VAEs rely on amortized inference and propose techniques for amortized inference regularization (AIR) that control the smoothness of the inference model. We demonstrate that, by applying AIR, it is possible to improve VAE generalization on both inference and generative performance. Our paper challenges the belief that amortized inference is simply a mechanism for approximating maximum likelihood training and illustrates that regularization of the amortization family provides a new direction for understanding and improving generalization in VAEs. For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall short in the finite bit-length regime, as it requires non-trivial tuning of hand-crafted codes and assumes infinite computational power for decoding. In this work, we propose Neural Error Correcting and Source Trimming ( ) codes to jointly learn the encoding and decoding processes in an end-to-end fashion. By adding noise into the latent codes to simulate the channel during training, we learn to both compress and error-correct given a fixed bit-length and computational budget. We obtain codes that are not only competitive against several capacity-approaching channel codes, but also learn useful robust representations of the data for downstream tasks such as classification. Finally, we learn an extremely fast neural decoder, yielding almost an order of magnitude in speedup compared to standard decoding methods based on iterative belief propagation. The cross-entropy loss commonly used in deep learning is closely related to the defining properties of optimal representations, but does not enforce some of the key properties. We show that this can be solved by adding a regularization term, which is in turn related to injecting multiplicative noise in the activations of a Deep Neural Network, a special case of which is the common practice of dropout. We show that our regularized loss function can be efficiently minimized using Information Dropout, a generalization of dropout rooted in information theoretic principles that automatically adapts to the data and can better exploit architectures of limited capacity. When the task is the reconstruction of the input, we show that our loss function yields a Variational Autoencoder as a special case, thus providing a link between representation learning, information theory and variational inference. Finally, we prove that we can promote the creation of optimal disentangled representations simply by enforcing a factorized prior, a fact that has been observed empirically in recent work. Our experiments validate the theoretical intuitions behind our method, and we find that Information Dropout achieves a comparable or better generalization performance than binary dropout, especially on smaller models, since it can automatically adapt the noise to the structure of the network, as well as to the test sample. Autoencoders provide a powerful framework for learning compressed representations by encoding all of the information needed to reconstruct a data point in a latent code. In some cases, autoencoders can "interpolate": By decoding the convex combination of the latent codes for two datapoints, the autoencoder can produce an output which semantically mixes characteristics from the datapoints. In this paper, we propose a regularization procedure which encourages interpolated outputs to appear more realistic by fooling a critic network which has been trained to recover the mixing coefficient from interpolated data. We then develop a simple benchmark task where we can quantitatively measure the extent to which various autoencoders can interpolate and show that our regularizer dramatically improves interpolation in this setting. We also demonstrate empirically that our regularizer produces latent codes which are more effective on downstream tasks, suggesting a possible link between interpolation abilities and learning useful representations. Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output variables. Using this representation we can calculate the optimal information theoretic limits of the DNN and obtain finite sample generalization bounds. The advantage of getting closer to the theoretical limit is quantifiable both by the generalization bound and by the network's simplicity. We argue that both the optimal architecture, number of layers and features connections at each layer, are related to the bifurcation points of the information bottleneck tradeoff, namely, relevant compression of the input layer with respect to the output layer. The hierarchical representations at the layered network naturally correspond to the structural phase transitions along the information curve. We believe that this new insight can lead to new optimality bounds and deep learning algorithms.