Here is presented an analysis of an autoencoder with binary activations $\{0, 1\}$ and binary $\{0, 1\}$ random weights. Such set up puts this model at the intersection of different fields: neuroscience, information theory, sparse coding, and machine learning. It is shown that the sparse activation of the hidden layer arises naturally in order to preserve information between layers. Furthermore, with a large enough hidden layer, it is possible to get zero reconstruction error for any input just by varying the thresholds of neurons. The model preserves the similarity of inputs at the hidden layer that is maximal for the dense hidden layer activation. By analyzing the mutual information between layers it is shown that the difference between sparse and dense representations is related to a memory-computation trade-off. The model is similar to an olfactory perception system of a fruit fly, and the presented theoretical results give useful insights toward understanding more complex neural networks.
Berkeley Center for Cosmological Physics（伯克利宇宙物理中心）；University of California（加利福尼亚大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Principal Component Analysis (PCA) minimizes the reconstruction error given a class of linear models of fixed component dimensionality. Probabilistic PCA adds a probabilistic structure by learning the probability distribution of the PCA latent space weights, thus creating a generative model. Autoencoders (AE) minimize the reconstruction error in a class of nonlinear models of fixed latent space dimensionality and outperform PCA at fixed dimensionality. Here, we introduce the Probabilistic Autoencoder (PAE) that learns the probability distribution of the AE latent space weights using a normaliz…
Fraunhofer ITWM（弗劳恩霍夫工业数学研究所）；Technical University of Kaiserslautern（凯泽斯劳滕工业大学）
We consider a variational autoencoder (VAE) for binary data. Our main innovations are an interpretable lower bound for its training objective, a modified initialization and architecture of such a VAE that leads to faster training, and a decision support for finding the appropriate dimension of the latent space via using a PCA. Numerical examples illustrate our theoretical result and the performance of the new architecture.
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Center for Applied Scientific Computing（应用科学计算中心）
The autoencoder is an artificial neural network model that learns hidden representations of unlabeled data. With a linear transfer function it is similar to the principal component analysis (PCA). While both methods use weight vectors for linear transformations, the autoencoder does not come with any indication similar to the eigenvalues in PCA that are paired with the eigenvectors. We propose a novel supervised node saliency (SNS) method that ranks the hidden nodes by comparing class distributions of latent representations against a fixed reference distribution. The latent representations of …
The autoencoder is an effective unsupervised learning model which is widely used in deep learning. It is well known that an autoencoder with a single fully-connected hidden layer, a linear activation function and a squared error cost function trains weights that span the same subspace as the one spanned by the principal component loading vectors, but that they are not identical to the loading vectors. In this paper, we show how to recover the loading vectors from the autoencoder weights.
An attractive approach for fast search in image databases is binary hashing, where each high-dimensional, real-valued image is mapped onto a low-dimensional, binary vector and the search is done in this binary space. Finding the optimal hash function is difficult because it involves binary constraints, and most approaches approximate the optimization by relaxing the constraints and then binarizing the result. Here, we focus on the binary autoencoder model, which seeks to reconstruct an image from the binary code produced by the hash function. We show that the optimization can be simplified wit…
We introduce a binary latent space autoencoder architecture to rehearse training samples for the continual learning of neural networks. The ability to extend the knowledge of a model with new data without forgetting previously learned samples is a fundamental requirement in continual learning. Existing solutions address it by either replaying past data from memory, which is unsustainable with growing training data, or by reconstructing past samples with generative models that are trained to generalize beyond training data and, hence, miss important details of individual samples. In this paper,…
Stable and Steerable Sparse Autoencoders with Weight Regularization
Department of Biology, University of Oxford, Oxford, UK（牛津大学生物学系）；Kavli Institute for Nanoscience Discovery, University of Oxford, Oxford, UK（牛津大学纳科学发现研究所）；Department of Chemistry, University of Oxford, Oxford, UK（牛津大学化学系）
Iowa State University（爱荷华州立大学）；Texas A&M University（得克萨斯农工大学）
We provide a series of results for unsupervised learning with autoencoders. Specifically, we study shallow two-layer autoencoder architectures with shared weights. We focus on three generative models for data that are common in statistical machine learning: (i) the mixture-of-gaussians model, (ii) the sparse coding model, and (iii) the sparsity model with non-negative coefficients. For each of these models, we prove that under suitable choices of hyperparameters, architectures, and initialization, autoencoders learned by gradient descent can successfully recover the parameters of the correspon…
Imperial College London（帝国理工学院）；Data Science Institute, Imperial College London（帝国理工学院数据科学研究所）
Denoising autoencoders (DAEs) are powerful deep learning models used for feature extraction, data generation and network pre-training. DAEs consist of an encoder and decoder which may be trained simultaneously to minimise a loss (function) between an input and the reconstruction of a corrupted version of the input. There are two common loss functions used for training autoencoders, these include the mean-squared error (MSE) and the binary cross-entropy (BCE). When training autoencoders on image data a natural choice of loss function is BCE, since pixel values may be normalised to take values i…
Discrete latent variables are considered important for real world data, which has motivated research on Variational Autoencoders (VAEs) with discrete latents. However, standard VAE training is not possible in this case, which has motivated different strategies to manipulate discrete distributions in order to train discrete VAEs similarly to conventional ones. Here we ask if it is also possible to keep the discrete nature of the latents fully intact by applying a direct discrete optimization for the encoding model. The approach is consequently strongly diverting from standard VAE-training by si…
University of Porto（波尔图大学）；Faculty of Engineering, University of Porto（波尔图大学工程学院）；INESC TEC - Institute for Systems and Computer Engineering, Technology and Science（INESC TEC——系统与计算机工程、技术与科学研究所）
Cancer is still one of the most devastating diseases of our time. One way of automatically classifying tumor samples is by analyzing its derived molecular information (i.e., its genes expression signatures). In this work, we aim to distinguish three different types of cancer: thyroid, skin, and stomach. For that, we compare the performance of a Denoising Autoencoder (DAE) used as weight initialization of a deep neural network. Although we address a different domain problem in this work, we have adopted the same methodology of Ferreira et al.. In our experiments, we assess two different approac…
We formulate learning of a binary autoencoder as a biconvex optimization problem which learns from the pairwise correlations between encoded and decoded bits. Among all possible algorithms that use this information, ours finds the autoencoder that reconstructs its inputs with worst-case optimal loss. The optimal decoder is a single layer of artificial neurons, emerging entirely from the minimax loss minimization, and with weights learned by convex optimization. All this is reflected in competitive experimental results, demonstrating that binary autoencoding can be done efficiently by conveying…
Beyond Activation Patterns: A Weight-Based Out-of-Context Explanation of Sparse Autoencoder Features
State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University（通用人工智能国家重点实验室，智能科学与技术学院，北京大学）
Fully connected deep neural networks (DNN) often include redundant weights leading to overfitting and high memory requirements. Additionally, the performance of DNN is often challenged by traditional machine learning models in tabular data classification. In this paper, we propose periodical perturbations (prune and regrow) of DNN weights, especially at the self-supervised pre-training stage of deep autoencoders. The proposed weight perturbation strategy outperforms dropout learning in four out of six tabular data sets in downstream classification tasks. The L1 or L2 regularization of weights …
Effectiveness of Binary Autoencoders for QUBO-Based Optimization Problems
Graduate School of Science and Technology, Keio University（Keio大学科学技术研究生院）；Keio University（Keio大学）；Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC)（Keio大学可持续量子人工智能中心）；Department of Applied Physics and Physico-Informatics, Keio University（Keio大学应用物理与物理信息学系）；Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q)（人类生物学-微生物组-量子研究中心）
The Voleon Group（Voleon集团）；Stanford University（斯坦福大学）
Autoencoders are among the earliest introduced nonlinear models for unsupervised learning. Although they are widely adopted beyond research, it has been a longstanding open problem to understand mathematically the feature extraction mechanism that trained nonlinear autoencoders provide. In this work, we make progress in this problem by analyzing a class of two-layer weight-tied nonlinear autoencoders in the mean field framework. Upon a suitable scaling, in the regime of a large number of neurons, the models trained with stochastic gradient descent are shown to admit a mean field limiting dynam…
University of Louisville（路易斯维尔大学）；University of Social Science（社会科学大学）；Information Technology Institute（信息技术研究所）
We demonstrate a new deep learning autoencoder network, trained by a nonnegativity constraint algorithm (NCAE), that learns features which show part-based representation of data. The learning algorithm is based on constraining negative weights. The performance of the algorithm is assessed based on decomposing data into parts and its prediction performance is tested on three standard image data sets and one text dataset. The results indicate that the nonnegativity constraint forces the autoencoder to learn features that amount to a part-based representation of data, while improving sparsity and…
LIPN（巴黎第十三大学计算机科学实验室）；Université Sorbonne Paris Nord（索邦巴黎北大学）；INRIA Paris（法国国家信息与自动化研究所巴黎分部）
Even though Variational Autoencoders (VAEs) are widely used for semi-supervised learning, the reason why they work remains unclear. In fact, the addition of the unsupervised objective is most often vaguely described as a regularization. The strength of this regularization is controlled by down-weighting the objective on the unlabeled part of the training set. Through an analysis of the objective of semi-supervised VAEs, we observe that they use the posterior of the learned generative model to guide the inference model in learning the partially observed latent variable. We show that given this …
Hyperspectral unmixing involves separating a pixel as a weighted combination of its constituent endmembers and corresponding fractional abundances, with the current state of the art results achieved by neural models on benchmark datasets. However, these networks are severely over-parameterized and consequently, the invariant endmember spectra extracted as decoder weights have a high variance over multiple runs. These approaches perform substantial post-processing while requiring an exact specification of the number of endmembers and specialized initialization of weights from other algorithms l…
Federated Learning (FL) solves many of this decade's concerns regarding data privacy and computation challenges. FL ensures no data leaves its source as the model is trained at where the data resides. However, FL comes with its own set of challenges. The communication of model weight updates in this distributed environment comes with significant network bandwidth costs. In this context, we propose a mechanism of compressing the weight updates using Autoencoders (AE), which learn the data features of the weight updates and subsequently perform compression. The encoder is set up on each of the n…
In this paper, we investigate the usage of autoencoders in modeling textual data. Traditional autoencoders suffer from at least two aspects: scalability with the high dimensionality of vocabulary size and dealing with task-irrelevant words. We address this problem by introducing supervision via the loss function of autoencoders. In particular, we first train a linear classifier on the labeled data, then define a loss for the autoencoder with the weights learned from the linear classifier. To reduce the bias brought by one single classifier, we define a posterior probability distribution on the…
Monash University（莫纳什大学）；Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Many applications, such as text modelling, high-throughput sequencing, and recommender systems, require analysing sparse, high-dimensional, and overdispersed discrete (count-valued or binary) data. Although probabilistic matrix factorisation and linear/nonlinear latent factor models have enjoyed great success in modelling such data, many existing models may have inferior modelling performance due to the insufficient capability of modelling overdispersion in count-valued data and model misspecification in general. In this paper, we comprehensively study these issues and propose a variational au…
University Paris-Est（巴黎东大学）；Ecole des Ponts ParisTech（巴黎高科桥路学院）
Given an initial recognition model already trained on a set of base classes, the goal of this work is to develop a meta-model for few-shot learning. The meta-model, given as input some novel classes with few training examples per class, must properly adapt the existing recognition model into a new model that can correctly classify in a unified way both the novel and the base classes. To accomplish this goal it must learn to output the appropriate classification weight vectors for those two types of classes. To build our meta-model we make use of two main innovations: we propose the use of a De…
Paul G. Allen School of Computer Science & Engineering（保罗·G·艾伦计算机科学与工程学院）；University of Washington（华盛顿大学）
Learning a generative model of visual information with sparse and compositional features has been a challenge for both theoretical neuroscience and machine learning communities. Sparse coding models have achieved great success in explaining the receptive fields of mammalian primary visual cortex with sparsely activated latent representation. In this paper, we focus on a recently proposed model, sparse coding variational autoencoder (SVAE) (Barello et al., 2018), and show that the end-to-end training scheme of SVAE leads to a large group of decoding filters not fully optimized with noise-like r…
Institute of Theoretical and Applied Informatics, Polish Academy of Sciences（波兰科学院理论与应用信息学研究所）；Silesian University of Technology（西里西亚工业大学）；Sapientia Hungarian University of Transylvania（特兰西瓦尼亚萨皮恩扎匈牙利大学）
Neural networks, in particular autoencoders, are one of the most promising solutions for unmixing hyperspectral data, i.e. reconstructing the spectra of observed substances (endmembers) and their relative mixing fractions (abundances), which is needed for effective hyperspectral analysis and classification. However, as we show in this paper, the training of autoencoders for unmixing is highly dependent on weights initialisation; some sets of weights lead to degenerate or low-performance solutions, introducing negative bias in the expected performance. In this work, we experimentally investigat…
Many powerful machine learning models are based on the composition of multiple processing layers, such as deep nets, which gives rise to nonconvex objective functions. A general, recent approach to optimise such "nested" functions is the method of auxiliary coordinates (MAC). MAC introduces an auxiliary coordinate for each data point in order to decouple the nested model into independent submodels. This decomposes the optimisation into steps that alternate between training single layers and updating the coordinates. It has the advantage that it reuses existing single-layer algorithms, introduc…
This paper proposes a deep autoencoder model based on Pytorch. This algorithm introduces the idea of Pytorch into the auto-encoder, and randomly clears the input weights connected to the hidden layer neurons with a certain probability, so as to achieve the effect of sparse network, which is similar to the starting point of the sparse auto-encoder. The new algorithm effectively solves the problem of possible overfitting of the model and improves the accuracy of image classification. Finally, the experiment is carried out, and the experimental results are compared with ELM, RELM, AE, SAE, DAE.
University of Louisville（路易斯维尔大学）；University of Social Science（社会科学大学）
Unsupervised feature extractors are known to perform an efficient and discriminative representation of data. Insight into the mappings they perform and human ability to understand them, however, remain very limited. This is especially prominent when multilayer deep learning architectures are used. This paper demonstrates how to remove these bottlenecks within the architecture of Nonnegativity Constrained Autoencoder (NCSAE). It is shown that by using both L1 and L2 regularization that induce nonnegativity of weights, most of the weights in the network become constrained to be nonnegative there…
Gravitational wave (GW) detection is now commonplace and as the sensitivity of the global network of GW detectors improves, we will observe $\mathcal{O}(100)$s of transient GW events per year. The current methods used to estimate their source parameters employ optimally sensitive but computationally costly Bayesian inference approaches where typical analyses have taken between 6 hours and 5 days. For binary neutron star and neutron star black hole systems prompt counterpart electromagnetic (EM) signatures are expected on timescales of 1 second -- 1 minute and the current fastest method for ale…
This paper proposes new nonnegative (shallow and multi-layer) autoencoders by combining the spiking Random Neural Network (RNN) model, the network architecture typical used in deep-learning area and the training technique inspired from nonnegative matrix factorization (NMF). The shallow autoencoder is a simplified RNN model, which is then stacked into a multi-layer architecture. The learning algorithm is based on the weight update rules in NMF, subject to the nonnegative probability constraints of the RNN. The autoencoders equipped with this learning algorithm are tested on typical image datas…
How Pruning Reshapes Features: Sparse Autoencoder Analysis of Weight-Pruned Language Models
organization= VRAIN -- Valencian Research Institute for Artificial Intelligence, Universitat Polit\`ecnica de Val\`encia , city= Valencia , country= Spain；organization= Department of Economics；organization= Department of Business Organisation, Universitat Polit\`ecnica de Val\`encia , city= Valencia , country= Spain
On the Limits of Sparse Autoencoders: A Theoretical Framework and Reweighted Remedy
State Key Lab of General AI, School of Intelligence Science and Technology, Peking University（1 人工智能通用基础研究实验室，智能科学与技术学院，北京大学）；Amazon AGI SF Lab（2 亚马逊人工智能实验室）；Institute for Artificial Intelligence, Peking University（3 人工智能研究院，北京大学）
Seoul National University（首尔国立大学）；Korea Institute for Advanced Study（韩国高等研究院）
The outstanding performance of deep learning in various fields has been a fundamental query, which can be potentially examined using information theory that interprets the learning process as the transmission and compression of information. Information plane analyses of the mutual information between the input-hidden-output layers demonstrated two distinct learning phases of fitting and compression. It is debatable if the compression phase is necessary to generalize the input-output relations extracted from training data. In this study, we investigated this through experiments with various spe…
Kyungpook National University（庆北国立大学）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院（KAIST））
This paper proposes a novel framework for unsupervised audio source separation using a deep autoencoder. The characteristics of unknown source signals mixed in the mixed input is automatically by properly configured autoencoders implemented by a network with many layers, and separated by clustering the coefficient vectors in the code layer. By investigating the weight vectors to the final target, representation layer, the primitive components of the audio signals in the frequency domain are observed. By clustering the activation coefficients in the code layer, the previously unknown source sig…
Delft University of technology（代尔夫特理工大学）；Axelera AI
Binary Neural Networks (BNNs) are compact and efficient by using binary weights instead of real-valued weights. Current BNNs use latent real-valued weights during training, where several training hyper-parameters are inherited from real-valued networks. The interpretation of several of these hyperparameters is based on the magnitude of the real-valued weights. For BNNs, however, the magnitude of binary weights is not meaningful, and thus it is unclear what these hyperparameters actually do. One example is weight-decay, which aims to keep the magnitude of real-valued weights small. Other exampl…
The classical sparse coding model represents visual stimuli as a linear combination of a handful of learned basis functions that are Gabor-like when trained on natural image data. However, the Gabor-like filters learned by classical sparse coding far overpredict well-tuned simple cell receptive field (SCRF) profiles. A number of subsequent models have either discarded the sparse dictionary learning framework entirely or have yet to take advantage of the surge in unrolled, neural dictionary learning architectures. A key missing theme of these updates is a stronger notion of \emph{structured spa…
Towards efficient deep autoencoders for multivariate time series anomaly detection
Institute of Electronics（电子学研究所）；AGH-UST（AGH科技大学）；Institute of Computer Science（计算机科学研究所）；Department of Computer Science（计算机科学系）；American University（美利坚大学）
Binary networks are extremely efficient as they use only two symbols to define the network: $\{+1,-1\}$. One can make the prior distribution of these symbols a design choice. The recent IR-Net of Qin et al. argues that imposing a Bernoulli distribution with equal priors (equal bit ratios) over the binary weights leads to maximum entropy and thus minimizes information loss. However, prior work cannot precisely control the binary weight distribution during training, and therefore cannot guarantee maximum entropy. Here, we show that quantizing using optimal transport can guarantee any bit ratio, …
École Polytechnique de Montréal（蒙特利尔综合理工学院）；Université de Montréal（蒙特利尔大学）
Deep Neural Networks (DNN) have achieved state-of-the-art results in a wide range of tasks, with the best results obtained with large training sets and large models. In the past, GPUs enabled these breakthroughs because of their greater computational speed. In the future, faster computation at both training and test time is likely to be crucial for further progress and for consumer applications on low-power devices. As a result, there is much interest in research and development of dedicated hardware for Deep Learning (DL). Binary weights, i.e., weights which are constrained to only two possib…
