In the Information Bottleneck (IB), when tuning the relative strength between compression and prediction terms, how do the two terms behave, and what's their relationship with the dataset and the learned representation? In this paper, we set out to answer these questions by studying multiple phase transitions in the IB objective: $\text{IB}_β[p(z|x)] = I(X; Z) - βI(Y; Z)$ defined on the encoding distribution p(z|x) for input $X$, target $Y$ and representation $Z$, where sudden jumps of $dI(Y; Z)/d β$ and prediction accuracy are observed with increasing $β$. We introduce a definition for IB phase transitions as a qualitative change of the IB loss landscape, and show that the transitions correspond to the onset of learning new classes. Using second-order calculus of variations, we derive a formula that provides a practical condition for IB phase transitions, and draw its connection with the Fisher information matrix for parameterized models. We provide two perspectives to understand the formula, revealing that each IB phase transition is finding a component of maximum (nonlinear) correlation between $X$ and $Y$ orthogonal to the learned representation, in close analogy with canonical-correlation analysis (CCA) in linear settings. Based on the theory, we present an algorithm for discovering phase transition points. Finally, we verify that our theory and algorithm accurately predict phase transitions in categorical datasets, predict the onset of learning new classes and class difficulty in MNIST, and predict prominent phase transitions in CIFAR10.
Tsinghua University（清华大学）；Louisiana State University（路易斯安那州立大学）
In multi-agent deep reinforcement learning, extracting sufficient and compact information of other agents is critical to attain efficient convergence and scalability of an algorithm. In canonical frameworks, distilling of such information is often done in an implicit and uninterpretable manner, or explicitly with cost functions not able to reflect the relationship between information compression and utility in representation. In this paper, we present Information-Bottleneck-based Other agents' behavior Representation learning for Multi-agent reinforcement learning (IBORM) to explicitly seek lo…
University of California, San Francisco（加利福尼亚大学旧金山分校）
Multiview data contain information from multiple modalities and have potentials to provide more comprehensive features for diverse machine learning tasks. A fundamental question in multiview analysis is what is the additional information brought by additional views and can quantitatively identify this additional information. In this work, we try to tackle this challenge by decomposing the entangled multiview features into shared latent representations that are common across all views and private representations that are specific to each single view. We formulate this feature disentanglement in…
Deep latent variable models are powerful tools for representation learning. In this paper, we adopt the deep information bottleneck model, identify its shortcomings and propose a model that circumvents them. To this end, we apply a copula transformation which, by restoring the invariance properties of the information bottleneck method, leads to disentanglement of the features in the latent space. Building on that, we show how this transformation translates to sparsity of the latent space in the new model. We evaluate our method on artificial and real data.
University of Amsterdam（阿姆斯特丹大学）；University of Exeter（埃克塞特大学）；Microsoft Research（微软研究院）；University of Tuebingen（蒂宾根大学）
The information bottleneck principle provides an information-theoretic method for representation learning, by training an encoder to retain all information which is relevant for predicting the label while minimizing the amount of other, excess information in the representation. The original formulation, however, requires labeled data to identify the superfluous information. In this work, we extend this ability to the multi-view unsupervised setting, where two views of the same underlying entity are provided but the label is unknown. This enables us to identify superfluous information as that n…
Representation Learning in Deep RL via Discrete Information Bottleneck
Mila（米拉人工智能研究所）；McGill University（麦吉尔大学）；Microsoft Research Montreal（微软研究院蒙特利尔分院）；Beijing Institute of Technology（北京理工大学）；AMII（阿尔伯塔机器智能研究所）；University of Alberta（阿尔伯塔大学）；University of Montreal（蒙特利尔大学）；University of Virginia（弗吉尼亚大学）；Google DeepMind（谷歌DeepMind）；Microsoft Research NYC（微软研究院纽约分院）
We propose the factorized action variational autoencoder (FAVAE), a state-of-the-art generative model for learning disentangled and interpretable representations from sequential data via the information bottleneck without supervision. The purpose of disentangled representation learning is to obtain interpretable and transferable representations from data. We focused on the disentangled representation of sequential data since there is a wide range of potential applications if disentanglement representation is extended to sequential data such as video, speech, and stock market. Sequential data a…
Combined Representation and Generation with Diffusive State Predictive Information Bottleneck
Department of Physics（物理系）；Institute for Physical Science and Technology（物理科学与技术研究院）；Institute for Health Computing（健康计算研究院）；Biophysics Program（生物物理项目）；Department of Chemistry and Biochemistry（化学与生物化学系）；University of Maryland（马里兰大学）
Trustworthy Representation Learning via Information Funnels and Bottlenecks
Christian Doppler Laboratory for Dependable Intelligent Systems in Harsh Environments（可信智能系统在恶劣环境中的克里斯蒂安·多普勒实验室）；Graz University of Technology（格拉茨技术大学）；Know Center Research GmbH（Know Center研究有限责任公司）
Disentangled Representation Learning with Transmitted Information Bottleneck
State Grid Shaanxi Electric Power Company Ltd.（国家电网陕西省电力公司）；State Grid Corporation of China（国家电网有限公司）；University of Science and Technology of China（中国科学技术大学）
Robust Training of Vector Quantized Bottleneck Models
NVIDIA Corporation（英伟达公司）；University of Wrocław（弗罗茨瓦夫大学）；Université de Toulon（土伦大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Massachusetts Institute of Technology（麻省理工学院）；Tallinn University of Technology（塔林理工大学）；Le Mans University（勒芒大学）
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
We propose a new concept of rateless auto-encoders (RL-AEs) that enable a flexible latent dimensionality, which can be seamlessly adjusted for varying distortion and dimensionality requirements. In the proposed RL-AEs, instead of a deterministic bottleneck architecture, we use an over-complete representation that is stochastically regularized with weighted dropouts, in a manner analogous to sparse AE (SAE). Unlike SAEs, our RL-AEs employ monotonically increasing dropout rates across the latent representation nodes such that the latent variables become sorted by importance like in principal com…
Facebook AI Research（脸书人工智能研究院）；CUNY Graduate Center（纽约市立大学研究生中心）
We address the question of characterizing and finding optimal representations for supervised learning. Traditionally, this question has been tackled using the Information Bottleneck, which compresses the inputs while retaining information about the targets, in a decoder-agnostic fashion. In machine learning, however, our goal is not compression but rather generalization, which is intimately linked to the predictive family or decoder of interest (e.g. linear classifier). We propose the Decodable Information Bottleneck (DIB) that considers information retention and compression from the perspecti…
University of California, San Diego（加州大学圣地亚哥分校）；Halıcıoğlu Data Science Institute（哈利哲奥卢数据科学研究所）
Randomly initialized wide neural networks transition to linear functions of weights as the width grows, in a ball of radius $O(1)$ around initialization. A necessary condition for this result is that all layers of the network are wide enough, i.e., all widths tend to infinity. However, the transition to linearity breaks down when this infinite width assumption is violated. In this work we show that linear networks with a bottleneck layer learn bilinear functions of the weights, in a ball of radius $O(1)$ around initialization. In general, for $B-1$ bottleneck layers, the network is a degree $B…
Universitat Politècnica de València（瓦伦西亚理工大学）；Institute for Infocomm Research（资讯通信研究所）
We present a comprehensive study on the use of autoencoders for modelling text data, in which (differently from previous studies) we focus our attention on the following issues: i) we explore the suitability of two different models bDA and rsDA for constructing deep autoencoders for text data at the sentence level; ii) we propose and evaluate two novel metrics for better assessing the text-reconstruction capabilities of autoencoders; and iii) we propose an automatic method to find the critical bottleneck dimensionality for text language representations (below which structural information is lo…
We propose a novel information bottleneck (IB) method named Drop-Bottleneck, which discretely drops features that are irrelevant to the target variable. Drop-Bottleneck not only enjoys a simple and tractable compression objective but also additionally provides a deterministic compressed representation of the input variable, which is useful for inference tasks that require consistent representation. Moreover, it can jointly learn a feature extractor and select features considering each feature dimension's relevance to the target task, which is unattainable by most neural network-based IB method…
This paper explores the bottleneck of feature representations of deep neural networks (DNNs), from the perspective of the complexity of interactions between input variables encoded in DNNs. To this end, we focus on the multi-order interaction between input variables, where the order represents the complexity of interactions. We discover that a DNN is more likely to encode both too simple interactions and too complex interactions, but usually fails to learn interactions of intermediate complexity. Such a phenomenon is widely shared by different DNNs for different tasks. This phenomenon indicate…
Estimating individual level treatment effects (ITE) from observational data is a challenging and important area in causal machine learning and is commonly considered in diverse mission-critical applications. In this paper, we propose an information theoretic approach in order to find more reliable representations for estimating ITE. We leverage the Information Bottleneck (IB) principle, which addresses the trade-off between conciseness and predictive power of representation. With the introduction of an extended graphical model for causal information bottleneck, we encourage the independence be…
Montreal Institute for Learning Algorithms (MILA)（蒙特利尔学习算法研究所（MILA））；McGill University（麦吉尔大学）；Facebook Artificial Intelligence Research (FAIR)（Facebook人工智能研究院（FAIR））
Deep reinforcement learning has recently shown many impressive successes. However, one major obstacle towards applying such methods to real-world problems is their lack of data-efficiency. To this end, we propose the Bottleneck Simulator: a model-based reinforcement learning method which combines a learned, factorized transition model of the environment with rollout simulations to learn an effective policy from few examples. The learned transition model employs an abstract, discrete (bottleneck) state, which increases sample efficiency by reducing the number of model parameters and by exploiti…
Department of Computer Science（计算机科学系）；Stanford University（斯坦福大学）
Representation learning of graph-structured data is challenging because both graph structure and node features carry important information. Graph Neural Networks (GNNs) provide an expressive way to fuse information from network structure and node features. However, GNNs are prone to adversarial attacks. Here we introduce Graph Information Bottleneck (GIB), an information-theoretic principle that optimally balances expressiveness and robustness of the learned representation of graph-structured data. Inheriting from the general Information Bottleneck (IB), GIB aims to learn the minimal sufficien…
Johns Hopkins University（约翰斯·霍普金斯大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We develop a novel method for ensuring fairness in machine learning which we term as the Renyi Fair Information Bottleneck (RFIB). We consider two different fairness constraints - demographic parity and equalized odds - for learning fair representations and derive a loss function via a variational approach that uses Renyi's divergence with its tunable parameter $α$ and that takes into account the triple constraints of utility, fairness, and compactness of representation. We then evaluate the performance of our method for image classification using the EyePACS medical imaging dataset, showing i…
Beijing University of Posts and Telecommunications（北京邮电大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
The information bottleneck principle is an elegant and useful approach to representation learning. In this paper, we investigate the problem of representation learning in the context of reinforcement learning using the information bottleneck framework, aiming at improving the sample efficiency of the learning algorithms. %by accelerating the process of discarding irrelevant information when the %input states are extremely high-dimensional. We analytically derive the optimal conditional distribution of the representation, and provide a variational lower bound. Then, we maximize this lower bound…
Learning effective joint embedding for cross-modal data has always been a focus in the field of multimodal machine learning. We argue that during multimodal fusion, the generated multimodal embedding may be redundant, and the discriminative unimodal information may be ignored, which often interferes with accurate prediction and leads to a higher risk of overfitting. Moreover, unimodal representations also contain noisy information that negatively influences the learning of cross-modal dynamics. To this end, we introduce the multimodal information bottleneck (MIB), aiming to learn a powerful an…
Institute for Communications Engineering, Technical University of Munich（慕尼黑工业大学通信工程研究所）；Signal Processing and Speech Communication Laboratory, Graz University of Technology（格拉茨技术大学信号处理与语音通信实验室）；Know-Center GmbH（Know-Center 有限公司）
In this theory paper, we investigate training deep neural networks (DNNs) for classification via minimizing the information bottleneck (IB) functional. We show that the resulting optimization problem suffers from two severe issues: First, for deterministic DNNs, either the IB functional is infinite for almost all values of network parameters, making the optimization problem ill-posed, or it is piecewise constant, hence not admitting gradient-based optimization methods. Second, the invariance of the IB functional under bijections prevents it from capturing properties of the learned representati…
Due to the nature of deep learning approaches, it is inherently difficult to understand which aspects of a molecular graph drive the predictions of the network. As a mitigation strategy, we constrain certain weights in a multi-task graph convolutional neural network according to the Gini index to maximize the "inequality" of the learned representations. We show that this constraint does not degrade evaluation metrics for some targets, and allows us to combine the outputs of the graph convolutional operation in a visually interpretable way. We then perform a proof-of-concept experiment on quant…
Mila（米拉）；Google（谷歌）；National University of Singapore（新加坡国立大学）
Vector Quantization (VQ) is a method for discretizing latent representations and has become a major part of the deep learning toolkit. It has been theoretically and empirically shown that discretization of representations leads to improved generalization, including in reinforcement learning where discretization can be used to bottleneck multi-agent communication to promote agent specialization and robustness. The discretization tightness of most VQ-based methods is defined by the number of discrete codes in the representation vector and the codebook size, which are fixed as hyperparameters. In…
We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The bound itself is bounded above by the variational information bottleneck objective, and the two methods coincide in the regime of single-shot Monte Carlo approximations. The notion of deficiency provides a principled way of approximating complicated channels by relatively simpler ones. We show that the deficiency of one channel with respect to another has an oper…
The Information Bottleneck (IB) is a conceptual method for extracting the most compact, yet informative, representation of a set of variables, with respect to the target. It generalizes the notion of minimal sufficient statistics from classical parametric statistics to a broader information-theoretic sense. The IB curve defines the optimal trade-off between representation complexity and its predictive power. Specifically, it is achieved by minimizing the level of mutual information (MI) between the representation and the original variables, subject to a minimal level of MI between the represen…
This paper introduces a novel method for the representation of images that is semantic by nature, addressing the question of computation intelligibility in computer vision tasks. More specifically, our proposition is to introduce what we call a semantic bottleneck in the processing pipeline, which is a crossing point in which the representation of the image is entirely expressed with natural language , while retaining the efficiency of numerical representations. We show that our approach is able to generate semantic representations that give state-of-the-art results on semantic content-based i…
In this paper, we explore the problem of deep multi-view subspace clustering framework from an information-theoretic point of view. We extend the traditional information bottleneck principle to learn common information among different views in a self-supervised manner, and accordingly establish a new framework called Self-supervised Information Bottleneck based Multi-view Subspace Clustering (SIB-MSC). Inheriting the advantages from information bottleneck, SIB-MSC can learn a latent space for each view to capture common information among the latent representations of different views by removin…
Speech and Vision Laboratory, IIIT Hyderabad（海得拉巴国际信息技术学院语音与视觉实验室）
In this paper, we describe a statistical parametric speech synthesis approach with unit-level acoustic representation. In conventional deep neural network based speech synthesis, the input text features are repeated for the entire duration of phoneme for mapping text and speech parameters. This mapping is learnt at the frame-level which is the de-facto acoustic representation. However much of this computational requirement can be drastically reduced if every unit can be represented with a fixed-dimensional representation. Using recurrent neural network based auto-encoder, we show that it is in…
University of Maryland Baltimore County（马里兰大学巴尔的摩县分校）
The existence of external (``side'') semantic knowledge has been shown to result in more expressive computational event models. To enable the use of side information that may be noisy or missing, we propose a semi-supervised information bottleneck-based discrete latent variable model. We reparameterize the model's discrete variables with auxiliary continuous latent variables and a light-weight hierarchical structure. Our model is learned to minimize the mutual information between the observed data and optional side knowledge that is not already captured by the new, auxiliary variables. We theo…
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
The information bottleneck (IB) principle has been adopted to explain deep learning in terms of information compression and prediction, which are balanced by a trade-off hyperparameter. How to optimize the IB principle for better robustness and figure out the effects of compression through the trade-off hyperparameter are two challenging problems. Previous methods attempted to optimize the IB principle by introducing random noise into learning the representation and achieved state-of-the-art performance in the nuisance information compression and semantic information extraction. However, their…
