Compact Graph Structure Learning via Mutual Information Compression
Beijing University of Posts and Telecommunications（北京邮电大学）；Peng Cheng Laboratory（鹏城实验室）；JD.COM Silicon Valley Research Center（京东硅谷研发中心）；Facebook AI（Facebook人工智能研究院）
Graph Structure Learning (GSL) recently has attracted considerable attentions in its capacity of optimizing graph structure as well as learning suitable parameters of Graph Neural Networks (GNNs) simultaneously. Current GSL methods mainly learn an optimal graph structure (final view) from single or multiple information sources (basic views), however the theoretical guidance on what is the optimal graph structure is still unexplored. In essence, an optimal graph structure should only contain the information about tasks while compress redundant noise as much as possible, which is defined as "minimal sufficient structure", so as to maintain the accurancy and robustness. How to obtain such structure in a principled way? In this paper, we theoretically prove that if we optimize basic views and final view based on mutual information, and keep their performance on labels simultaneously, the final view will be a minimal sufficient structure. With this guidance, we propose a Compact GSL architecture by MI compression, named CoGSL. Specifically, two basic views are extracted from original graph as two inputs of the model, which are refinedly reestimated by a view estimator. Then, we propose an adaptive technique to fuse estimated views into the final view. Furthermore, we maintain the performance of estimated views and the final view and reduce the mutual information of every two views. To comprehensively evaluate the performance of CoGSL, we conduct extensive experiments on several datasets under clean and attacked conditions, which demonstrate the effectiveness and robustness of CoGSL.
EECS University of Michigan（密歇根大学EECS学院）；CSE University of Maine（缅因大学计算机科学与工程学院）
Most approaches to deep neural network compression via pruning either evaluate a filter's importance using its weights or optimize an alternative objective function with sparsity constraints. While these methods offer a useful way to approximate contributions from similar filters, they often either ignore the dependency between layers or solve a more difficult optimization objective than standard cross-entropy. Our method, Mutual Information-based Neuron Trimming (MINT), approaches deep compression via pruning by enforcing sparsity based on the strength of the relationship between filters of a…
Seoul National University（首尔国立大学）；Samsung Advanced Institute of Technology（三星综合技术院）
We propose an information-theoretic knowledge distillation approach for the compression of generative adversarial networks, which aims to maximize the mutual information between teacher and student networks via a variational optimization based on an energy-based model. Because the direct computation of the mutual information in continuous domains is intractable, our approach alternatively optimizes the student network by maximizing the variational lower bound of the mutual information. To achieve a tight lower bound, we introduce an energy-based model relying on a deep neural network to repres…
Model compression has become necessary when applying neural networks (NN) into many real application tasks that can accept slightly-reduced model accuracy with strict tolerance to model complexity. Recently, Knowledge Distillation, which distills the knowledge from well-trained and highly complex teacher model into a compact student model, has been widely used for model compression. However, under the strict requirement on the resource cost, it is quite challenging to achieve comparable performance with the teacher model, essentially due to the drastically-reduced expressiveness ability of the…
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…
Stanford University（斯坦福大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
This paper investigates deep neural network (DNN) compression from the perspective of compactly representing and storing trained parameters. We explore the previously overlooked opportunity of cross-layer architecture-agnostic representation sharing for DNN parameters. To do this, we decouple feedforward parameters from DNN architectures and leverage additive quantization, an extreme lossy compression method invented for image descriptors, to compactly represent the parameters. The representations are then finetuned on task objectives to improve task accuracy. We conduct extensive experiments …
In the era of big data, learning from categorical features with very large vocabularies (e.g., 28 million for the Criteo click prediction dataset) has become a practical challenge for machine learning researchers and practitioners. We design a highly-scalable vocabulary compression algorithm that seeks to maximize the mutual information between the compressed categorical feature and the target binary labels and we furthermore show that its solution is guaranteed to be within a $1-1/e \approx 63\%$ factor of the global optimal solution. To achieve this, we introduce a novel re-parametrization o…
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
We study the flow of information and the evolution of internal representations during deep neural network (DNN) training, aiming to demystify the compression aspect of the information bottleneck theory. The theory suggests that DNN training comprises a rapid fitting phase followed by a slower compression phase, in which the mutual information $I(X;T)$ between the input $X$ and internal representations $T$ decreases. Several papers observe compression of estimated mutual information on different DNN models, but the true $I(X;T)$ over these networks is provably either constant (discrete $X$) or …
We review the current literature concerned with information plane analyses of neural network classifiers. While the underlying information bottleneck theory and the claim that information-theoretic compression is causally linked to generalization are plausible, empirical evidence was found to be both supporting and conflicting. We review this evidence together with a detailed analysis of how the respective information quantities were estimated. Our survey suggests that compression visualized in information planes is not necessarily information-theoretic, but is rather often compatible with geo…
University of Virginia（弗吉尼亚大学）；State University of New York at Buffalo（纽约州立大学布法罗分校）；University of Electronic Science and Technology of China（电子科技大学）
Machine learning models are generally vulnerable to adversarial examples, which is in contrast to the robustness of humans. In this paper, we try to leverage one of the mechanisms in human recognition and propose a bio-inspired classification framework in which model inference is conditioned on label hypothesis. We provide a class of training objectives for this framework and an information bottleneck regularizer which utilizes the advantage that label information can be discarded during inference. This framework enables better compression of the mutual information between inputs and latent re…
This paper describes a new approach for learning structures of large Bayesian networks based on blocks resulting from feature space clustering. This clustering is obtained using normalized mutual information. And the subsequent aggregation of blocks is done using classical learning methods except that they are input with compressed information about combinations of feature values for each block. Validation of this approach is done for Hill-Climbing as a graph enumeration algorithm for two score functions: BIC and MI. In this way, potentially parallelizable block learning can be implemented eve…
Model compression and acceleration are attracting increasing attentions due to the demand for embedded devices and mobile applications. Research on efficient convolutional neural networks (CNNs) aims at removing feature redundancy by decomposing or optimizing the convolutional calculation. In this work, feature redundancy is assumed to exist among channels in CNN architectures, which provides some leeway to boost calculation efficiency. Aiming at channel compression, a novel convolutional construction named compact convolution is proposed to embrace the progress in spatial convolution, channel…
Tehran Institute for Advanced Studies, Khatam University（哈塔姆大学德黑兰高等研究院）；INRIA（法国国家信息与自动化研究所）；ENS – PSL Research University（PSL研究大学巴黎高等师范学院）
Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting different complexity notions such as the mutual information between the data sample and the algorithm output, compressibility of the hypothesis space, and the fractal dimension of the hypothesis space. While these bounds have illuminated the problem at hand from different angles, their suggested complexity notions might appear seemingly unrelated, thereby res…
This paper introduces ASCAI, a novel adaptive sampling methodology that can learn how to effectively compress Deep Neural Networks (DNNs) for accelerated inference on resource-constrained platforms. Modern DNN compression techniques comprise various hyperparameters that require per-layer customization to ensure high accuracy. Choosing such hyperparameters is cumbersome as the pertinent search space grows exponentially with the number of model layers. To effectively traverse this large space, we devise an intelligent sampling mechanism that adapts the sampling strategy using customized operatio…
IBM Research – Almaden（IBM阿尔马登研究中心）；Khoury College of Computer Sciences, Northeastern University（东北大学库里计算机学院）
We provide an information-theoretic framework for studying the generalization properties of machine learning algorithms. Our framework ties together existing approaches, including uniform convergence bounds and recent methods for adaptive data analysis. Specifically, we use Conditional Mutual Information (CMI) to quantify how well the input (i.e., the training data) can be recognized given the output (i.e., the trained model) of the learning algorithm. We show that bounds on CMI can be obtained from VC dimension, compression schemes, differential privacy, and other methods. We then show that b…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Google Research（谷歌研究院）
We introduce the Mutual Information Machine (MIM), a probabilistic auto-encoder for learning joint distributions over observations and latent variables. MIM reflects three design principles: 1) low divergence, to encourage the encoder and decoder to learn consistent factorizations of the same underlying distribution; 2) high mutual information, to encourage an informative relation between data and latent variables; and 3) low marginal entropy, or compression, which tends to encourage clustered latent representations. We show that a combination of the Jensen-Shannon divergence and the joint ent…
University of California, San Diego（加州大学圣地亚哥分校）；Beihang University（北京航空航天大学）；Microsoft Research Asia（微软亚洲研究院）
In this paper, we propose a novel model compression approach to effectively compress BERT by progressive module replacing. Our approach first divides the original BERT into several modules and builds their compact substitutes. Then, we randomly replace the original modules with their substitutes to train the compact modules to mimic the behavior of the original modules. We progressively increase the probability of replacement through the training. In this way, our approach brings a deeper level of interaction between the original and compact models. Compared to the previous knowledge distillat…
We examine a class of deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical physics methods, under the assumption that weight matrices are independent and orthogonally-invariant. (ii) We extend particular cases in which this result is known to be rigorously exact by providing a proof for two-layers networks with Gaussian random weights, using the recently introduced adaptive interpolation method. (iii) We propose an experiment framewo…
Computing approximate nearest neighbors in high dimensional spaces is a central problem in large-scale data mining with a wide range of applications in machine learning and data science. A popular and effective technique in computing nearest neighbors approximately is the locality-sensitive hashing (LSH) scheme. In this paper, we aim to develop LSH schemes for distance functions that measure the distance between two probability distributions, particularly for f-divergences as well as a generalization to capture mutual information loss. First, we provide a general framework to design LHS scheme…
An Information Theoretic Perspective on Agentic System Design
Department of Computer Science, Stanford University（斯坦福大学计算机科学系）；Department of Statistics, Stanford University（斯坦福大学统计学系）；Wu Tsai Neurosciences Institute, Stanford University（斯坦福大学吴泰教授神经科学研究所）
