We address two fundamental questions about graph neural networks (GNNs). First, we prove that several important graph properties cannot be computed by GNNs that rely entirely on local information. Such GNNs include the standard message passing models, and more powerful spatial variants that exploit local graph structure (e.g., via relative orientation of messages, or local port ordering) to distinguish neighbors of each node. Our treatment includes a novel graph-theoretic formalism. Second, we provide the first data dependent generalization bounds for message passing GNNs. This analysis explicitly accounts for the local permutation invariance of GNNs. Our bounds are much tighter than existing VC-dimension based guarantees for GNNs, and are comparable to Rademacher bounds for recurrent neural networks.
University of Michigan（密歇根大学）；University of British Columbia（不列颠哥伦比亚大学）
Graph-structured data are ubiquitous. However, graphs encode diverse types of information and thus play different roles in data representation. In this paper, we distinguish the \textit{representational} and the \textit{correlational} roles played by the graphs in node-level prediction tasks, and we investigate how Graph Neural Network (GNN) models can effectively leverage both types of information. Conceptually, the representational information provides guidance for the model to construct better node features; while the correlational information indicates the correlation between node outcomes…
Graph Representational Learning: When Does More Expressivity Hurt Generalization?
Aleph Alpha Research（Aleph Alpha 研究院）；LMU Munich（慕尼黑大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；TU Wien（维也纳工业大学）；DLR-German Aerospace Center（德国航空航天中心）；University of Tromsø（特罗姆瑟大学）；CNRS（法国国家科学研究中心）；Institut Polytechnique de Paris（巴黎理工学院）
Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks
SISSA Trieste, Italy（意大利特里斯特SISSA研究所）；Theoretical and Scientific Data Science (TSDS) group at the International School for Advanced Studies (SISSA)（国际先进研究学院（SISSA）理论与科学数据科学（TSDS）小组）；Condensed Matter and Statistical Physics section at the International Centre for Theoretical Physics (ICTP)（国际理论物理中心（ICTP）凝聚态与统计物理部门）
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that different instances of the same network architecture encode the same representational similarity matrix, and their neural activity patterns are connected by orthogonal transformations. However, it is unclear if this holds for non-linear networks. Using a shared response model, we show that different neural networks encode the same input examples as different o…
IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）；IBM Research（IBM研究院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；Northwestern University（西北大学）
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting structure-aware neural methods to work with the underlying graph representations of logical expressions. While more effective than character and token-level approaches, graph-based methods have often made representational trade-offs that limited their ability to capture key structural properties of their inputs. In this work we propose a novel approach for e…
University of St.Gallen（圣加仑大学）；University Passau（帕绍大学）
There is some theoretical evidence that deep neural networks with multiple hidden layers have a potential for more efficient representation of multidimensional mappings than shallow networks with a single hidden layer. The question is whether it is possible to exploit this theoretical advantage for finding such representations with help of numerical training methods. Tests using prototypical problems with a known mean square minimum did not confirm this hypothesis. Minima found with the help of deep networks have always been worse than those found using shallow networks. This does not directly…
MRC Cognition and Brain Science Unit（医学研究委员会认知与脑科学单元）
Deep neural networks (DNNs) provide useful models of visual representational transformations. We present a method that enables a DNN (student) to learn from the internal representational spaces of a reference model (teacher), which could be another DNN or, in the future, a biological brain. Representational spaces of the student and the teacher are characterized by representational distance matrices (RDMs). We propose representational distance learning (RDL), a stochastic gradient descent method that drives the RDMs of the student to approximate the RDMs of the teacher. We demonstrate that RDL…
The presence of Long Distance Dependencies (LDDs) in sequential data poses significant challenges for computational models. Various recurrent neural architectures have been designed to mitigate this issue. In order to test these state-of-the-art architectures, there is growing need for rich benchmarking datasets. However, one of the drawbacks of existing datasets is the lack of experimental control with regards to the presence and/or degree of LDDs. This lack of control limits the analysis of model performance in relation to the specific challenge posed by LDDs. One way to address this is to u…
Similarity of Neural Network Models: A Survey of Functional and Representational Measures
University of Passau（帕绍大学）；University of Mannheim（曼海姆大学）；RWTH Aachen University（亚琛工业大学）；GESIS - Leibniz Institute for the Social Sciences（GESIS莱布尼茨社会科学研究所）；Complexity Science Hub Vienna（维也纳复杂性科学中心）
Neural networks trained on standard image classification data sets are shown to be less resistant to data set bias. It is necessary to comprehend the behavior objective function that might correspond to superior performance for data with biases. However, there is little research on the selection of the objective function and its representational structure when trained on data set with biases. In this paper, we investigate the performance and internal representational structure of convolution-based neural networks (e.g., ResNets) trained on biased data using various objective functions. We spec…
Zuckerman Mind Brain Behavior Institute, Columbia University, New York, NY, USA 10027（美国纽约州纽约市哥伦比亚大学祖克曼心智脑行为研究所）
Representational similarity analysis (RSA) has been shown to be an effective framework to characterize brain-activity profiles and deep neural network activations as representational geometry by computing the pairwise distances of the response patterns as a representational dissimilarity matrix (RDM). However, how to properly analyze and visualize the representational geometry as dynamics over the time course from stimulus onset to offset is not well understood. In this work, we formulated the pipeline to understand representational dynamics with RDM movies and Procrustes-aligned Multidimensio…
Partial Soft-Matching Distance for Neural Representational Comparison with Partial Unit Correspondence
Department of Cognitive Science University of California, San Diego（认知科学系加州大学圣地亚哥分校）；Center for Neural Science, New York University（纽约大学神经科学中心）；Center for Computational Neuroscience, Flatiron Institute（Flatiron研究所计算神经科学中心）；Department of Cognitive Science Department of Computer Science and Engineering University of California, San Diego（认知科学系计算机科学与工程系加州大学圣地亚哥分校）
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；University of Alberta（阿尔伯塔大学）；Purdue University Fort Wayne（普渡大学韦恩堡分校）
Similarity analysis is one of the crucial steps in most fMRI studies. Representational Similarity Analysis (RSA) can measure similarities of neural signatures generated by different cognitive states. This paper develops Deep Representational Similarity Learning (DRSL), a deep extension of RSA that is appropriate for analyzing similarities between various cognitive tasks in fMRI datasets with a large number of subjects, and high-dimensionality -- such as whole-brain images. Unlike the previous methods, DRSL is not limited by a linear transformation or a restricted fixed nonlinear kernel functio…
ReSi: A Comprehensive Benchmark for Representational Similarity Measures
University of Passau（帕绍大学）；German Cancer Research Center (DKFZ)（德国癌症研究中心）；Helmholtz Imaging（亥姆霍兹成像中心）；University of Heidelberg（海德堡大学）；University of Mannheim（曼海姆大学）；RWTH Aachen University（亚琛工业大学）；Heidelberg University Hospital（海德堡大学医院）；National Center for Tumor Diseases (NCT) Heidelberg（海德堡国家肿瘤疾病中心）；GESIS - Leibniz Institute for the Social Sciences（莱布尼茨社会科学研究所GESIS）；Complexity Science Hub（复杂性科学中心）
Flatiron Institute（熨斗研究所）；New York University（纽约大学）
Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams…
DeepMind（深度思维）；Facebook AI Research (FAIR)（脸书人工智能研究院）；Google Brain（谷歌大脑）；Cornell University（康奈尔大学）
Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks is fundamentally difficult as the structure of representations varies greatly, even across groups of networks trained on identical tasks, and over the course of training. Here, we develop projection weighted CCA (Canonical Correlation Analysis) as a tool for understanding neural networks, building off of SVCCA, a recently proposed method (Raghu et al., 2017)…
University of Maryland, College Park（马里兰大学帕克分校）；Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）；PUCRS（巴西圣保罗天主教大学）；The Alan Turing Institute（艾伦·图灵研究所）；University of Cambridge（剑桥大学）
A major challenge in studying robustness in deep learning is defining the set of ``meaningless'' perturbations to which a given Neural Network (NN) should be invariant. Most work on robustness implicitly uses a human as the reference model to define such perturbations. Our work offers a new view on robustness by using another reference NN to define the set of perturbations a given NN should be invariant to, thus generalizing the reliance on a reference ``human NN'' to any NN. This makes measuring robustness equivalent to measuring the extent to which two NNs share invariances, for which we pro…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Washington State University（华盛顿州立大学）；Siemens Corporate Technology（西门子公司企业技术部）
Human activity recognition (HAR) research has increased in recent years due to its applications in mobile health monitoring, activity recognition, and patient rehabilitation. The typical approach is training a HAR classifier offline with known users and then using the same classifier for new users. However, the accuracy for new users can be low with this approach if their activity patterns are different than those in the training data. At the same time, training from scratch for new users is not feasible for mobile applications due to the high computational cost and training time. To address t…
A burgeoning line of research leverages deep neural networks to approximate the solutions to high dimensional PDEs, opening lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of dimensionality. However, most prior theoretical analyses have been limited to linear PDEs. In this work, we take a step towards studying the representational power of neural networks for approximating solutions to nonlinear PDEs. We focus on a class of PDEs known as \emph{nonlinear elliptic variational PDEs}, whose solutions minimize an \emph{Euler-Lagrange} energy …
There has been a large amount of interest, both in the past and particularly recently, into the power of different families of universal approximators, e.g. ReLU networks, polynomials, rational functions. However, current research has focused almost exclusively on understanding this problem in a worst-case setting, e.g. bounding the error of the best infinity-norm approximation in a box. In this setting a high-degree polynomial is required to even approximate a single ReLU. However, in real applications with high dimensional data we expect it is only important to approximate the desired functi…
Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are trained on, or biologically adapted to, similar tasks. A standardized set of analysis tools is now needed to identify how network-level covariates -- such as architecture, anatomical brain region, and model organism -- impact neural representations (hidden layer activations). Here, we provide a rigorous foundation for these analyses by defining a broad family of …
Harvard University（哈佛大学）；Weizmann Institute of Science（魏茨曼科学研究所）
Deep neural network (DNN) models for computer vision are now capable of human-level object recognition. Consequently, similarities in the performance and vulnerabilities of DNN and human vision are of great interest. Here we characterize the response of the VGG-19 DNN to images of the Scintillating Grid visual illusion, in which white dots are perceived to be partially black. We observed a significant deviation from the expected monotonic relation between VGG-19 representational dissimilarity and dot whiteness in the Scintillating Grid. That is, a linear increase in dot whiteness leads to a no…
Behavioural vs. Representational Systematicity in End-to-End Models: An Opinionated Survey
School of Informatics, University of Edinburgh（信息学院，爱丁堡大学）；Chemnitz University of Technology（技术大学，克明茨）；Institute of Logic, Language, and Computation, University of Amsterdam（逻辑、语言与计算研究所，阿姆斯特丹大学）；School of Philosophy, Psychology & Language Sciences, University of Edinburgh（哲学、心理学与语言科学学院，爱丁堡大学）
Dimensions underlying the representational alignment of deep neural networks with humans
Max Planck Institute for Human Cognitive and Brain Sciences（马克斯·普朗克人类认知与脑科学研究所）；Donders Institute for Brain, Cognition and Behaviour（唐德斯脑、认知与行为研究所）；Technische Universität Berlin（柏林工业大学）；Berlin Institute for the Foundations of Learning and Data (BIFOLD)（柏林学习与数据基础研究所）；Justus Liebig University（尤斯图斯·李比希大学）；Center for Mind, Brain and Behavior, Universities of Marburg, Giessen, and Darmstadt（马尔堡、吉森和达姆施塔特大学心智、大脑与行为中心）；Google DeepMind（谷歌DeepMind）
Feature Learning beyond the Lazy-Rich Dichotomy: Insights from Representational Geometry
Center for Computational Neuroscience, Flatiron Institute（计算神经科学中心，扁铁研究所）；University of California, UCLA（加州大学，UCLA）；Center for Neural Science, New York University（神经科学中心，纽约大学）
Achieving More Human Brain-Like Vision via Human EEG Representational Alignment
Department of Psychology, The Ohio State University（心理学系，俄亥俄州立大学）；McGovern Institute for Brain Research, Massachusetts Institute of Technology（脑科学研究所，麻省理工学院）；Department of Neuroscience, The University of Texas at Dallas（神经科学系，德克萨斯大学达拉斯分校）
Time to Spike? Understanding the Representational Power of Spiking Neural Networks in Discrete Time
Department of Mathematics, Ludwig-Maximilians-Universität München, Germany（慕尼黑大学数学系）；Munich Center for Machine Learning (MCML), Munich, Germany（慕尼黑机器学习中心）；Institute of Robotics and Mechatronics, DLR-German Aerospace Center, Germany（德国航空航天中心机器人与机电研究所）；Department of Physics and Technology, University of Tromsø, Tromsø, Norway（特罗姆瑟大学物理与技术系）
Training and using modern neural-network based latent-variable generative models (like Variational Autoencoders) often require simultaneously training a generative direction along with an inferential(encoding) direction, which approximates the posterior distribution over the latent variables. Thus, the question arises: how complex does the inferential model need to be, in order to be able to accurately model the posterior distribution of a given generative model? In this paper, we identify an important property of the generative map impacting the required size of the encoder. We show that if t…
When Does Closeness in Distribution Imply Representational Similarity? An Identifiability Perspective
Technical University of Denmark（丹麦技术大学）；University of Trento, Italy（意大利特伦托大学）；Helmholtz AI, Munich（慕尼黑海德堡人工智能研究所）；Technical University of Munich（慕尼黑技术大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；University of Copenhagen（哥本哈根大学）
University of Pennsylvania（宾夕法尼亚大学）；Mila Québec AI Institute（米拉魁北克人工智能研究所）；McGill University（麦吉尔大学）
Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting the layer-by-layer construction of useful representations: perhaps the role of each layer is to reformat information to reduce the "distance" to the desired outputs. With this framework, the layer-wise computation implemented by a deep neural network can be viewed as a path through a high-dimensional representation space. We formalize this intuitive idea of…
Large width limits have been a recent focus of deep learning research: modulo computational practicalities, do wider networks outperform narrower ones? Answering this question has been challenging, as conventional networks gain representational power with width, potentially masking any negative effects. Our analysis in this paper decouples capacity and width via the generalization of neural networks to Deep Gaussian Processes (Deep GP), a class of nonparametric hierarchical models that subsume neural nets. In doing so, we aim to understand how width affects (standard) neural networks once they…
Parameter symmetries determine representational geometry in overparameterized nonlinear networks
University of Tübingen（图宾根大学）；International Max Planck Research School for Intelligent Systems（国际马克斯·普朗克智能系统研究学院）；Allen Institute for Neural Dynamics（艾伦神经动力学研究所）；Gatsby Computational Neuroscience Unit, University College London（伦敦大学学院盖茨比计算神经科学中心）；Sainsbury Wellcome Centre, University College London（伦敦大学学院塞恩斯伯里惠康中心）；University of Alberta（阿尔伯塔大学）；Amii（艾伯塔机器智能研究所）
Understanding Task Representations in Neural Networks via Bayesian Ablation
Princeton Laboratory for Artificial Intelligence, Princeton University（普林斯顿大学普林斯顿人工智能实验室）；Princeton Neuroscience Institute, Princeton University（普林斯顿大学普林斯顿神经科学研究所）；Department of Psychology, Princeton University（普林斯顿大学心理学系）；Department of Philosophy and Center for Statistics and Machine Learning, Princeton University（普林斯顿大学哲学系与统计与机器学习中心）
