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Register a new userWhat Can Neural Networks Reason About?
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Keyulu Xu
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically, there is limited understanding of why and when a network structure generalizes better than others, although they have equal expressive power. In this paper, we develop a framework to characterize which reasoning tasks a network can learn well, by studying how well its computation structure aligns with the algorithmic structure of the relevant reasoning process. We formally define this algorithmic alignment and derive a sample complexity bound that decreases with better alignment. This framework offers an explanation for the empirical success of popular reasoning models, and suggests their limitations. As an example, we unify seemingly different reasoning tasks, such as intuitive physics, visual question answering, and shortest paths, via the lens of a powerful algorithmic paradigm, dynamic programming (DP). We show that GNNs align with DP and thus are expected to solve these tasks. On several reasoning tasks, our theory is supported by empirical results.
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Filter is the key component in modern convolutional neural networks (CNNs). However, since CNNs are usually over-parameterized, a pre-trained network always contain some invalid (unimportant) filters. These filters have relatively small $l_{1}$ norm and contribute little to the output (textbf{Reason}). While filter pruning removes these invalid filters for efficiency consideration, we tend to reactivate them to improve the representation capability of CNNs. In this paper, we introduce filter grafting (textbf{Method}) to achieve this goal. The activation is processed by grafting external information (weights) into invalid filters. To better perform the grafting, we develop a novel criterion to measure the information of filters and an adaptive weighting strategy to balance the grafted information among networks. After the grafting operation, the network has fewer invalid filters compared with its initial state, enpowering the model with more representation capacity. Meanwhile, since grafting is operated reciprocally on all networks involved, we find that grafting may lose the information of valid filters when improving invalid filters. To gain a universal improvement on both valid and invalid filters, we compensate grafting with distillation (textbf{Cultivation}) to overcome the drawback of grafting . Extensive experiments are performed on the classification and recognition tasks to show the superiority of our method. Code is available at textcolor{black}{emph{https://github.com/fxmeng/filter-grafting}}.
We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) -- structured networks with MLP modules -- have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify the observation that ReLU MLPs quickly converge to linear functions along any direction from the origin, which implies that ReLU MLPs do not extrapolate most nonlinear functions. But, they can provably learn a linear target function when the training distribution is sufficiently diverse. Second, in connection to analyzing the successes and limitations of GNNs, these results suggest a hypothesis for which we provide theoretical and empirical evidence: the success of GNNs in extrapolating algorithmic tasks to new data (e.g., larger graphs or edge weights) relies on encoding task-specific non-linearities in the architecture or features. Our theoretical analysis builds on a connection of over-parameterized networks to the neural tangent kernel. Empirically, our theory holds across different training settings.
To make advanced learning machines such as Deep Neural Networks (DNNs) more transparent in decision making, explainable AI (XAI) aims to provide interpretations of DNNs predictions. These interpretations are usually given in the form of heatmaps, each one illustrating relevant patterns regarding the prediction for a given instance. Bayesian approaches such as Bayesian Neural Networks (BNNs) so far have a limited form of transparency (model transparency) already built-in through their prior weight distribution, but notably, they lack explanations of their predictions for given instances. In this work, we bring together these two perspectives of transparency into a holistic explanation framework for explaining BNNs. Within the Bayesian framework, the network weights follow a probability distribution. Hence, the standard (deterministic) prediction strategy of DNNs extends in BNNs to a predictive distribution, and thus the standard explanation extends to an explanation distribution. Exploiting this view, we uncover that BNNs implicitly employ multiple heterogeneous prediction strategies. While some of these are inherited from standard DNNs, others are revealed to us by considering the inherent uncertainty in BNNs. Our quantitative and qualitative experiments on toy/benchmark data and real-world data from pathology show that the proposed approach of explaining BNNs can lead to more effective and insightful explanations.
Traditional deep neural networks (NNs) have significantly contributed to the state-of-the-art performance in the task of classification under various application domains. However, NNs have not considered inherent uncertainty in data associated with the class probabilities where misclassification under uncertainty may easily introduce high risk in decision making in real-world contexts (e.g., misclassification of objects in roads leads to serious accidents). Unlike Bayesian NN that indirectly infer uncertainty through weight uncertainties, evidential NNs (ENNs) have been recently proposed to explicitly model the uncertainty of class probabilities and use them for classification tasks. An ENN offers the formulation of the predictions of NNs as subjective opinions and learns the function by collecting an amount of evidence that can form the subjective opinions by a deterministic NN from data. However, the ENN is trained as a black box without explicitly considering inherent uncertainty in data with their different root causes, such as vacuity (i.e., uncertainty due to a lack of evidence) or dissonance (i.e., uncertainty due to conflicting evidence). By considering the multidimensional uncertainty, we proposed a novel uncertainty-aware evidential NN called WGAN-ENN (WENN) for solving an out-of-distribution (OOD) detection problem. We took a hybrid approach that combines Wasserstein Generative Adversarial Network (WGAN) with ENNs to jointly train a model with prior knowledge of a certain class, which has high vacuity for OOD samples. Via extensive empirical experiments based on both synthetic and real-world datasets, we demonstrated that the estimation of uncertainty by WENN can significantly help distinguish OOD samples from boundary samples. WENN outperformed in OOD detection when compared with other competitive counterparts.
While the advent of Graph Neural Networks (GNNs) has greatly improved node and graph representation learning in many applications, the neighborhood aggregation scheme exposes additional vulnerabilities to adversaries seeking to extract node-level information about sensitive attributes. In this paper, we study the problem of protecting sensitive attributes by information obfuscation when learning with graph structured data. We propose a framework to locally filter out pre-determined sensitive attributes via adversarial training with the total variation and the Wasserstein distance. Our method creates a strong defense against inference attacks, while only suffering small loss in task performance. Theoretically, we analyze the effectiveness of our framework against a worst-case adversary, and characterize an inherent trade-off between maximizing predictive accuracy and minimizing information leakage. Experiments across multiple datasets from recommender systems, knowledge graphs and quantum chemistry demonstrate that the proposed approach provides a robust defense across various graph structures and tasks, while producing competitive GNN encoders for downstream tasks.
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