Quanshi Zhang

Jiexing Qi, Jingyao Tang, Ziwei He et al. · meta-ai, mila

Relational structures such as schema linking and schema encoding have been validated as a key component to qualitatively translating natural language into SQL queries. However, introducing these structural relations comes with prices: they often result in a specialized model structure, which largely prohibits using large pretrained models in text-to-SQL. To address this problem, we propose RASAT: a Transformer seq2seq architecture augmented with relation-aware self-attention that could leverage a variety of relational structures while inheriting the pretrained parameters from the T5 model effectively. Our model can incorporate almost all types of existing relations in the literature, and in addition, we propose introducing co-reference relations for the multi-turn scenario. Experimental results on three widely used text-to-SQL datasets, covering both single-turn and multi-turn scenarios, have shown that RASAT could achieve state-of-the-art results across all three benchmarks (75.5% EX on Spider, 52.6% IEX on SParC, and 37.4% IEX on CoSQL).

Sha Yuan, Hanyu Zhao, Shuai Zhao et al. · bytedance, pku

With the rapid development of deep learning, training Big Models (BMs) for multiple downstream tasks becomes a popular paradigm. Researchers have achieved various outcomes in the construction of BMs and the BM application in many fields. At present, there is a lack of research work that sorts out the overall progress of BMs and guides the follow-up research. In this paper, we cover not only the BM technologies themselves but also the prerequisites for BM training and applications with BMs, dividing the BM review into four parts: Resource, Models, Key Technologies and Application. We introduce 16 specific BM-related topics in those four parts, they are Data, Knowledge, Computing System, Parallel Training System, Language Model, Vision Model, Multi-modal Model, Theory&Interpretability, Commonsense Reasoning, Reliability&Security, Governance, Evaluation, Machine Translation, Text Generation, Dialogue and Protein Research. In each topic, we summarize clearly the current studies and propose some future research directions. At the end of this paper, we conclude the further development of BMs in a more general view.

Qihan Ren, Huiqi Deng, Yunuo Chen et al.

In this paper, we focus on mean-field variational Bayesian Neural Networks (BNNs) and explore the representation capacity of such BNNs by investigating which types of concepts are less likely to be encoded by the BNN. It has been observed and studied that a relatively small set of interactive concepts usually emerge in the knowledge representation of a sufficiently-trained neural network, and such concepts can faithfully explain the network output. Based on this, our study proves that compared to standard deep neural networks (DNNs), it is less likely for BNNs to encode complex concepts. Experiments verify our theoretical proofs. Note that the tendency to encode less complex concepts does not necessarily imply weak representation power, considering that complex concepts exhibit low generalization power and high adversarial vulnerability. The code is available at https://github.com/sjtu-xai-lab/BNN-concepts.

Jie Ren, Mingjie Li, Meng Zhou et al. · cmu

This paper aims to theoretically analyze the complexity of feature transformations encoded in piecewise linear DNNs with ReLU layers. We propose metrics to measure three types of complexities of transformations based on the information theory. We further discover and prove the strong correlation between the complexity and the disentanglement of transformations. Based on the proposed metrics, we analyze two typical phenomena of the change of the transformation complexity during the training process, and explore the ceiling of a DNN's complexity. The proposed metrics can also be used as a loss to learn a DNN with the minimum complexity, which also controls the over-fitting level of the DNN and influences adversarial robustness, adversarial transferability, and knowledge consistency. Comprehensive comparative studies have provided new perspectives to understand the DNN.

Quanshi Zhang, Xu Cheng, Yilan Chen et al.

Compared to traditional learning from scratch, knowledge distillation sometimes makes the DNN achieve superior performance. This paper provides a new perspective to explain the success of knowledge distillation, i.e., quantifying knowledge points encoded in intermediate layers of a DNN for classification, based on the information theory. To this end, we consider the signal processing in a DNN as the layer-wise information discarding. A knowledge point is referred to as an input unit, whose information is much less discarded than other input units. Thus, we propose three hypotheses for knowledge distillation based on the quantification of knowledge points. 1. The DNN learning from knowledge distillation encodes more knowledge points than the DNN learning from scratch. 2. Knowledge distillation makes the DNN more likely to learn different knowledge points simultaneously. In comparison, the DNN learning from scratch tends to encode various knowledge points sequentially. 3. The DNN learning from knowledge distillation is often optimized more stably than the DNN learning from scratch. In order to verify the above hypotheses, we design three types of metrics with annotations of foreground objects to analyze feature representations of the DNN, \textit{i.e.} the quantity and the quality of knowledge points, the learning speed of different knowledge points, and the stability of optimization directions. In experiments, we diagnosed various DNNs for different classification tasks, i.e., image classification, 3D point cloud classification, binary sentiment classification, and question answering, which verified above hypotheses.

Mingjie Li, Quanshi Zhang

Recently, a series of studies have tried to extract interactions between input variables modeled by a DNN and define such interactions as concepts encoded by the DNN. However, strictly speaking, there still lacks a solid guarantee whether such interactions indeed represent meaningful concepts. Therefore, in this paper, we examine the trustworthiness of interaction concepts from four perspectives. Extensive empirical studies have verified that a well-trained DNN usually encodes sparse, transferable, and discriminative concepts, which is partially aligned with human intuition.

Huilin Zhou, Hao Zhang, Huiqi Deng et al.

This paper explains the generalization power of a deep neural network (DNN) from the perspective of interactions. Although there is no universally accepted definition of the concepts encoded by a DNN, the sparsity of interactions in a DNN has been proved, i.e., the output score of a DNN can be well explained by a small number of interactions between input variables. In this way, to some extent, we can consider such interactions as interactive concepts encoded by the DNN. Therefore, in this paper, we derive an analytic explanation of inconsistency of concepts of different complexities. This may shed new lights on using the generalization power of concepts to explain the generalization power of the entire DNN. Besides, we discover that the DNN with stronger generalization power usually learns simple concepts more quickly and encodes fewer complex concepts. We also discover the detouring dynamics of learning complex concepts, which explains both the high learning difficulty and the low generalization power of complex concepts. The code will be released when the paper is accepted.

Huiqi Deng, Na Zou, Mengnan Du et al.

Various attribution methods have been developed to explain deep neural networks (DNNs) by inferring the attribution/importance/contribution score of each input variable to the final output. However, existing attribution methods are often built upon different heuristics. There remains a lack of a unified theoretical understanding of why these methods are effective and how they are related. To this end, for the first time, we formulate core mechanisms of fourteen attribution methods, which were designed on different heuristics, into the same mathematical system, i.e., the system of Taylor interactions. Specifically, we prove that attribution scores estimated by fourteen attribution methods can all be reformulated as the weighted sum of two types of effects, i.e., independent effects of each individual input variable and interaction effects between input variables. The essential difference among the fourteen attribution methods mainly lies in the weights of allocating different effects. Based on the above findings, we propose three principles for a fair allocation of effects to evaluate the faithfulness of the fourteen attribution methods.

Ling Tang, Wen Shen, Zhanpeng Zhou et al.

In this paper, we prove the representation defects of a cascaded convolutional decoder network, considering the capacity of representing different frequency components of an input sample. We conduct the discrete Fourier transform on each channel of the feature map in an intermediate layer of the decoder network. Then, we extend the 2D circular convolution theorem to represent the forward and backward propagations through convolutional layers in the frequency domain. Based on this, we prove three defects in representing feature spectrums. First, we prove that the convolution operation, the zero-padding operation, and a set of other settings all make a convolutional decoder network more likely to weaken high-frequency components. Second, we prove that the upsampling operation generates a feature spectrum, in which strong signals repetitively appear at certain frequencies. Third, we prove that if the frequency components in the input sample and frequency components in the target output for regression have a small shift, then the decoder usually cannot be effectively learned.

Lu Chen, Siyu Lou, Keyan Zhang et al.

The Shapley value is widely regarded as a trustworthy attribution metric. However, when people use Shapley values to explain the attribution of input variables of a deep neural network (DNN), it usually requires a very high computational cost to approximate relatively accurate Shapley values in real-world applications. Therefore, we propose a novel network architecture, the HarsanyiNet, which makes inferences on the input sample and simultaneously computes the exact Shapley values of the input variables in a single forward propagation. The HarsanyiNet is designed on the theoretical foundation that the Shapley value can be reformulated as the redistribution of Harsanyi interactions encoded by the network.

Quanshi Zhang, Xin Wang, Jie Ren et al.

Although many methods have been proposed to enhance the transferability of adversarial perturbations, these methods are designed in a heuristic manner, and the essential mechanism for improving adversarial transferability is still unclear. This paper summarizes the common mechanism shared by twelve previous transferability-boosting methods in a unified view, i.e., these methods all reduce game-theoretic interactions between regional adversarial perturbations. To this end, we focus on the attacking utility of all interactions between regional adversarial perturbations, and we first discover and prove the negative correlation between the adversarial transferability and the attacking utility of interactions. Based on this discovery, we theoretically prove and empirically verify that twelve previous transferability-boosting methods all reduce interactions between regional adversarial perturbations. More crucially, we consider the reduction of interactions as the essential reason for the enhancement of adversarial transferability. Furthermore, we design the interaction loss to directly penalize interactions between regional adversarial perturbations during attacking. Experimental results show that the interaction loss significantly improves the transferability of adversarial perturbations.

Mingjie Li, Quanshi Zhang

In this technical note, we aim to explain a deep neural network (DNN) by quantifying the encoded interactions between input variables, which reflects the DNN's inference logic. Specifically, we first rethink the definition of interactions, and then formally define faithfulness and conciseness for interaction-based explanation. To this end, we propose two kinds of interactions, i.e., the AND interaction and the OR interaction. For faithfulness, we prove the uniqueness of the AND (OR) interaction in quantifying the effect of the AND (OR) relationship between input variables. Besides, based on AND-OR interactions, we design techniques to boost the conciseness of the explanation, while not hurting the faithfulness. In this way, the inference logic of a DNN can be faithfully and concisely explained by a set of symbolic concepts.

Wen Shen, Lei Cheng, Yuxiao Yang et al.

In this paper, we explain the inference logic of large language models (LLMs) as a set of symbolic concepts. Many recent studies have discovered that traditional DNNs usually encode sparse symbolic concepts. However, because an LLM has much more parameters than traditional DNNs, whether the LLM also encodes sparse symbolic concepts is still an open problem. Therefore, in this paper, we propose to disentangle the inference score of LLMs for dialogue tasks into a small number of symbolic concepts. We verify that we can use those sparse concepts to well estimate all inference scores of the LLM on all arbitrarily masking states of the input sentence. We also evaluate the transferability of concepts encoded by an LLM and verify that symbolic concepts usually exhibit high transferability across similar input sentences. More crucially, those symbolic concepts can be used to explain the exact reasons accountable for the LLM's prediction errors.

Huilin Zhou, Huijie Tang, Mingjie Li et al.

The AI model has surpassed human players in the game of Go, and it is widely believed that the AI model has encoded new knowledge about the Go game beyond human players. In this way, explaining the knowledge encoded by the AI model and using it to teach human players represent a promising-yet-challenging issue in explainable AI. To this end, mathematical supports are required to ensure that human players can learn accurate and verifiable knowledge, rather than specious intuitive analysis. Thus, in this paper, we extract interaction primitives between stones encoded by the value network for the Go game, so as to enable people to learn from the value network. Experiments show the effectiveness of our method.

Xu Cheng, Hao Zhang, Yue Xin et al.

This paper mathematically derives an analytic solution of the adversarial perturbation on a ReLU network, and theoretically explains the difficulty of adversarial training. Specifically, we formulate the dynamics of the adversarial perturbation generated by the multi-step attack, which shows that the adversarial perturbation tends to strengthen eigenvectors corresponding to a few top-ranked eigenvalues of the Hessian matrix of the loss w.r.t. the input. We also prove that adversarial training tends to strengthen the influence of unconfident input samples with large gradient norms in an exponential manner. Besides, we find that adversarial training strengthens the influence of the Hessian matrix of the loss w.r.t. network parameters, which makes the adversarial training more likely to oscillate along directions of a few samples, and boosts the difficulty of adversarial training. Crucially, our proofs provide a unified explanation for previous findings in understanding adversarial training.

Zhanpeng Zhou, Wen Shen, Huixin Chen et al.

In this paper, we prove the effects of the BN operation on the back-propagation of the first and second derivatives of the loss. When we do the Taylor series expansion of the loss function, we prove that the BN operation will block the influence of the first-order term and most influence of the second-order term of the loss. We also find that such a problem is caused by the standardization phase of the BN operation. Experimental results have verified our theoretical conclusions, and we have found that the BN operation significantly affects feature representations in specific tasks, where losses of different samples share similar analytic formulas.

Ling Tang, Jilin Mei, Qian Chen et al.

Large language models (LLMs) can simulate human-like reasoning and decision-making in individual agents. LLM-powered multi-agent systems (MAS) combine such agents to simulate population-scale social phenomena such as polarization, information cascades, and market panics. Such studies require attributing macro emergence to individual agents, but existing axiomatic methods scale combinatorially in $N$ and have been confined to $N \lesssim 10^3$, while the phenomena they explain occur at $N \geq 10^6$. We address this gap by adapting Aumann--Shapley path-integral attribution to LLM-powered MAS at million-agent scale; the resulting method satisfies all four axioms, runs four to five orders of magnitude faster than sampled Shapley on the same hardware. We use this method to test the scale gap empirically: across 14 days of public Bluesky data ($1{,}671{,}587$ active users), we compute the attribution at both full scale and the visibility-biased $N = 10^2$ convenience sample used by small-scale studies, and the two disagree structurally. At full scale the long tail and middle tier jointly carry the majority; the biased small panel attributes almost everything to a few high-follower accounts. We then prove that under any nonlinear macro indicator the disagreement cannot be reduced by post-hoc rescaling: an Attribution Scaling Bias theorem shows that no global rescaling factor can reconcile small-scale and full-scale attribution. Full-scale attribution is therefore not a methodological choice but a theoretical requirement for any nonlinear macro indicator.

Ling Tang, Qian Chen, Jilin Mei et al.

Clinical electroencephalogram (EEG) analysis rests on a hand-crafted feature catalog refined over decades, \emph{e.g.,} band power, connectivity, complexity, and more. Modern EEG foundation models bypass this catalog, learn directly from raw signals via self-supervised pretraining, and match or outperform feature-engineered baselines on most clinical benchmarks. Whether the two representations align is an open question, which we decompose into three sub-questions: \emph{what does the model learn}, \emph{what does the model use}, and \emph{how much can be explained}. We answer them with layer-wise ridge probing, LEACE-style cross-covariance subspace erasure, and a transparent classifier benchmarked against a random-feature baseline. The audit covers three foundation models (CSBrain, CBraMod, LaBraM), five clinical tasks (MDD, Stress, ISRUC-Sleep, TUSL, Siena), and a 6-family 63-feature lexicon. Of the $945$ (model, task, feature) units, $648$ ($68.6\%$) are representation-causal and $199$ ($21.1\%$) are encoded-only. Across tasks, $50$ features qualify as universal candidates with strong support (all three architectures RC) in two or more tasks. Frequency-domain features dominate, but the other five families each contribute substantial causal mass. Confirmed features recover, on average, $79.3\%$ of the foundation model's advantage over the random baseline, with a clean task gradient (MDD $\approx 0.99$ down to Stress $\approx 0.56$): tasks near ceiling are almost fully recovered by the lexicon, while harder tasks leave a non-trivial residual that pinpoints a concrete target for future concept discovery.

Xinhao Zheng, Huiqi Deng, Quanshi Zhang

This paper focuses on the fundamental challenge of partitioning input variables in attribution methods for Explainable AI, particularly in Shapley value-based approaches. Previous methods always compute attributions given a predefined partition but lack theoretical guidance on how to form meaningful variable partitions. We identify that attribution conflicts arise when the attribution of a coalition differs from the sum of its individual variables' attributions. To address this, we analyze the numerical effects of AND-OR interactions in AI models and extend the Shapley value to a new attribution metric for variable coalitions. Our theoretical findings reveal that specific interactions cause attribution conflicts, and we propose three metrics to evaluate coalition faithfulness. Experiments on synthetic data, NLP, image classification, and the game of Go validate our approach, demonstrating consistency with human intuition and practical applicability.

Qihan Ren, Junpeng Zhang, Yang Xu et al.

This study proves the two-phase dynamics of a deep neural network (DNN) learning interactions. Despite the long disappointing view of the faithfulness of post-hoc explanation of a DNN, a series of theorems have been proven in recent years to show that for a given input sample, a small set of interactions between input variables can be considered as primitive inference patterns that faithfully represent a DNN's detailed inference logic on that sample. Particularly, Zhang et al. have observed that various DNNs all learn interactions of different complexities in two distinct phases, and this two-phase dynamics well explains how a DNN changes from under-fitting to over-fitting. Therefore, in this study, we mathematically prove the two-phase dynamics of interactions, providing a theoretical mechanism for how the generalization power of a DNN changes during the training process. Experiments show that our theory well predicts the real dynamics of interactions on different DNNs trained for various tasks.

Xu Cheng, Lei Cheng, Zhaoran Peng et al.

This paper aims to explain how a deep neural network (DNN) gradually extracts new knowledge and forgets noisy features through layers in forward propagation. Up to now, although the definition of knowledge encoded by the DNN has not reached a consensus, Previous studies have derived a series of mathematical evidence to take interactions as symbolic primitive inference patterns encoded by a DNN. We extend the definition of interactions and, for the first time, extract interactions encoded by intermediate layers. We quantify and track the newly emerged interactions and the forgotten interactions in each layer during the forward propagation, which shed new light on the learning behavior of DNNs. The layer-wise change of interactions also reveals the change of the generalization capacity and instability of feature representations of a DNN.

Lu Chen, Siyu Lou, Benhao Huang et al. · cmu

Faithfully summarizing the knowledge encoded by a deep neural network (DNN) into a few symbolic primitive patterns without losing much information represents a core challenge in explainable AI. To this end, Ren et al. (2024) have derived a series of theorems to prove that the inference score of a DNN can be explained as a small set of interactions between input variables. However, the lack of generalization power makes it still hard to consider such interactions as faithful primitive patterns encoded by the DNN. Therefore, given different DNNs trained for the same task, we develop a new method to extract interactions that are shared by these DNNs. Experiments show that the extracted interactions can better reflect common knowledge shared by different DNNs.

Junpeng Zhang, Qing Li, Liang Lin et al.

This paper investigates the dynamics of a deep neural network (DNN) learning interactions. Previous studies have discovered and mathematically proven that given each input sample, a well-trained DNN usually only encodes a small number of interactions (non-linear relationships) between input variables in the sample. A series of theorems have been derived to prove that we can consider the DNN's inference equivalent to using these interactions as primitive patterns for inference. In this paper, we discover the DNN learns interactions in two phases. The first phase mainly penalizes interactions of medium and high orders, and the second phase mainly learns interactions of gradually increasing orders. We can consider the two-phase phenomenon as the starting point of a DNN learning over-fitted features. Such a phenomenon has been widely shared by DNNs with various architectures trained for different tasks. Therefore, the discovery of the two-phase dynamics provides a detailed mechanism for how a DNN gradually learns different inference patterns (interactions). In particular, we have also verified the claim that high-order interactions have weaker generalization power than low-order interactions. Thus, the discovered two-phase dynamics also explains how the generalization power of a DNN changes during the training process.

Siyu Lou, Yuntian Chen, Xiaodan Liang et al.

In this study, we propose an axiomatic system to define and quantify the precise memorization and in-context reasoning effects used by the large language model (LLM) for language generation. These effects are formulated as non-linear interactions between tokens/words encoded by the LLM. Specifically, the axiomatic system enables us to categorize the memorization effects into foundational memorization effects and chaotic memorization effects, and further classify in-context reasoning effects into enhanced inference patterns, eliminated inference patterns, and reversed inference patterns. Besides, the decomposed effects satisfy the sparsity property and the universal matching property, which mathematically guarantee that the LLM's confidence score can be faithfully decomposed into the memorization effects and in-context reasoning effects. Experiments show that the clear disentanglement of memorization effects and in-context reasoning effects enables a straightforward examination of detailed inference patterns encoded by LLMs.

Huiqi Deng, Hongbin Pei, Quanshi Zhang et al.

Attribution explanation is a typical approach for explaining deep neural networks (DNNs), inferring an importance or contribution score for each input variable to the final output. In recent years, numerous attribution methods have been developed to explain DNNs. However, a persistent concern remains unresolved, i.e., whether and which attribution methods faithfully reflect the actual contribution of input variables to the decision-making process. The faithfulness issue undermines the reliability and practical utility of attribution explanations. We argue that these concerns stem from three core challenges. First, difficulties arise in comparing attribution methods due to their unstructured heterogeneity, differences in heuristics, formulations, and implementations that lack a unified organization. Second, most methods lack solid theoretical underpinnings, with their rationales remaining absent, ambiguous, or unverified. Third, empirically evaluating faithfulness is challenging without ground truth. Recent theoretical advances provide a promising way to tackle these challenges, attracting increasing attention. We summarize these developments, with emphasis on three key directions: (i) Theoretical unification, which uncovers commonalities and differences among methods, enabling systematic comparisons; (ii) Theoretical rationale, clarifying the foundations of existing methods; (iii) Theoretical evaluation, rigorously proving whether methods satisfy faithfulness principles. Beyond a comprehensive review, we provide insights into how these studies help deepen theoretical understanding, inform method selection, and inspire new attribution methods. We conclude with a discussion of promising open problems for further work.

Ling Tang, Yuefeng Chen, Hui Xue et al.

This paper proves a new watermarking method to embed the ownership information into a deep neural network (DNN), which is robust to fine-tuning. Specifically, we prove that when the input feature of a convolutional layer only contains low-frequency components, specific frequency components of the convolutional filter will not be changed by gradient descent during the fine-tuning process, where we propose a revised Fourier transform to extract frequency components from the convolutional filter. Additionally, we also prove that these frequency components are equivariant to weight scaling and weight permutations. In this way, we design a watermark module to encode the watermark information to specific frequency components in a convolutional filter. Preliminary experiments demonstrate the effectiveness of our method.

Shuai Fu, Jian Zhou, Qi Chen et al.

Diffusion probabilistic models (DPMs) have demonstrated remarkable progress in generative tasks, such as image and video synthesis. However, they still often produce hallucinated samples (hallucinations) that conflict with real-world knowledge, such as generating an implausible duplicate cup floating beside another cup. Despite their prevalence, the lack of feasible methodologies for systematically quantifying such hallucinations hinders progress in addressing this challenge and obscures potential pathways for designing next-generation generative models under factual constraints. In this work, we bridge this gap by focusing on a specific form of hallucination, which we term counting hallucination, referring to the generation of an incorrect number of instances or structured objects, such as a hand image with six fingers, despite such patterns being absent from the training data. To this end, we construct a dataset suite CountHalluSet, with well-defined counting criteria, comprising ToyShape, SimObject, and RealHand. Using these datasets, we develop a standardized evaluation protocol for quantifying counting hallucinations, and systematically examine how different sampling conditions in DPMs, including solver type, ODE solver order, sampling steps, and initial noise, affect counting hallucination levels. Furthermore, we analyze their correlation with common evaluation metrics such as FID, revealing that this widely used image quality metric fails to capture counting hallucinations consistently. This work aims to take the first step toward systematically quantifying hallucinations in diffusion models and offer new insights into the investigation of hallucination phenomena in image generation.

Yuxuan He, Junpeng Zhang, Lei Cheng et al.

This paper proposes a new perspective for analyzing the generalization power of deep neural networks (DNNs), i.e., directly disentangling and analyzing the dynamics of generalizable and non-generalizable interaction encoded by a DNN through the training process. Specifically, this work builds upon the recent theoretical achievement in explainble AI, which proves that the detailed inference logic of DNNs can be can be strictly rewritten as a small number of AND-OR interaction patterns. Based on this, we propose an efficient method to quantify the generalization power of each interaction, and we discover a distinct three-phase dynamics of the generalization power of interactions during training. In particular, the early phase of training typically removes noisy and non-generalizable interactions and learns simple and generalizable ones. The second and the third phases tend to capture increasingly complex interactions that are harder to generalize. Experimental results verify that the learning of non-generalizable interactions is the the direct cause for the gap between the training and testing losses.

Lei Cheng, Junpeng Zhang, Qihan Ren et al.

This paper aims to analyze the generalization power of deep neural networks (DNNs) from the perspective of interactions. Unlike previous analysis of a DNN's generalization power in a highdimensional feature space, we find that the generalization power of a DNN can be explained as the generalization power of the interactions. We found that the generalizable interactions follow a decay-shaped distribution, while non-generalizable interactions follow a spindle-shaped distribution. Furthermore, our theory can effectively disentangle these two types of interactions from a DNN. We have verified that our theory can well match real interactions in a DNN in experiments.

Junpeng Zhang, Lei Cheng, Qing Li et al.

In this paper, we find that the complexity of interactions encoded by a deep neural network (DNN) can explain its generalization power. We also discover that the confusing samples of a DNN, which are represented by non-generalizable interactions, are determined by its low-layer parameters. In comparison, other factors, such as high-layer parameters and network architecture, have much less impact on the composition of confusing samples. Two DNNs with different low-layer parameters usually have fully different sets of confusing samples, even though they have similar performance. This finding extends the understanding of the lottery ticket hypothesis, and well explains distinctive representation power of different DNNs.

Qihan Ren, Jiayang Gao, Wen Shen et al.

This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i) The high-order derivatives of the network output with respect to the input variables are all zero. (ii) The DNN can be used on occluded samples and when the input sample is less occluded, the DNN will yield higher confidence. (iii) The confidence of the DNN does not significantly degrade on occluded samples. These conditions are quite common, and we prove that under these conditions, the DNN will only encode a relatively small number of sparse interactions between input variables. Moreover, we can consider such interactions as symbolic primitive inference patterns encoded by a DNN, because we show that inference scores of the DNN on an exponentially large number of randomly masked samples can always be well mimicked by numerical effects of just a few interactions.

Huiqi Deng, Qihan Ren, Hao Zhang et al.

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 indicates a cognition gap between DNNs and human beings, and we call it a representation bottleneck. We theoretically prove the underlying reason for the representation bottleneck. Furthermore, we propose a loss to encourage/penalize the learning of interactions of specific complexities, and analyze the representation capacities of interactions of different complexities.

Jie Ren, Mingjie Li, Qirui Chen et al.

This paper aims to illustrate the concept-emerging phenomenon in a trained DNN. Specifically, we find that the inference score of a DNN can be disentangled into the effects of a few interactive concepts. These concepts can be understood as causal patterns in a sparse, symbolic causal graph, which explains the DNN. The faithfulness of using such a causal graph to explain the DNN is theoretically guaranteed, because we prove that the causal graph can well mimic the DNN's outputs on an exponential number of different masked samples. Besides, such a causal graph can be further simplified and re-written as an And-Or graph (AOG), without losing much explanation accuracy.

Wen Shen, Qihan Ren, Dongrui Liu et al.

In this paper, we evaluate the quality of knowledge representations encoded in deep neural networks (DNNs) for 3D point cloud processing. We propose a method to disentangle the overall model vulnerability into the sensitivity to the rotation, the translation, the scale, and local 3D structures. Besides, we also propose metrics to evaluate the spatial smoothness of encoding 3D structures, and the representation complexity of the DNN. Based on such analysis, experiments expose representation problems with classic DNNs, and explain the utility of the adversarial training.

Jie Ren, Die Zhang, Yisen Wang et al.

This paper provides a unified view to explain different adversarial attacks and defense methods, \emph{i.e.} the view of multi-order interactions between input variables of DNNs. Based on the multi-order interaction, we discover that adversarial attacks mainly affect high-order interactions to fool the DNN. Furthermore, we find that the robustness of adversarially trained DNNs comes from category-specific low-order interactions. Our findings provide a potential method to unify adversarial perturbations and robustness, which can explain the existing defense methods in a principle way. Besides, our findings also make a revision of previous inaccurate understanding of the shape bias of adversarially learned features.

Mingjie Li, Shaobo Wang, Quanshi Zhang

This paper proposes a method to visualize the discrimination power of intermediate-layer visual patterns encoded by a DNN. Specifically, we visualize (1) how the DNN gradually learns regional visual patterns in each intermediate layer during the training process, and (2) the effects of the DNN using non-discriminative patterns in low layers to construct disciminative patterns in middle/high layers through the forward propagation. Based on our visualization method, we can quantify knowledge points (i.e., the number of discriminative visual patterns) learned by the DNN to evaluate the representation capacity of the DNN. Furthermore, this method also provides new insights into signal-processing behaviors of existing deep-learning techniques, such as adversarial attacks and knowledge distillation.

Yuxiang Wu, Shang Wu, Xin Wang et al.

Advanced volumetric imaging methods and genetically encoded activity indicators have permitted a comprehensive characterization of whole brain activity at single neuron resolution in \textit{Caenorhabditis elegans}. The constant motion and deformation of the nematode nervous system, however, impose a great challenge for consistent identification of densely packed neurons in a behaving animal. Here, we propose a cascade solution for long-term and rapid recognition of head ganglion neurons in a freely moving \textit{C. elegans}. First, potential neuronal regions from a stack of fluorescence images are detected by a deep learning algorithm. Second, 2-dimensional neuronal regions are fused into 3-dimensional neuron entities. Third, by exploiting the neuronal density distribution surrounding a neuron and relative positional information between neurons, a multi-class artificial neural network transforms engineered neuronal feature vectors into digital neuronal identities. With a small number of training samples, our bottom-up approach is able to process each volume - $1024 \times 1024 \times 18$ in voxels - in less than 1 second and achieves an accuracy of $91\%$ in neuronal detection and above $80\%$ in neuronal tracking over a long video recording. Our work represents a step towards rapid and fully automated algorithms for decoding whole brain activity underlying naturalistic behaviors.

Xin Wang, Shuyun Lin, Hao Zhang et al.

This paper aims to explain adversarial attacks in terms of how adversarial perturbations contribute to the attacking task. We estimate attributions of different image regions to the decrease of the attacking cost based on the Shapley value. We define and quantify interactions among adversarial perturbation pixels, and decompose the entire perturbation map into relatively independent perturbation components. The decomposition of the perturbation map shows that adversarially-trained DNNs have more perturbation components in the foreground than normally-trained DNNs. Moreover, compared to the normally-trained DNN, the adversarially-trained DNN have more components which mainly decrease the score of the true category. Above analyses provide new insights into the understanding of adversarial attacks.

Xu Cheng, Xin Wang, Haotian Xue et al.

This paper proposes a hypothesis for the aesthetic appreciation that aesthetic images make a neural network strengthen salient concepts and discard inessential concepts. In order to verify this hypothesis, we use multi-variate interactions to represent salient concepts and inessential concepts contained in images. Furthermore, we design a set of operations to revise images towards more beautiful ones. In experiments, we find that the revised images are more aesthetic than the original ones to some extent.

Quanshi Zhang, Tian Han, Lixin Fan et al.

This is the Proceedings of ICML 2021 Workshop on Theoretic Foundation, Criticism, and Application Trend of Explainable AI. Deep neural networks (DNNs) have undoubtedly brought great success to a wide range of applications in computer vision, computational linguistics, and AI. However, foundational principles underlying the DNNs' success and their resilience to adversarial attacks are still largely missing. Interpreting and theorizing the internal mechanisms of DNNs becomes a compelling yet controversial topic. This workshop pays a special interest in theoretic foundations, limitations, and new application trends in the scope of XAI. These issues reflect new bottlenecks in the future development of XAI.

Wen Shen, Zhihua Wei, Shikun Huang et al.

The reasonable definition of semantic interpretability presents the core challenge in explainable AI. This paper proposes a method to modify a traditional convolutional neural network (CNN) into an interpretable compositional CNN, in order to learn filters that encode meaningful visual patterns in intermediate convolutional layers. In a compositional CNN, each filter is supposed to consistently represent a specific compositional object part or image region with a clear meaning. The compositional CNN learns from image labels for classification without any annotations of parts or regions for supervision. Our method can be broadly applied to different types of CNNs. Experiments have demonstrated the effectiveness of our method.

Xu Cheng, Chuntung Chu, Yi Zheng et al.

In this paper, we rethink how a DNN encodes visual concepts of different complexities from a new perspective, i.e. the game-theoretic multi-order interactions between pixels in an image. Beyond the categorical taxonomy of objects and the cognitive taxonomy of textures and shapes, we provide a new taxonomy of visual concepts, which helps us interpret the encoding of shapes and textures, in terms of concept complexities. In this way, based on multi-order interactions, we find three distinctive signal-processing behaviors of DNNs encoding textures. Besides, we also discover the flexibility for a DNN to encode shapes is lower than the flexibility of encoding textures. Furthermore, we analyze how DNNs encode outlier samples, and explore the impacts of network architectures on interactions. Additionally, we clarify the crucial role of the multi-order interactions in real-world applications. The code will be released when the paper is accepted.

Jie Ren, Zhanpeng Zhou, Qirui Chen et al.

Masking some input variables of a deep neural network (DNN) and computing output changes on the masked input sample represent a typical way to compute attributions of input variables in the sample. People usually mask an input variable using its baseline value. However, there is no theory to examine whether baseline value faithfully represents the absence of an input variable, \emph{i.e.,} removing all signals from the input variable. Fortunately, recent studies show that the inference score of a DNN can be strictly disentangled into a set of causal patterns (or concepts) encoded by the DNN. Therefore, we propose to use causal patterns to examine the faithfulness of baseline values. More crucially, it is proven that causal patterns can be explained as the elementary rationale of the Shapley value. Furthermore, we propose a method to learn optimal baseline values, and experimental results have demonstrated its effectiveness.

Jie Ren, Die Zhang, Yisen Wang et al.

This paper provides a unified view to explain different adversarial attacks and defense methods, i.e. the view of multi-order interactions between input variables of DNNs. Based on the multi-order interaction, we discover that adversarial attacks mainly affect high-order interactions to fool the DNN. Furthermore, we find that the robustness of adversarially trained DNNs comes from category-specific low-order interactions. Our findings provide a potential method to unify adversarial perturbations and robustness, which can explain the existing defense methods in a principle way. Besides, our findings also make a revision of previous inaccurate understanding of the shape bias of adversarially learned features.

Hao Zhang, Xu Cheng, Yiting Chen et al.

In this study, we define interaction components of different orders between two input variables based on game theory. We further prove that interaction components of different orders satisfy several desirable properties.

Hao Zhang, Yichen Xie, Longjie Zheng et al.

This paper aims to explain deep neural networks (DNNs) from the perspective of multivariate interactions. In this paper, we define and quantify the significance of interactions among multiple input variables of the DNN. Input variables with strong interactions usually form a coalition and reflect prototype features, which are memorized and used by the DNN for inference. We define the significance of interactions based on the Shapley value, which is designed to assign the attribution value of each input variable to the inference. We have conducted experiments with various DNNs. Experimental results have demonstrated the effectiveness of the proposed method.

Xin Wang, Jie Ren, Shuyun Lin et al.

In this paper, we use the interaction inside adversarial perturbations to explain and boost the adversarial transferability. We discover and prove the negative correlation between the adversarial transferability and the interaction inside adversarial perturbations. The negative correlation is further verified through different DNNs with various inputs. Moreover, this negative correlation can be regarded as a unified perspective to understand current transferability-boosting methods. To this end, we prove that some classic methods of enhancing the transferability essentially decease interactions inside adversarial perturbations. Based on this, we propose to directly penalize interactions during the attacking process, which significantly improves the adversarial transferability.

Hao Zhang, Sen Li, Yinchao Ma et al.

This paper aims to understand and improve the utility of the dropout operation from the perspective of game-theoretic interactions. We prove that dropout can suppress the strength of interactions between input variables of deep neural networks (DNNs). The theoretic proof is also verified by various experiments. Furthermore, we find that such interactions were strongly related to the over-fitting problem in deep learning. Thus, the utility of dropout can be regarded as decreasing interactions to alleviate the significance of over-fitting. Based on this understanding, we propose an interaction loss to further improve the utility of dropout. Experimental results have shown that the interaction loss can effectively improve the utility of dropout and boost the performance of DNNs.

Shufan Wang, Ningyi Liao, Liyao Xiang et al.

Network pruning has been known to produce compact models without much accuracy degradation. However, how the pruning process affects a network's robustness and the working mechanism behind remain unresolved. In this work, we theoretically prove that the sparsity of network weights is closely associated with model robustness. Through experiments on a variety of adversarial pruning methods, we find that weights sparsity will not hurt but improve robustness, where both weights inheritance from the lottery ticket and adversarial training improve model robustness in network pruning. Based on these findings, we propose a novel adversarial training method called inverse weights inheritance, which imposes sparse weights distribution on a large network by inheriting weights from a small network, thereby improving the robustness of the large network.

Die Zhang, Huilin Zhou, Hao Zhang et al.

This paper proposes a method to disentangle and quantify interactions among words that are encoded inside a DNN for natural language processing. We construct a tree to encode salient interactions extracted by the DNN. Six metrics are proposed to analyze properties of interactions between constituents in a sentence. The interaction is defined based on Shapley values of words, which are considered as an unbiased estimation of word contributions to the network prediction. Our method is used to quantify word interactions encoded inside the BERT, ELMo, LSTM, CNN, and Transformer networks. Experimental results have provided a new perspective to understand these DNNs, and have demonstrated the effectiveness of our method.