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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…

Machine Learning · Computer Science 2024-09-16 Huilin Zhou , Hao Zhang , Huiqi Deng , Dongrui Liu , Wen Shen , Shih-Han Chan , Quanshi Zhang

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…

Machine Learning · Computer Science 2024-09-16 Xu Cheng , Lei Cheng , Zhaoran Peng , Yang Xu , Tian Han , 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…

Machine Learning · Computer Science 2024-09-16 Mingjie Li , Quanshi Zhang

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…

Machine Learning · Computer Science 2025-02-17 Lei Cheng , Junpeng Zhang , Qihan Ren , Quanshi Zhang

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…

Machine Learning · Computer Science 2025-05-21 Yuxuan He , Junpeng Zhang , Lei Cheng , Hongyuan Zhang , Quanshi Zhang

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)…

Machine Learning · Computer Science 2024-09-16 Qihan Ren , Jiayang Gao , Wen Shen , Quanshi Zhang

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…

Machine Learning · Computer Science 2022-11-08 Huiqi Deng , Qihan Ren , Hao Zhang , Quanshi Zhang

Deep neural networks (DNNs) with high expressiveness have achieved state-of-the-art performance in many tasks. However, their distributed feature representations are difficult to interpret semantically. In this work, human-interpretable…

Computer Vision and Pattern Recognition · Computer Science 2019-10-22 Jindong Gu , Volker Tresp

Understanding what kinds of cooperative structures deep neural networks (DNNs) can represent remains a fundamental yet insufficiently understood problem. In this work, we treat interactions as the fundamental units of such structure and…

Machine Learning · Computer Science 2025-12-23 Huiqi Deng , Qihan Ren , Zhuofan Chen , Zhenyuan Cui , Wen Shen , Peng Zhang , Hongbin Pei , Quanshi Zhang

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…

Machine Learning · Computer Science 2025-02-13 Junpeng Zhang , Lei Cheng , Qing Li , Liang Lin , Quanshi Zhang

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…

Machine Learning · Computer Science 2021-02-04 Hao Zhang , Yichen Xie , Longjie Zheng , Die Zhang , Quanshi Zhang

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…

Machine Learning · Computer Science 2024-11-26 Qihan Ren , Junpeng Zhang , Yang Xu , Yue Xin , Dongrui Liu , 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,…

Machine Learning · Computer Science 2024-08-02 Mingjie Li , Quanshi Zhang

A robust theoretical framework that can describe and predict the generalization ability of deep neural networks (DNNs) in general circumstances remains elusive. Classical attempts have produced complexity metrics that rely heavily on global…

Machine Learning · Computer Science 2020-01-20 Marelie H. Davel , Marthinus W. Theunissen , Arnold M. Pretorius , Etienne Barnard

Interpretability of deep neural networks (DNNs) is essential since it enables users to understand the overall strengths and weaknesses of the models, conveys an understanding of how the models will behave in the future, and how to diagnose…

Computer Vision and Pattern Recognition · Computer Science 2017-03-31 Yinpeng Dong , Hang Su , Jun Zhu , Bo Zhang

Deep neural networks (DNNs) have demonstrated impressive performance on a wide array of tasks, but they are usually considered opaque since internal structure and learned parameters are not interpretable. In this paper, we re-examine the…

Computer Vision and Pattern Recognition · Computer Science 2017-08-21 Yinpeng Dong , Hang Su , Jun Zhu , Fan Bao

Deep Neural Networks (DNNs) achieve state-of-the-art performance on numerous applications. However, it is difficult to tell beforehand if a DNN receiving an input will deliver the correct output since their decision criteria are usually…

Machine Learning · Computer Science 2021-09-07 Julia Lust , Alexandru Paul Condurache

Knowledge is a formal way of understanding the world, providing a human-level cognition and intelligence for the next-generation artificial intelligence (AI). One of the representations of knowledge is semantic relations between entities.…

Computation and Language · Computer Science 2021-02-09 Hailin Wang , Ke Qin , Rufai Yusuf Zakari , Guoming Lu , Jin Yin

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Machine Learning · Computer Science 2021-06-22 Nathan Dahlin , Krishna Chaitanya Kalagarla , Nikhil Naik , Rahul Jain , Pierluigi Nuzzo

It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with…

Information Theory · Computer Science 2019-05-17 Shao-Lun Huang , Xiangxiang Xu , Lizhong Zheng , Gregory W. Wornell
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