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The gradient of a deep neural network (DNN) w.r.t. the input provides information that can be used to explain the output prediction in terms of the input features and has been widely studied to assist in interpreting DNNs. In a linear model (i.e., g(x) = wx + b), the gradient corresponds to the weights w. Such a model can reasonably locally-linearly approximate a smooth nonlinear DNN, and hence the weights of this local model are the gradient. The bias b, however, is usually overlooked in attribution methods. In this paper, we observe that since the bias in a DNN also has a non-negligible contribution to the correctness of predictions, it can also play a significant role in understanding DNN behavior. We propose a backpropagation-type algorithm “bias back-propagation (BBp)” that starts at the output layer and iteratively attributes the bias of each layer to its input nodes as well as combining the resulting bias term of the previous layer. Together with the backpropagation of the gradient generating w, we can fully recover the locally linear model g(x) = wx + b. In experiments, we show that BBp can generate complementary and highly interpretable explanations.
Author Information
Shengjie Wang ("University of Washington, Seattle")
Tianyi Zhou (University of Washington)

Tianyi Zhou is a tenure-track assistant professor of Computer Science and UMIACS at the University of Maryland, College Park. He received his Ph.D. from the University of Washington, Seattle. His research interests are machine learning, optimization, and natural language processing. His recent works focus on curriculum learning, hybrid human-artificial intelligence, trustworthy and robust AI, plasticity-stability trade-off in ML, large language and multi-modality models, reinforcement learning, federated learning, and meta-learning. He has published ~90 papers at NeurIPS, ICML, ICLR, AISTATS, ACL, EMNLP, NAACL, COLING, CVPR, KDD, ICDM, AAAI, IJCAI, ISIT, Machine Learning (Springer), IEEE TIP/TNNLS/TKDE, etc. He is the recipient of the Best Student Paper Award at ICDM 2013 and the 2020 IEEE TCSC Most Influential Paper Award. He served as an SPC member or area chair in AAAI, IJCAI, KDD, WACV, etc. Tianyi was a visiting research scientist at Google and a research intern at Microsoft Research Redmond and Yahoo! Labs.
Jeff Bilmes (UW)
Related Events (a corresponding poster, oral, or spotlight)
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2019 Oral: Bias Also Matters: Bias Attribution for Deep Neural Network Explanation »
Thu. Jun 13th 12:00 -- 12:05 AM Room Seaside Ballroom
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