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 solely 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 other part, however, of a local linear model, i.e., the bias $b$, is usually overlooked in attribution methods since it is not part of the gradient. In this paper, we observe that since the bias in a DNN also has a nonnegligible contribution to the correctness of predictions, it can also play a significant role in understanding DNN behaviors. In particular, we study how to attribute a DNN's bias to its input features. We propose a backpropagationtype algorithm ``bias backpropagation (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. This process stops at the input layer, where summing up the attributions over all the input features exactly recovers $b$. Together with the backpropagation of the gradient generating $w$, we can fully recover the locally linear model $g(x)=wx+b$. Hence, the attribution of the DNN outputs to its inputs is decomposed into two parts, the gradient $w$ and the bias attribution, providing separate and complementary explanations. We study several possible attribution methods applied to the bias of each layer in BBp. In experiments, we show that BBp can generate complementary and highly interpretable explanations of DNNs in addition to gradientbased attributions.
Author Information
Shengjie Wang ("University of Washington, Seattle")
Tianyi Zhou (University of Washington)
Jeff Bilmes (UW)
Related Events (a corresponding poster, oral, or spotlight)

2019 Poster: Bias Also Matters: Bias Attribution for Deep Neural Network Explanation »
Wed Jun 12th 06:30  09:00 PM Room Pacific Ballroom
More from the Same Authors

2019 Poster: Jumpout : Improved Dropout for Deep Neural Networks with ReLUs »
Shengjie Wang · Tianyi Zhou · Jeff Bilmes 
2019 Poster: Combating Label Noise in Deep Learning using Abstention »
Sunil Thulasidasan · Tanmoy Bhattacharya · Jeff Bilmes · Gopinath Chennupati · Jamal MohdYusof 
2019 Oral: Jumpout : Improved Dropout for Deep Neural Networks with ReLUs »
Shengjie Wang · Tianyi Zhou · Jeff Bilmes 
2019 Oral: Combating Label Noise in Deep Learning using Abstention »
Sunil Thulasidasan · Tanmoy Bhattacharya · Jeff Bilmes · Gopinath Chennupati · Jamal MohdYusof 
2018 Poster: Constrained Interacting Submodular Groupings »
Andrew Cotter · Mahdi Milani Fard · Seungil You · Maya Gupta · Jeff Bilmes 
2018 Poster: Greed is Still Good: Maximizing Monotone Submodular+Supermodular (BP) Functions »
Wenruo Bai · Jeff Bilmes 
2018 Oral: Constrained Interacting Submodular Groupings »
Andrew Cotter · Mahdi Milani Fard · Seungil You · Maya Gupta · Jeff Bilmes 
2018 Oral: Greed is Still Good: Maximizing Monotone Submodular+Supermodular (BP) Functions »
Wenruo Bai · Jeff Bilmes