Journal
THEORETICAL COMPUTER SCIENCE
Volume 939, Issue -, Pages 48-62Publisher
ELSEVIER
DOI: 10.1016/j.tcs.2022.09.035
Keywords
Deep neural networks; Non -atomic congestion game; Wardrop equilibria; Local minima
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From a game theoretical perspective, this paper presents a theoretical analysis of deep neural networks. It shows that deep neural networks can be transformed into non-atomic congestion games, and learning the weight and bias vectors is equivalent to computing an optimal solution for the corresponding game.
We devote this paper to a theoretic analysis of deep neural networks from a gametheoretical perspective. We consider a general deep neural network D with linear activation functions f (x) = x + b. We show that the deep neural network can be transformed into a non-atomic congestion game, regardless whether it is fully connected or locally connected. Moreover, we show that learning the weight and bias vectors of D for a training set H is equivalent to computing an optimal solution of the corresponding non-atomic congestion game. In particular, when D is a deep neural network for a classification task, then the learning is equivalent to computing a Wardrop equilibrium of the corresponding non-atomic congestion game. (c) 2022 Elsevier B.V. All rights reserved.
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