Redesigning deep neural networks: Bridging game theory and statistical physics

We propose an innovative deep-graphical representation that combines game theory principles with statistical physics to enable unified feature extraction and pattern classification. In this framework, network neurons act as (i) players in a game-theory model, and (ii) evolve as particles governed by laws of statistical physics. These neurons adopt a set of actions that correspond to their activation values. The neural network layers are treated as sequential cooperative games, where the feed-forward process in deep learning is interpreted as a series of games that involve multiple players. During training, neurons are iteratively assessed and filtered on the basis of their contributions to a payoff function, quantified through the Shapley value derived from an energy function. Neurons with significant contributions form strong coalitions and are exclusively permitted to transmit information to subsequent layers. The Shapley value acts as a model regularization tool, improving overall performance. Additionally, explainability is enhanced through the concept of pathways, leveraging the Banzhaf Power Index. We validated this hybrid model by applying it to facial age estimation and gender classification tasks, demonstrating its superiority over traditional multilayer perceptron and convolutional neural network models in both efficiency and accuracy.