Naotake Natori

Keiichi Tamai, Tsuyoshi Okubo, Truong Vinh Truong Duy et al.

We demonstrate that conventional artificial deep neural networks operating near the phase boundary of the signal propagation dynamics, also known as the edge of chaos, exhibit universal scaling laws of absorbing phase transitions in non-equilibrium statistical mechanics. We exploit the fully deterministic nature of the propagation dynamics to elucidate an analogy between a signal collapse in the neural networks and an absorbing state (a state that the system can enter but cannot escape from). Our numerical results indicate that the multilayer perceptrons and the convolutional neural networks belong to the mean-field and the directed percolation universality classes, respectively. Also, the finite-size scaling is successfully applied, suggesting a potential connection to the depth-width trade-off in deep learning. Furthermore, our analysis of the training dynamics under the gradient descent reveals that hyperparameter tuning to the phase boundary is necessary but insufficient for achieving optimal generalization in deep networks. Remarkably, nonuniversal metric factors associated with the scaling laws are shown to play a significant role in concretizing the above observations. These findings highlight the usefulness of the notion of criticality for analyzing the behavior of artificial deep neural networks and offer new insights toward a unified understanding of the essential relationship between criticality and intelligence.

Shin-ichi Ikegawa, Ryuji Saiin, Yoshihide Sawada et al.

Biologically inspired spiking neural networks (SNNs) are widely used to realize ultralow-power energy consumption. However, deep SNNs are not easy to train due to the excessive firing of spiking neurons in the hidden layers. To tackle this problem, we propose a novel but simple normalization technique called postsynaptic potential normalization. This normalization removes the subtraction term from the standard normalization and uses the second raw moment instead of the variance as the division term. The spike firing can be controlled, enabling the training to proceed appropriating, by conducting this simple normalization to the postsynaptic potential. The experimental results show that SNNs with our normalization outperformed other models using other normalizations. Furthermore, through the pre-activation residual blocks, the proposed model can train with more than 100 layers without other special techniques dedicated to SNNs.