Absorbing Phase Transitions in Artificial Deep Neural Networks

Theoretical understanding of the behavior of infinitely-wide neural networks has been rapidly developed for various architectures due to the celebrated mean-field theory. However, there is a lack of a clear, intuitive framework for extending our understanding to finite networks that are of more practical and realistic importance. In the present contribution, we demonstrate that the behavior of properly initialized neural networks can be understood in terms of universal critical phenomena in absorbing phase transitions. More specifically, we study the order-to-chaos transition in the fully-connected feedforward neural networks and the convolutional ones to show that (i) there is a well-defined transition from the ordered state to the chaotics state even for the finite networks, and (ii) difference in architecture is reflected in that of the universality class of the transition. Remarkably, the finite-size scaling can also be successfully applied, indicating that intuitive phenomenological argument could lead us to semi-quantitative description of the signal propagation dynamics.

Rethinking the role of normalization and residual blocks for spiking neural networks

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.