Backward Signal Propagation: A Symmetry-Based Training Method for Neural Networks

While backpropagation (BP) has long served as the cornerstone of training deep neural networks, it relies heavily on strict differentiation logic and global gradient information, lacking biological plausibility. In this paper, we systematically present a novel neural network training paradigm that depends solely on signal propagation, which we term Backward Signal Propagation (BSP). The core idea of this framework is to reinterpret network training as a symmetry-driven process of discovering inverse causal relationships. Starting from symmetry principles, we define symmetric differential equations and leverage their inherent properties to implement a learning mechanism analogous to differentiation. Furthermore, we introduce the concept of causal distance, a core invariant that bridges the forward propagation and inverse learning processes. It quantifies the influence strength between any two elements in the network, leading to a generalized form of the chain rule. With these innovations, we achieve precise, pointwise adjustment of model parameters. Unlike traditional BP, the BSP method enables parameter updates based solely on local signal features. This work offers a new direction toward efficient and biologically plausible learning algorithms.