From a neuroscience perspective, artificial neural networks are regarded as abstract models of biological neurons, yet they rely on biologically implausible backpropagation for training. Energy-based models represent a class of brain-inspired learning frameworks that adjust system states by minimizing an energy function. Predictive coding (PC), a theoretical model within energy-based models, constructs its energy function from forward prediction errors, with optimization achieved by minimizing local layered errors. Owing to its local plasticity, PC emerges as the most promising alternative to backpropagation. However, PC face gradient explosion and vanishing challenges in deep networks with multiple layers. Gradient explosion occurs when layer-wise prediction errors are excessively large, while gradient vanishing arises when they are excessively small. To address these challenges, we propose bidirectional energy to stabilize prediction errors and mitigate gradient explosion, while using skip connections to resolve gradient vanishing problems. We also introduce a layer-adaptive learning rate (LALR) to enhance training efficiency. Our model achieves accuracies of 99.22% on MNIST, 93.78% on CIFAR-10, 83.96% on CIFAR-100, and 73.35% on Tiny ImageNet, comparable to the performance of identically structed networks trained with backprop. Finally, we developed a Jax-based framework for efficient training of energy-based models, reducing training time by half compared to PyTorch.
Chen et al. (Tue,) studied this question.