How to Train Your Wide Neural Network Without Backprop: An Input-Weight Alignment Perspective
This provides a biologically plausible alternative to backpropagation for training wide networks, addressing challenges in modeling biological neural systems.
The paper tackled the problem of training wide neural networks without backpropagation by deriving a family of biologically-motivated learning rules based on input-weight alignment, showing comparable performance to backpropagation on benchmark tasks, especially in low data regimes.
Recent works have examined theoretical and empirical properties of wide neural networks trained in the Neural Tangent Kernel (NTK) regime. Given that biological neural networks are much wider than their artificial counterparts, we consider NTK regime wide neural networks as a possible model of biological neural networks. Leveraging NTK theory, we show theoretically that gradient descent drives layerwise weight updates that are aligned with their input activity correlations weighted by error, and demonstrate empirically that the result also holds in finite-width wide networks. The alignment result allows us to formulate a family of biologically-motivated, backpropagation-free learning rules that are theoretically equivalent to backpropagation in infinite-width networks. We test these learning rules on benchmark problems in feedforward and recurrent neural networks and demonstrate, in wide networks, comparable performance to backpropagation. The proposed rules are particularly effective in low data regimes, which are common in biological learning settings.