Title: Scaling Direct Feedback Learning with Theoretical Guarantees
Primary area: optimization
Keywords: backpropagation-free learning, optimization

Abstract: Deep neural networks rely on backpropagation (BP) for optimization, but its strictly sequential backward pass hinders parallelism and scalability. Direct Feedback Alignment (DFA) has been proposed as a promising approach for parallel learning of deep neural networks, relying on fixed random projections to enable layer-wise parallel updates, but fails on deep convolutional networks, and performs poorly on modern transformer architectures.
We introduce GrAPE (Gradient-Aligned Projected Error), a hybrid feedback-alignment method that (i) estimates rank-1 Jacobians via forward-mode JVPs and (ii) aligns each layer’s feedback matrix by minimizing a local cosine-alignment loss. To curb drift in very deep models, GrAPE performs infrequent BP anchor steps on a single mini-batch, preserving mostly parallel updates. We prove positive expected alignment from the forward-gradient estimator and invoke Zoutendijk-style arguments to guarantee convergence to stationary points. Empirically, GrAPE consistently outperforms prior alternatives to BP, enabling the training of modern architectures, closing a large fraction of the gap to BP while retaining layer-parallel updates for the vast majority of steps.