Forward Learning with Top-Down Feedback: Empirical and Analytical Characterization

"Forward-only" algorithms, which train neural networks while avoiding a backward pass, have recently gained attention as a way of solving the biologically unrealistic aspects of backpropagation. Here, we first discuss the similarities between two "forward-only" algorithms, the Forward-Forward and PEPITA frameworks, and demonstrate that PEPITA is equivalent to a Forward-Forward with top-down feedback connections. Then, we focus on PEPITA to address compelling challenges related to the "forward-only" rules, which include providing an analytical understanding of their dynamics and reducing the gap between their performance and that of backpropagation. We propose a theoretical analysis of the dynamics of PEPITA. In particular, we show that PEPITA is well-approximated by an "adaptive-feedback-alignment" algorithm and we analytically track its performance during learning in a prototype high-dimensional setting. Finally, we develop a strategy to apply the weight mirroring algorithm on "forward-only" algorithms with top-down feedback and we show how it impacts PEPITA's accuracy and convergence rate.