  Backpropagation (BP), a foundational algorithm for training artificial neural
networks, predominates in contemporary deep learning. Although highly
successful, it is often considered biologically implausible. A significant
limitation arises from the need for precise symmetry between connections in the
backward and forward pathways to backpropagate gradient signals accurately,
which is not observed in biological brains. Researchers have proposed several
algorithms to alleviate this symmetry constraint, such as feedback alignment
and direct feedback alignment. However, their divergence from backpropagation
dynamics presents challenges, particularly in deeper networks and convolutional
layers. Here we introduce the Product Feedback Alignment (PFA) algorithm. Our
findings demonstrate that PFA closely approximates BP and achieves comparable
performance in deep convolutional networks while avoiding explicit weight
symmetry. Our results offer a novel solution to the longstanding weight
symmetry problem, leading to more biologically plausible learning in deep
convolutional networks compared to earlier methods.
