Weight Perturbation Learning Performs Similarly or Better than Node Perturbation on Broad Classes of Temporally Extended Tasks

Abstract

Biological constraints often impose restrictions for plausible plasticity rules such as locality and reward-based rather than supervised learning. Two learning rules that comply with these restrictions are weight (WP) and node (NP) perturbation. NP is often used in learning studies, in particular as a benchmark; it is considered to be superior to WP and more likely neurobiologically realized, as the number of weights and therefore their perturbation dimension typically massively exceeds the number of nodes. Here we show that this conclusion no longer holds when we take two biologically relevant properties into account: First, tasks extend in time. This increases the perturbation dimension of NP but not WP. Second, tasks are low dimensional, with many weight configurations providing solutions. We analytically delineate regimes where these properties let WP perform as well as or better than NP. Furthermore we find that the changes in weight space directions that are irrelevant for the task differ qualitatively between WP and NP and that only in WP gathering batches of subtasks in a trial decreases the number of trials required. This may allow to experimentally distinguish which of the two rules underlies a learning process. Our insights suggest new learning rules, which combine for specific task types the advantages of WP and NP. If the inputs are similarly correlated, temporally correlated perturbations improve NP. Using numerical simulations, we generalize the results to networks with various architectures solving biologically relevant and standard network learning tasks. Our findings, together with WPs practicability suggest WP as a useful benchmark and plausible model for learning in the brain.