Adaptive Tuning Curve Widths Improve Sample Efficient Learning

Abstract

Natural brains perform miraculously well in learning new tasks from a small number of samples, whereas sample efficient learning is still a major open problem in the field of machine learning. Here, we raise the question, how the neural coding scheme affects sample efficiency, and make first progress on this question by proposing and analyzing a learning algorithm that uses a simple reinforce-type plasticity mechanism and does not require any gradients to learn low dimensional mappings. It harnesses three bio-plausible mechanisms, namely, population codes with bell shaped tuning curves, continous attractor mechanisms and probabilistic synapses, to achieve sample efficient learning. We show both theoretically and by simulations that population codes with broadly tuned neurons lead to high sample efficiency, whereas codes with sharply tuned neurons account for high final precision. Moreover, a dynamic adaptation of the tuning width during learning gives rise to both, high sample efficiency and high final precision. We prove a sample efficiency guarantee for our algorithm that lies within a logarithmic factor from the information theoretical optimum. Our simulations show that for low dimensional mappings, our learning algorithm achieves comparable sample efficiency to multi-layer perceptrons trained by gradient descent, although it does not use any gradients. Furthermore, it achieves competitive sample efficiency in low dimensional reinforcement learning tasks. From a machine learning perspective, these findings may inspire novel approaches to improve sample efficiency. From a neuroscience perspective, these findings suggest sample efficiency as a yet unstudied functional role of adaptive tuning curve width.K eywords sample efficiency · neural tuning curves · population codes · gradient-free learning · reinforcement learning 6 if L(x, y) ≥L then c ij = c ij − 1 for all (i, j) ∈ I × J; 7 else c ij = c ij − 1 for all (i, j) ∈ I × J; 8 for (i, j) ∈ I × J do 9 if c ij ≤ 0 then p ij = 0;

Population codes enable learning from few examples by shaping inductive bias

“…These codes may be shaped through evolution or themselves be learned through experience [55]. Prior related work demonstrated the dependence of sample-efficient learning of a two-angle estimation task on the width of the individual neural tuning curves [72] and additive function approximation properties of sparsely connected random networks [73].…”