Strong anti-Hebbian plasticity alters the convexity of network attractor landscapes

TL;DR

This paper investigates how anti-Hebbian plasticity fundamentally changes the shape of neural network attractor landscapes, leading to multiple equilibria and loss of convexity, with implications for learning and optimization.

Contribution

It provides a formal analysis showing that anti-Hebbian learning causes a bifurcation that destroys convexity in attractor landscapes, revealing new effects of plasticity rules.

Findings

Anti-Hebbian plasticity causes a pitchfork bifurcation.

Loss of convexity leads to multiple stable equilibria.

Attractor landscapes are more sensitive to slower learning rates.

Abstract

In this paper, we study recurrent neural networks in the presence of pairwise learning rules. We are specifically interested in how the attractor landscapes of such networks become altered as a function of the strength and nature (Hebbian vs. anti-Hebbian) of learning, which may have a bearing on the ability of such rules to mediate large-scale optimization problems. Through formal analysis, we show that a transition from Hebbian to anti-Hebbian learning brings about a pitchfork bifurcation that destroys convexity in the network attractor landscape. In larger-scale settings, this implies that anti-Hebbian plasticity will bring about multiple stable equilibria, and such effects may be outsized at interconnection or `choke' points. Furthermore, attractor landscapes are more sensitive to slower learning rates than faster ones. These results provide insight into the types of objective functions that can be encoded via different pairwise plasticity rules.