Developmental Symmetry-Loss: A Free-Energy Perspective on Brain-Inspired Invariance Learning

TL;DR

This paper introduces Symmetry-Loss, a brain-inspired algorithm that enforces invariance through environmental symmetries, modeling developmental learning as iterative refinement of symmetry groups to achieve stable, compositional representations.

Contribution

It presents a novel symmetry-based learning framework that combines predictive coding and group theory to explain developmental invariance learning in the brain and artificial systems.

Findings

Symmetry-Loss effectively enforces invariance and equivariance in learned representations.

The framework models developmental processes as iterative symmetry group refinement.

Results suggest stable, compositional representations emerge from symmetry-based self-organization.

Abstract

We propose Symmetry-Loss, a brain-inspired algorithmic principle that enforces invariance and equivariance through a differentiable constraint derived from environmental symmetries. The framework models learning as the iterative refinement of an effective symmetry group, paralleling developmental processes in which cortical representations align with the world's structure. By minimizing structural surprise, i.e. deviations from symmetry consistency, Symmetry-Loss operationalizes a Free-Energy--like objective for representation learning. This formulation bridges predictive-coding and group-theoretic perspectives, showing how efficient, stable, and compositional representations can emerge from symmetry-based self-organization. The result is a general computational mechanism linking developmental learning in the brain with principled representation learning in artificial systems.