🤖 AI Summary
Representation learning in artificial systems suffers from a fundamental lack of invariance and equivariance, limiting generalization and compositional reasoning.
Method: We propose the Symmetry-Loss principle—a differentiable group-constrained optimization framework grounded in environmental symmetry priors. It models representation learning as a progressive developmental refinement of effective symmetry groups, driven by minimization of structural surprise (a free-energy-like objective). The approach integrates Lie group priors, differentiable symmetry constraints, free-energy minimization, and prediction-error optimization.
Contribution/Results: This work unifies cortical development mechanisms, predictive coding, and group theory under a novel free-energy principle for symmetry self-organization. Experiments demonstrate that learned representations exhibit high efficiency, robustness to perturbations, and compositional structure. The framework provides a biologically plausible, brain-inspired theoretical foundation for both cortical development modeling and embodied intelligence.
📝 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.