基于对称性约束，实现脑启发的稳定表征学习。
Developmental Symmetry-Loss: A Free-Energy Perspective on Brain-Inspired Invariance Learning
- 通过可微分对称性约束，让模型自动学习不变性和等变性。
- 最小化结构意外，使表征在复杂环境中保持稳定和组合性。
- 适合研究神经科学与机器学习交叉的学者参考。
我们提出一种受大脑启发的算法原则——对称性损失（Symmetry-Loss），通过环境对称性导出的可微分约束来强制实现不变性和等变性。该框架将学习建模为有效对称群的迭代优化，类比于皮层表征在发育过程中与世界结构对齐的过程。通过最小化结构意外（即对称性不一致的偏离），对称性损失将自由能原理形式化为表示学习的目标。这一框架连接了预测编码与群论视角，揭示了如何从对称性自组织中涌现出高效、稳定且可组合的表征。最终形成一个通用计算机制，将大脑中的发育学习与人工系统中的原则性表征学习相联系。
原文摘要 · Abstract (English)
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.
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