symmetry

This paper empirically measures the symmetry–data exchange rate predicted by equivariance theory, finding that wrong-group symmetry constraints are actively harmful, augmentation with test-time orbit averaging matches equivariant architectures, and the theoretical |G|-fold sample complexity reduction is only weakly confirmed with wide confidence intervals. The study is explicitly exploratory and not pre-registered.

This exploratory study empirically measures the symmetry–data exchange rate predicted by equivariance theory on controlled C_n-symmetric tasks, finding that wrong-group constraints are actively harmful, augmentation with test-time orbit averaging matches equivariant models exactly, and the empirical exchange rate is broadly consistent with theory but statistically inconclusive. The authors emphasize the study's exploratory nature and call for registered replications.

This paper presents a method to automatically generate local search neighborhoods from constraint specifications using symmetry properties, evaluated on six optimization problems.

Researchers introduce symmetry-compatible optimizers that respect the equivariance structures of neural network parameters, improving training stability and performance over traditional methods like Adam. The approach is validated on various language model architectures including Qwen3-0.6B, Gemma 3 1B, and OLMoE-1B-7B.