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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 investigates the role of group-equivariant architectures in neural fluid dynamics surrogates, introducing the AB-GATr model. It finds that equivariance is beneficial when data lacks strong alignment, but can degrade performance on highly aligned datasets.
Introduces a symmetry-compatible principle for LLM optimizer design, yielding a layerwise optimizer stack with principled updates for embeddings, LM heads, SwiGLU MLPs, and MoE routers, showing improved validation loss over AdamW across multiple architectures.
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.
This paper introduces steerable neural ordinary differential equations on homogeneous spaces, providing a geometric framework for learning continuous-time equivariant dynamics.