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About this paper
Marvin F. da Silva, Felix Dangel, Sageev Oore
The authors introduce geodesic sharpness, a symmetry-aware measure that treats equivalent parameter settings as one function and evaluates loss increases along quotient-geometry paths. For attention, it approximates these paths with a second-order correction. Across 35 BERT models fine-tuned on MNLI, it correlated with the generalization gap at τ = 0.38, versus 0.06 for adaptive sharpness; on ImageNet, correlation was negative.
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