Excess risk decomposes into independent alignment (trace of inverse average Hessian times gradient covariance) and curvature terms, so both flatness and gradient alignment are required; SAGE achieves this and sets new SOTA on DomainBed.
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Flatness and Gradient Alignment Are Both Necessary: Spectral-Aware Gradient-Aligned Exploration for Multi-Distribution Learning
Excess risk decomposes into independent alignment (trace of inverse average Hessian times gradient covariance) and curvature terms, so both flatness and gradient alignment are required; SAGE achieves this and sets new SOTA on DomainBed.