Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
International Conference on Learning Representations , year=
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2026 8representative citing papers
LE-SAM inverts SAM by fixing the loss budget instead of the parameter-space radius, yielding better generalization across benchmarks.
Self-pretraining improves Transformer sequence classification by enabling learning of proximity-biased attention from positional encodings that label supervision alone cannot easily acquire from random starts.
Adam's adaptive preconditioning and first-moment averaging improve high-probability tracking error in noise-dominated nonstationary regimes but can increase it under strong drift, where SGD achieves a smaller floor, with explicit beta-dependent bounds.
Sharpness-aware pretraining and related flat-minima interventions reduce catastrophic forgetting by up to 80% after post-training across 20M-150M models and by 31-40% at 1B scale.
E-value sequential tests enable early stopping of MCMC sampling in Bayesian deep ensembles, often needing only a fraction of the full budget while improving over standard deep ensembles.
Zeroth-order optimization is underexplored rather than underpowered in deep learning, with limitations stemming from full-space designs that can be addressed via subspace, spectral, and systems-aware approaches.
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Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization
LE-SAM inverts SAM by fixing the loss budget instead of the parameter-space radius, yielding better generalization across benchmarks.