Wolkowicz-Styan Upper Bound on the Hessian Eigenspectrum for Cross-Entropy Loss in Nonlinear Smooth Neural Networks
Neural networks (NNs) are central to modern machine learning and achieve state-of-the-art results in many applications. However, the relationship between loss geometry and generalization is still not well understood. The local geometry of the loss function near a critical point is well-approximated by its quadratic form, obtained through a second-order Taylor expansion. The coefficients of the quadratic term correspond to the Hessian matrix, whose eigenspectrum allows us to evaluate the sharpness of the loss at the critical point. Extensive research suggests flat critical points generalize better, while sharp ones lead to higher generalization error. However, sharpness requires the Hessia...
| Authors | Yuto Omae, Kazuki Sakai, Yohei Kakimoto et al. |
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| Primary category | cs.LG |
| Published | 11 April 2026 |
| Last updated at source | 14 April 2026 |
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