Hirotaka Takahashi
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126
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ML×1AI×1Neural Computing×1
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2026
Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks
This paper derives the gradient of the Wolkowicz-Styan upper bound on the maximum eigenvalue of the cross-entropy loss Hessian in three-layer NNs to characterize directions leading to flat minima and proposes Hessian Spectral Range Regularization.
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cs.LGcs.AIcs.NETheoreticalRecentJun 27, 2026
Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks
Yuto Omae, Kazuki Sakai, Yohei Kakimoto, Makoto Sasaki +2 more
This paper derives the gradient of the Wolkowicz-Styan upper bound on the maximum eigenvalue of the cross-entropy loss Hessian in three-layer NNs to characterize directions leading to flat minima and…
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