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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Andy Irawan
Fakultas Sains dan Teknologi UIN Maulana Malik Ibrahim
Mathematics

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A Damped Hessian-Free Newton--Conjugate Gradient Method for Weighted Multiclass Neural Classification Andy Irawan; Zainal Abidin; Mohammad Jamhuri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40243

Abstract

This study presents a deterministic damped Hessian-free Newton--CG method for weighted multiclass neural classification. The method is built from a weighted categorical cross-entropy objective, a damped local quadratic model, and a matrix-free curvature representation through Hessian--vector products. The search direction is computed by an inexact conjugate gradient solve, while Armijo backtracking and adaptive damping are used to improve stability. The method is implemented for the classification of academic predicate categories using preprocessed student data with mixed categorical and numerical features. Its numerical behavior is compared with SGD with momentum, RMSProp, and Adam under the same loss, initialization, and network architecture. The proposed method is computationally feasible, attains the best overall weighted test-set performance among the compared methods, and exhibits a distinct optimization trajectory driven by curvature-informed updates. These results show that a damped Hessian-free formulation provides a mathematically transparent, reproducible, and practically competitive framework for second-order optimization in multiclass neural classification.
Co-Authors Mohammad Jamhuri Zainal Abidin