[2512.06737] Arc Gradient Descent: A Geometrically Motivated Gradient Descent-based Optimiser with Phase-Aware, User-Controlled Step Dynamics (proof-of-concept)

Computer Science > Machine Learning arXiv:2512.06737 (cs) [Submitted on 7 Dec 2025 (v1), last revised 23 Mar 2026 (this version, v3)] Title:Arc Gradient Descent: A Geometrically Motivated Gradient Descent-based Optimiser with Phase-Aware, User-Controlled Step Dynamics (proof-of-concept) Authors:Nikhil Verma, Joonas Linnosmaa, Leonardo Espinosa-Leal, Napat Vajragupta View a PDF of the paper titled Arc Gradient Descent: A Geometrically Motivated Gradient Descent-based Optimiser with Phase-Aware, User-Controlled Step Dynamics (proof-of-concept), by Nikhil Verma and 3 other authors View PDF Abstract:The paper presents the formulation, implementation, and evaluation of the ArcGD optimiser. The evaluation is conducted initially on a non-convex benchmark function and subsequently on a real-world ML dataset. The initial comparative study using the Adam optimiser is conducted on a stochastic variant of the highly non-convex and notoriously challenging Rosenbrock function, renowned for its narrow, curved valley, across dimensions ranging from 2D to 1000D and an extreme case of 50,000D. Two configurations were evaluated to eliminate learning-rate bias: (i) both using ArcGD's effective learning rate and (ii) both using Adam's default learning rate. ArcGD consistently outperformed Adam under the first setting and, although slower under the second, achieved superior final solutions in most cases. In the second evaluation, ArcGD is evaluated against state-of-the-art optimizers (Adam, Ada...