arXiv:2512.06737v2 Announce Type: replace 
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, AdamW, Lion, SGD) on the CIFAR-10 image classification dataset across 8 diverse MLP architectures ranging from 1 to 5 hidden layers. ArcGD achieved the highest average test accuracy (50.7%) at 20,000 iterations, outperforming AdamW (46.6%), Adam (46.8%), SGD (49.6%), and Lion (43.4%), winning or tying on 6 of 8 architectures. Notably, while Adam and AdamW showed strong early convergence at 5,000 iterations, but regressed with extended training, whereas ArcGD continued improving, demonstrating generalization and resistance to overfitting without requiring early stopping tuning. Strong performance on geometric stress tests and standard deep-learning benchmarks indicates broad applicability, highlighting the need for further exploration. Moreover, it is also shown that a limiting variant of ArcGD can be interpreted as a sign-based momentum-like update, highlighting conceptual connections between the inherent mechanisms of ArcGD and the Lion optimiser.

يقدم المقال المحسن Arc Gradient Descent (ArcGD)، وهو إعادة صياغة للطرق التقليدية في الانحدار، مع التركيز على ديناميات خطوة مدروسة من قبل المستخدم وواعية للمرحلة. تظهر التقييمات الأولية على وظائف مرجعية غير محدبة ومجموعات بيانات حقيقية، بما في ذلك CIFAR-10، أن ArcGD يتفوق على المحسنين المعروفين مثل Adam، خاصة في القضاء على تحيز معدل التعلم.

El artículo presenta el optimizador Arc Gradient Descent (ArcGD), una reformulación de los métodos tradicionales de descenso de gradiente, que enfatiza dinámicas de paso controladas por el usuario y conscientes de la fase. Las evaluaciones iniciales en funciones de referencia no convexas y conjuntos de datos del mundo real, incluido CIFAR-10, demuestran que ArcGD supera a optimizadores establecidos como Adam, especialmente en la eliminación del sesgo de tasa de aprendizaje.

L'article présente l'optimiseur Arc Gradient Descent (ArcGD), une reformulation des méthodes de descente de gradient traditionnelles, mettant l'accent sur des dynamiques de pas contrôlées par l'utilisateur et conscientes de la phase. Les évaluations initiales sur des fonctions de référence non convexes et des ensembles de données réels, y compris CIFAR-10, montrent que l'ArcGD surpasse les optimisateurs établis comme Adam, en particulier pour éliminer le biais de taux d'apprentissage.

The paper introduces the Arc Gradient Descent (ArcGD) optimizer, a reformulation of traditional gradient descent methods, emphasizing phase-aware and user-controlled step dynamics. Initial evaluations on non-convex benchmark functions and real-world datasets, including CIFAR-10, demonstrate ArcGD's superior performance compared to established optimizers like Adam, particularly in eliminating learning-rate bias.