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arXiv · 2609.11867

AdamX: Cosine similarity meets gradient descent

Francisco Caldas·Ruben Belo·Cláudia Soares
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Abstract

We introduce AdamX, a first-order optimizer that incorporates cosine similarity as an adaptive mechanism for controlling update magnitudes. The proposed method is scalable, model-agnostic, and straightforward to integrate into existing training pipelines. We further introduce a variance rectification scheme that promotes smoother optimization during the early stages of training. Overall, we provide empirical evidence that AdamX achieves competitive convergence rates across a range of benchmark datasets and architectures. Performance is evaluated in terms of the number of epochs required to reach predefined performance thresholds under a fixed hyperparameter budget. Code and Experiments available at: https://github.com/FranciscoCaldas/adamX.

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Francisco Caldas, Ruben Belo, Cláudia Soares. 2026-09-10. AdamX: Cosine similarity meets gradient descent. https://arxiv.org/abs/2609.11867

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