AdamX: Cosine similarity meets gradient descent

arXiv:2609.11867 · cs.LG, math.OC · Submitted 2026-09-10 · Read on arXiv

cs.LG, math.OC

Submitted: 2026-09-10

Updated: 2026-09-10

Code: https://github.com/FranciscoCaldas/adamX

License: http://creativecommons.org/licenses/by/4.0/

The gist: We introduce AdamX, a first-order optimizer that incorporates cosine similarity as an adaptive mechanism for controlling update magnitudes.

Terminology

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.

Related papers