{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11867",
  "author_total": 3,
  "authors": [
    {
      "name": "Francisco Caldas"
    },
    {
      "name": "Ruben Belo"
    },
    {
      "name": "Cláudia Soares"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bpvwryg7asv5m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11867",
  "fulltext_url": null,
  "id": "bpvwryg7asv5m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11867",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7212264808",
  "pdf_url": "https://arxiv.org/pdf/2609.11867",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bpvwryg7asv5m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11867",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11867"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "AdamX: Cosine similarity meets gradient descent",
  "title_text": "AdamX: Cosine similarity meets gradient descent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/bpvwryg7asv5m",
  "venue": "arXiv",
  "versions": []
}