{
  "abstract": "Equilibrium Propagation (EP) is a biologically motivated alternative to backpropagation but requires free and nudged equilibrium phases, raising questions about the biological plausibility of phase-separated learning. We introduce Neuromodulated Equilibrium Learning (NEL), a single-equilibrium reward-based framework inspired by Attention-Gated Brain Propagation and neuromodulatory signaling. After reaching a free equilibrium, NEL propagates a reward-dependent modulatory signal derived from the selected action through reciprocal feedback connections to drive local synaptic updates, eliminating both the reward-nudged equilibrium and contrastive update. We evaluate NEL on MNIST, Fashion-MNIST, and CIFAR-10 using multilayer perceptrons and convolutional networks, with symmetric three-phase REP and standard EP as multi-phase baselines. NEL approaches three-phase REP in shallow architectures, with gaps of 0.79 and 1.31 percentage points on MNIST and one-hidden-layer Fashion-MNIST, while larger gaps of 3.13 and 6.21 percentage points emerge in the deeper Fashion-MNIST and CIFAR-10 settings. A direct cost feedback control using the full supervised output error also remains below three-phase EP, indicating that sparse reward information alone does not explain the performance gap between single-equilibrium and multi-phase learning. These results show that effective reward-driven learning can arise from a single free equilibrium while suggesting that computations introduced by additional nudged relaxations become increasingly important in more challenging architectures.",
  "abstract_shown": true,
  "affiliations": [
    "Lakehead University"
  ],
  "article_type": "New results",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Y. Kubo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jfqbt31q0c3s.bib",
  "cited_by": 0,
  "doi": "10.64898/2026.08.28.747901",
  "fulltext_url": "https://www.biorxiv.org/content/10.64898/2026.08.28.747901v1.full",
  "id": "6jfqbt31q0c3s",
  "issns": [],
  "landing_url": "https://www.biorxiv.org/content/10.64898/2026.08.28.747901v1",
  "language": null,
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "biorxiv",
      "neuroscience"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7208708380",
  "pdf_url": "https://www.biorxiv.org/content/10.64898/2026.08.28.747901v1.full.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jfqbt31q0c3s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:16Z",
      "native_id": "10.64898/2026.08.28.747901",
      "source": "biorxiv",
      "url": "https://www.biorxiv.org/content/10.64898/2026.08.28.747901v2"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "biorxiv:neuroscience",
      "subfield": "neuroscience"
    }
  ],
  "title": "Neuromodulated Equilibrium Learning",
  "title_text": "Neuromodulated Equilibrium Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/6jfqbt31q0c3s",
  "venue": "bioRxiv",
  "versions": []
}