{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/dynamic-metastability-in-the-self-attention","title":"Dynamic metastability in the self-attention model","arxiv_id":"2410.06833","date":"2024-10-09","proceeding":null,"authors":["Borjan Geshkovski","Hugo Koubbi","Yury Polyanskiy","Philippe Rigollet"],"abstract":"We consider the self-attention model - an interacting particle system on the unit sphere, which serves as a toy model for Transformers, the deep neural network architecture behind the recent successes of large language models. We prove the appearance of dynamic metastability conjectured in [GLPR23] - although particles collapse to a single cluster in infinite time, they remain trapped near a configuration of several clusters for an exponentially long period of time. By leveraging a gradient flow interpretation of the system, we also connect our result to an overarching framework of slow motion of gradient flows proposed by Otto and Reznikoff [OR07] in the context of coarsening and the Allen-Cahn equation. We finally probe the dynamics beyond the exponentially long period of metastability, and illustrate that, under an appropriate time-rescaling, the energy reaches its global maximum in finite time and has a staircase profile, with trajectories manifesting saddle-to-saddle-like behavior, reminiscent of recent works in the analysis of training dynamics via gradient descent for two-layer neural networks.","url_abs":"https://arxiv.org/abs/2410.06833v1","url_pdf":"https://arxiv.org/pdf/2410.06833v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"dynamic-metastability-in-the-self-attention","repo_url":"https://github.com/hugokoubbi/2024-transformers-dotm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"model","task_name":"model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2410.06833","atlas_url":"https://app.syntology.ai/?focus=2410.06833","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2410.06833"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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