GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets

[2605.18475] GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets Skip to main content Search Submit Donate Log in Computer Science > Machine Learning arXiv:2605.18475 (cs) [Submitted on 18 May 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets Authors: Zhangyang Yao , Haiyan Zhao , Haoyu Wang , Xu Han View PDF HTML (experimental) Abstract: Mixed-precision quantization improves the budget--accuracy trade-off for large language models (LLMs) by allocating more bits to sensitive modules. However, automating this allocation at LLM scale faces a unique combination of constraints: learnable approaches require quantization-aware training, which is infeasible for billion-parameter models; training-free alternatives rely on static proxy metrics that miss cross-module interactions and must be recomputed per target budget; and search-based methods are expensive without guaranteeing exact budget compliance. We propose GAMMA, a quantizer-agnostic framework that learns module-wise precision preferences entirely within a post-training pipeline. GAMMA optimizes a teacher-forced hidden-state reconstruction objective under an augmented Lagrangian constraint, and projects the learned preferences into exact budget-feasible discrete assignments via integer programming. A key property is score reuse: because the learned preferences encode a stable sensitivity ranking rather than budget-specific weights, a single training run serves arbitrary deployment targets by re-solving only the integer program, reducing per-budget adaptation from hours to a few minutes. Across Llama and Qwen models (8B--32B), GAMMA outperforms both fixed-precision baselines (up to +12.99 Avg.) and search-based mixed-precision methods (up to +7.00 Avg.), and can match fixed 3-bit quality at 2.5-bit average precision, enabling deployment at substantially smaller memory footprints. Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2605.18475 [cs.LG] (or arXiv:2605.18475v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2605.18475 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Zhangyang Yao [ view email ] [v1] Mon, 18 May 2026 14:30:58 UTC (1,066 KB) [v2] Thu, 27 Aug 2026 09:00:41 UTC (1,066 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG < prev | next > new | recent | 2026-05 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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