GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918509340000256 |
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| author | Yao, Zhangyang Zhao, Haiyan Wang, Haoyu Huang, Tianbo Zhang, Lihua Han, Xu |
| author_facet | Yao, Zhangyang Zhao, Haiyan Wang, Haoyu Huang, Tianbo Zhang, Lihua Han, Xu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18475 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets Yao, Zhangyang Zhao, Haiyan Wang, Haoyu Huang, Tianbo Zhang, Lihua Han, Xu Machine Learning Artificial Intelligence 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. |
| title | GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.18475 |