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

arXiv: https://arxiv.org/abs/2605.18475 · HTML: https://mlsanity.com/paper/2605.18475/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 18 of 18)

- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [Structured Pruning of Large Language Models](https://mlsanity.com/paper/1910.04732/) (2019)
- [Mixed Precision Quantization of ConvNets via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.00090/) (2018)
- [OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting](https://mlsanity.com/paper/2501.13987/) (2025)
- [QTIP: Quantization with Trellises and Incoherence Processing](https://mlsanity.com/paper/2406.11235/) (2024)
- [BSQ: Exploring Bit-Level Sparsity for Mixed-Precision Neural Network Quantization](https://mlsanity.com/paper/2102.10462/) (2021)
- [BitStack: Any-Size Compression of Large Language Models in Variable Memory Environments](https://mlsanity.com/paper/2410.23918/) (2024)
- [MSQ: Memory-Efficient Bit Sparsification Quantization](https://mlsanity.com/paper/2507.22349/) (2025)

## Built on by (most cited first, 1 of 1)

- [Quantization Error Is Spectrally Flat: A Single Random Probe Is a Calibrated, Data-Free Sensitivity Estimator, with Application to Budget-Targeted Mixed-Precision Quantization](https://mlsanity.com/paper/2609.33923/) (2026)

## Abstract (arXiv)

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.