@inproceedings{zhao-etal-2026-coopq,
    title = "{C}oop{Q}: Cooperative Game Inspired Layerwise Mixed Precision Quantization for {LLM}s",
    author = "Zhao, Junchen  and
      Derakhshan, Ali  and
      Hyman, Jayden  and
      Dong, Junhao  and
      Jyothi, Sangeetha Abdu  and
      Harris, Ian",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.373/",
    pages = "7566--7578",
    ISBN = "979-8-89176-395-1",
    abstract = "Large Language Models (LLMs) promise impressive capabilities, yet their multi-billion parameter scale makes on-device or low-resource deployment prohibitive. Mixed precision quantization offers a compelling solution, but existing methods struggle when the average precision drops below four bits, as they rely on isolated, layer-specific metrics that overlook critical inter-layer interactions affecting overall performance. To address these limitations, we first frame the mixed-precision quantization problem as a cooperative game among layers and introduce Shapley-based Progressive Quantization Estimation (SPQE) to efficiently obtain accurate Shapley estimates of layer sensitivities and inter-layer interactions. Leveraging the SPQE estimates, we propose Cooperative Game Inspired Mixed-Precision Quantization (CoopQ) which translates these Shapley estimates into a binary quadratic optimization formulation, assigning either 2 or 4-bit precision to layers under strict memory constraints. Comprehensive experiments conducted on Llama-3, Gemma-2, and Qwen models across three independent PTQ backends (Quanto, HQQ, GPTQ) demonstrate CoopQ{'}s scalability and consistently superior performance compared to methods relying solely on isolated metrics. Across average precisions spanning 4 bit down to 2 bit, CoopQ cuts Perplexity by 20 {--} 80 {\%} relative to the best baseline, with the margin growing as the bit-width tightens."
}