# Hierarchical Shapley Allocation (HiSA)

Binarization-based post-training quantization for LLMs has carried hidden overhead: scaling factors, group parameters and outlier indices push nominally 1-bit weights into an effective 2-4-bit range. AF1 pairs a double-factor binary decomposition with null-space compensation of discrete projection error, then allocates structural budget through hierarchical Shapley values, quantizing under a strict 1.0 effective BPW for target linear weights. On LLaMA-3-70B it reaches 61.80 average zero-shot accuracy over seven tasks and 8.91 WikiText2 perplexity, above the 3.25-bit HBLLM baseline.

Binarization-based post-training quantization for LLMs has carried hidden overhead: scaling factors, group parameters and outlier indices push nominally 1-bit weights into an effective 2-4-bit range. AF1 pairs a double-factor binary decomposition with null-space compensation of discrete projection error, then allocates structural budget through hierarchical Shapley values, quantizing under a strict 1.0 effective BPW for target linear weights. On LLaMA-3-70B it reaches 61.80 average zero-shot accuracy over seven tasks and 8.91 WikiText2 perplexity, above the 3.25-bit HBLLM baseline.