Activation-Weighted Seeded Residual Coding for Low-Bit LLM Weight Repair

Low-bit weight quantization saves storage but leaves errors that degrade LLM quality. We introduce activation-weighted seeded residual coding (AWSRC), a compact repair codec for an existing quantization backbone. Given a reconstructed weight $W_0$, AWSRC encodes the residual $W-W_0$ using deterministic seed-generated bases. The sidecar stores seed selectors, low-bit coefficients, and scales rather than an explicit codebook. Two variants combine activation weighting with per-module byte quotas ($\mathrm{AWSRC\text{-}U}$), or blended activation/Fisher weighting with globally ranked progressive prefixes ($\mathrm{AWSRC\text{-}P}_{F}$) that support multiple byte budgets without refitting. On Qwen2.5-3B-Instruct, adding $0.162$ scope-bits/weight to an RTN-INT4 baseline closes $88.2\%$, $78.9\%$, and $71.3\%$ of the PPL, KL, and 11-task mean-accuracy gaps to BF16, respectively. AWSRC achieves the highest mean downstream accuracy in byte-matched residual-codec ablations and improves all metrics across model families with up to 32B parameters.