BlockFAMQ: Realized-Residual Curvature for Complete-Checkpoint Mamba Quantization

Mixed-precision quantization must decide which realized rounding residuals receive scarce high-precision bytes, but diagonal sensitivity scores discard the signed coordinate interactions that distinguish deterministic candidates. We introduce BlockFAMQ, a matrix-free allocator that scores squared per-token gradient–residual products and solves the resulting integer-byte multiple-choice problem under a complete-checkpoint budget. Across Mamba-1 130M, 370M, 1.4B, and 2.8B, the mean BlockFAMQ-minus-diagonal WikiText-2 NLL gap contracts from −0.218 at 2.5 effective bits to −0.026 at 4.0 bits and −0.009 at 4.5 bits. At 3.5 bits, BlockFAMQ improves six-task accuracy by 2.08 points and recovers 65.7–80.1% of the diagonal quantization gap; an activation-weighted reconstruction baseline narrows but does not remove the advantage. At 3.0 bits, direct candidate KL improves on BlockFAMQ by 0.038 nats across 1.4B and 2.8B, while a feasibility-anchored block-to-KL shortlist recovers 0.033 nats at 1.62× the block-scoring cost on average. Precision shifts toward x_proj and in_proj, whose realized residuals have the largest cross-term tails, and the block effect is larger on Mamba-1 1.4B than on matched-scale Pythia-1.4B. The direction persists on Mamba-2 2.7B and Falcon-Mamba 7B; packed W4A8 composition retains 96.8–97.7% of Quamba2 decode throughput while lowering NLL. These results support realized block curvature as a budget-dependent allocation correction, with direct KL becoming more useful when aggressive quantization leaves the local quadratic regime.