Escaping Rounding Barriers in Large Language Model Quantization via Transverse-Field Ising Optimization

Abstract

Weight-only post-training quantization (PTQ) pipelines such as AWQ ultimately commit to a deterministic rounding decision for every scalar weight, and recent discrete coordinate-descent quantizers refine those decisions one weight at a time. We show that both are blocked by the same obstacle: correlated activation channels create multi-spin energy barriers in the discrete rounding landscape — configurations in which no single rounding flip helps, yet a small group of coordinated flips strictly reduces the layer reconstruction error. We characterize these barriers exactly under the empirical activation metric and prove that they arise only from frustration between local quantization fields and cross-channel couplings. Building on this analysis we propose Transverse-Field Ising Correction (TFIC), a barrier-aware discrete optimizer that post-processes any AWQ-style pipeline. TFIC casts fixed-grid rounding as a classical Ising ground-state problem, selects the spins near a rounding boundary as a mobile pool, drives that pool to a single-flip local minimum by exact coordinate descent, and then crosses barriers with cluster moves that flip small groups of coupled spins together. Every accepted move is scored against the exact reconstruction energy, and a robust per-layer noise-floor acceptance rule prunes flips whose apparent gain is within calibration-estimation noise; together these guarantee that each layer’s calibration reconstruction error is monotonically non-increasing. TFIC requires no gradients and no architectural changes. On Mistral-7B and Llama-3-8B, applying TFIC on top of a 4-bit AWQ baseline consistently reduces WikiText-2 and C4 perplexity, at a per-layer cost of tens of seconds and with no inference-time overhead.