Two-pass Trajectory Calibration for Compensation-based Post-training Quantization

In post-training quantization (PTQ), learned per-row codebooks are typically fitted once on the weights where an error compensation engine such as GPTQ or LDLQ starts from. The engine, however, does not round those weights: after each column is rounded, the remaining columns are updated to compensate for its rounding error. By the time a later column is rounded, its values have therefore already been shifted by the compensation from every column rounded before it. We call this sequence of shifted values the layer's trajectory. We propose 2-Pass Trajectory Calibration (2PTC), a drop-in correction for the mismatch between the static weights a codebook is fit on and the shifted trajectory the engine actually rounds: run the engine once to record the trajectory, refit the codebook on it, and rerun the same engine on the same starting weights with the refitted grid. 2PTC stores a single codebook of the same memory size and leaves inference unchanged; it only costs one additional offline pass. Across six open LLMs and two compensation engines, on top of QEP inter-layer correction, per-channel 2PTC lowers perplexity at every bit-width with GPTQ and at 2 and 3 bits with LDLQ. The gains are largest at 2 bits: WikiText-2 perplexity decreases in 36 of 36 paired runs, by 15.5% on average with GPTQ and 5.7% with LDLQ, and average zero-shot accuracy improves by up to 9.4 points.