ARCH-CPTQ: Replay-Free Continual Post-Training Quantization with Curvature History and Anchoring

Calibration-based post-training quantization (PTQ) can be sensitive to differences between calibration and deployment data, especially at very low precision. Adaptive quantization addresses distribution shifts, but updates based only on current reconstruction objectives may degrade accuracy on earlier domains. We therefore formalize replay-free continual PTQ (CPTQ), which retains reconstruction history while updating a shared low-bit checkpoint using unlabeled calibration data and a fixed high-precision reference. Our derivation shows that weighted quadratic reconstruction losses on fixed inputs can be represented exactly by one fixed-dimensional curvature matrix per layer, but this representation alone does not determine how to guide subsequent updates. We propose anchored reconstruction with curvature history (ARCH)-CPTQ, which emphasizes poorly reconstructed current units, balances current and historical curvature using a Riemannian discrepancy, and penalizes changes from the previous checkpoint along historically sensitive directions. Across six large language models and five precision settings, ARCH-CPTQ improves model-averaged sequence-wide average performance (AP) and retention over equal-domain curvature averaging (CPTQ-AVG) under matched solver and representation settings, with a 2.16-percentage-point AP gain in our main W2A16 (2-bit weights, 16-bit activations) setting. In this setting, all six models achieve higher final accuracy on earlier domains, on average, than their own scores immediately after each domain was first calibrated, without replay.