Quantization PTQ/QAT

Quantization maps FP16 weights $W$ to low-bit integers $x_q = \text{round}(x/s) + z$ with scale $s = (x_{\max}-x_{\min})/(2^b-1)$ and zero-point $z$ aligned to the b-bit range. PTQ (Post-Training Quantization) calibrates an already-trained model with a small calibration set, no retraining needed; QAT (Quantization-Aware Training) simulates quantization error during training via STE (straight-through estimator: quantized forward, approximate straight-through backward), making the model adapt to quantization.

PTQ dominates LLM inference deployment (GPTQ, AWQ, etc.) since large models cannot afford retraining — calibration takes minutes; QAT fits extreme low-bit (INT4/INT3 or lower) and accuracy-critical vertical scenarios, or joint quantization during fine-tuning.

naive uniform quantization collapses due to activation outliers and distribution mismatch; PTQ uses calibration and error compensation to contain the loss, while QAT trains weights to match the quantizer — a speed-vs-accuracy trade-off: PTQ is fast but lower ceiling, QAT is slow but higher ceiling.

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