OAC: Output-adaptive Calibration for Accurate Post-training Quantization

Deployment of LLMs has major computational costs, due to their rapidly expanding size. Compression of LLMs reduces the memory footprint, latency, and energy required for their inference. Post-training Quantization (PTQ) techniques have been developed to compress LLMs while avoiding expensive re-training. Most PTQ approaches formulate the quantization error based on a layer-wise $\ell2$ loss, ignoring the model output. Then, each layer is calibrated using its layer-wise Hessian to update the weights towards minimizing the $\ell2$ quantization error. The Hessian is also used for detecting the most salient weights to quantization. Such PTQ approaches are prone to accuracy drop in low-precision quantization. We propose Output-adaptive Calibration (OAC) to incorporate the model output in the calibration process. We formulate the quantization error based on the distortion of the output cross-entropy loss. OAC approximates the output-adaptive Hessian for each layer under reasonable assumptions to reduce the computational complexity. The output-adaptive Hessians are used to update the weight matrices and detect the salient weights towards maintaining the model output. Our proposed method outperforms the state-of-the-art baselines such as SpQR and BiLLM, especially, at extreme low-precision (2-bit and binary) quantization.