  Deployment of Large Language Models (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 $\ell_2$ loss, ignoring the model output. Then,
each layer is calibrated using its layer-wise Hessian to update the weights
towards minimizing the $\ell_2$ 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.
