Layerwise Error Attribution for Fast and Robust Mixed-Precision Post-Training Quantization

Mixed-precision post-training quantization is a network compression method that assigns bits layer by layer, under a global memory budget using a small calibration set. The main difficulties are to overcome the combinatorial nature of the allocation problem and to manage the sensitivity to small, potentially corrupted databases. Hence, an efficient allocation method should be fast to compute and preserve model quality when calibration data are corrupted. To design such a method, we derive a layerwise probabilistic analysis of the quantization error that separates propagated error from the local perturbation introduced at a given layer. We use this local term to build a separable score for a simple allocation algorithm, that requires no external solver. The probabilistic nature of our approach brings robustness to corrupted data. On denoising tasks with DRUNet, with an average budget of $4$ bits per weight, our method matches or improves state-of-the-art mixed-precision baselines under clean calibration, and is more robust to corrupted calibration, with PSNR gains of up to $7.5$ dB under the tested corruptions. Experiments show bit-allocation speed-ups from $28\times$ to $2,570\times$ over the studied baselines. For quantized diffusion models, our experiments show that a direct application of our framework also improves the state-of-the-art.