On the impact of the parametrization of deep convolutional neural networks on post-training quantization
Samy Houache, Jean François Aujol, Yann Traonmilin
TL;DR
This paper tackles the challenge of guaranteeing performance when post-training quantization is applied to CNNs. It develops a theory that replaces the depth-heavy worst-case bound with a layerwise mean norm, introducing the mean norm $r_{mean}$ and showing that $\sup_{x\in\Omega} \|R_\theta(x) - R_{\theta'}(x)\|_{\infty}$ scales as $\max(D,1) (r_{mean})^{L-1} \sum_{\ell} N_{\ell-1} \|\theta-\theta'\|_\infty$, with CNN-specific refinements using $r_{conv}$ and $p_l^2 c_{l-1}$. The results relax earlier assumptions (arbitrary $r_\ell$) and provide far tighter bounds than prior work, validated on pretrained ResNet and MobileNetV2 models and multiple quantization schemes. The practical impact is twofold: it explains why weight quantization can work well in real networks and guides preprocessing steps like cross-layer equalization to tighten the bounds further. The work also outlines future directions toward Transformers and probabilistic analyses to complement the deterministic guarantees.
Abstract
This paper introduces novel theoretical approximation bounds for the output of quantized neural networks, with a focus on convolutional neural networks (CNN). By considering layerwise parametrization and focusing on the quantization of weights, we provide bounds that gain several orders of magnitude compared to state-of-the-art results on classical deep convolutional neural networks such as MobileNetV2 or ResNets. These gains are achieved by improving the behaviour of the approximation bounds with respect to the depth parameter, which has the most impact on the approximation error induced by quantization. To complement our theoretical result, we provide a numerical exploration of our bounds on MobileNetV2 and ResNets.