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.

翻译：本文针对量化神经网络的输出提出了新的理论近似界，重点关注卷积神经网络（CNN）。通过考虑逐层参数化并聚焦于权重量化，我们在经典深度卷积神经网络（如MobileNetV2和ResNets）上获得了比现有最优结果高出数个数量级的界。这一改进是通过优化近似界相对于深度参数的行为而实现的，该参数对量化引起的近似误差具有最关键的影响。为补充理论结果，我们在MobileNetV2和ResNets上对所得界进行了数值验证。