Establishing the Relationship Between Jacobian Sensitivity and Perturbation Propagation in Post-Training Quantized Convolutional Neural Networks

Abstract

Post-training quantization (PTQ) is widely used to deploy convolutional neural networks (CNNs) on resource-constrained edge devices because it reduces model size, memory use and computational requirements without retraining. However, PTQ introduces numerical approximation errors whose effects may differ across architectures. This study examined the relationship between Jacobian sensitivity and perturbation propagation in post-training quantized CNNs using an Affine-Jacobian framework. Six architectures, MobileNetV2, InceptionV3, DenseNet121, VGG16, NASNetMobile and EfficientNetB0, were quantized from FP32 to INT8 using TensorFlow Lite without retraining. Local sensitivity was quantified using the Frobenius norm of the Jacobian matrix, while post-quantization robustness was evaluated through progressively increasing Gaussian perturbations on a Raspberry Pi edge platform. The architectures showed substantial differences in Jacobian sensitivity and perturbation response. MobileNetV2 recorded the largest mean Jacobian norm, whereas InceptionV3 showed the largest accuracy degradation at the highest reported noise level. Exploratory architecture-level analysis nevertheless indicated a positive association between Jacobian sensitivity and degradation, although the relationship was not perfectly monotonic and, with only six architectures, was not statistically conclusive at the 0.05 level. The findings therefore support the Affine-Jacobian framework as a promising sensitivity-based explanation of quantization robustness rather than as definitive proof of a universal predictor. The study provides a basis for sensitivity-aware model selection and further validation across additional architectures and deployment conditions.