InfoQ: Mixed-Precision Quantization via Global Information Flow

Mixed-precision quantization (MPQ) is crucial for deploying deep neural networks on resource-constrained devices, but finding the optimal bit-width for each layer represents a complex combinatorial optimization problem. Current state-of-the-art methods rely on computationally expensive search algorithms or local sensitivity heuristic proxies like the Hessian, which fail to capture the cascading global effects of quantization error. In this work, we argue that the quantization sensitivity of a layer should not be measured by its local properties, but by its impact on the information flow throughout the entire network. We introduce InfoQ, a novel framework for mixed-precision quantization that is training-free in the bit-width search phase. InfoQ assesses layer importance by performing a single forward pass to measure the change in mutual information in the remaining part of the network, thus creating a global sensitivity score. This approach directly quantifies how quantizing one layer degrades the information characteristics of subsequent layers. The resulting scores are used to formulate bit-width allocation as an integer linear programming problem, which is solved efficiently to minimize total sensitivity under a given budget (e.g., model size or BitOps). Our retraining-free search phase provides a superior search-time/accuracy trade-off (using two orders of magnitude less data compared to state-of-the-art methods such as LIMPQ), while yielding up to a 1\% accuracy improvement for MobileNetV2 and ResNet18 on ImageNet at high compression rates (14.00$\times$ and 10.66$\times$).