FlowPrune: Accelerating Attention Flow Calculation by Pruning Flow Network

The Transformer architecture serves as the foundation of modern AI systems, powering recent advances in Large Language Models (LLMs) and Large Multimodal Models (LMMs). Central to these models, attention mechanisms capture contextual dependencies via token interactions. Beyond inference, attention has been widely adopted for interpretability, offering insights into model behavior. Among interpretability techniques, attention flow --- which traces global information transfer across layers --- provides a more comprehensive perspective than single-layer attention maps. However, computing attention flow is computationally intensive due to the high complexity of max-flow algorithms. To address this challenge, we introduce FlowPrune, a novel framework that accelerates attention flow analysis by pruning the attention graph before applying max-flow computations. FlowPrune uses the Max-Flow Min-Cut Theorem and two structural properties of Transformer to identify and eliminate non-critical graph regions. It comprises two components: Edge Pruning, which removes insignificant attention edges, and Layer Compression, which discards layers with minimal contributions to the flow. We conduct extensive experiments on LLaMA and LLaVA to evaluate the robustness and effectiveness of FlowPrune. Our results show that FlowPrune achieves high agreement with the original attention flow in both absolute and relative error metrics, as well as in identifying influential input tokens. Finally, case studies in both NLP and vision domains demonstrate that FlowPrune produces consistent interpretability outcomes as the original Attention Flow, validating its practical utility. The code for this paper is publicly available.