Atomic Information Flow: A Network Flow Model for Tool Attributions in RAG Systems

Many tool-based Retrieval Augmented Generation (RAG) systems lack precise mechanisms for tracing final responses back to specific tool components – a critical gap as systems scale to complex multi-agent architectures. We present $\mathbf{\text{Atomic}}\mathbf{\text{Information}}\mathbf{\text{Flow}}\mathbf{\text{(AIF)}}$, a graph-based network flow model that decomposes tool outputs and LLM calls into atoms: indivisible, self-contained units of information. By modeling LLM orchestration as a directed flow of atoms from tool and LLM nodes to a response super-sink, AIF enables granular attribution metrics for AI explainability. Motivated by the max-flow min-cut theorem in network flow theory, we train a lightweight Gemma3 (4B parameter) language model as a context compressor to approximate the minimum cut of tool atoms using flow signals computed offline by AIF. We note that the base Gemma3-4B model struggles to identify critical information with $\mathbf{\text{54.7\%}}$ accuracy on HotpotQA, barely outperforming lexical baselines (BM25). However, post-training on AIF signals boosts accuracy to $\mathbf{\text{82.71\%}}$ (+28.01 points) while achieving $\mathbf{\text{87.52\%}}$ (+1.85%) context token compression – bridging the gap with the Gemma3-27B variant, a model nearly $7\times$ larger.