Circuit Condensation: Post-Training that Concentrates a Behavior's Causal Circuit

One approach to mechanistic interpretability explains behavior through circuits: the components and connections that carry it. Frozen discovery often returns hundreds of edges, making them hard to inspect, compare, or verify exhaustively. We introduce Circuit Condensation, which post-trains models to concentrate behaviors into smaller causal graphs. Each round prunes low-attribution edges and trains a low-rank adapter to match the original through what remains, retaining the cut only if task performance and general capability survive. Across four behaviors and eight models, condensed circuits are smaller than the strongest frozen baseline in 30 of 32 settings, by $8.1\times$ on average and up to $316\times$. Repeating the search without weight updates produces larger circuits in 29 of 32 settings, showing that weight updates, rather than search alone, drive the reduction. Testing every subset of 19 circuits finds 11 that cannot be reduced and reveals removable edges in the rest. Pair ablations expose dependencies between edges, showing that their effects cannot be understood independently. On indirect object identification, condensation isolates 24 heads, 17 of them with documented roles, against 61 heads and 36 undocumented ones for the matched frozen circuit: a sufficient sub-circuit of the published mechanism rather than a reconstruction of it. The resulting circuit tracks the original model's next-token distribution and predicts its errors.

Human-Guided Causal Knowledge Injection for Virtual Cells

Virtual cells employ machine learning models to simulate and predict cellular behaviors, serving as a critical computational framework for investigating health and disease. Injecting causal graphs into virtual cells can improve the interpretability, but such graphs are usually not available in real-world applications. Recently, many methods have been proposed to construct causal graphs from data, which group genes based on their similarities to form concepts and extract their causal relationships. However, since this automatic process is unsupervised, the causal graphs usually contain errors. In this paper, we propose a human-guided causal knowledge injection method for virtual cells. We developed a gene-similarity-aware causal graph visualization supported by a hybrid optimization algorithm to help explore both the causal relationships between concepts and the similarities between genes. Based on the exploration, we further developed a counterfactual analysis strategy supported by a counterfactual visualization and a causal path visualization to help validate and refine causal graphs. The effectiveness of our method is demonstrated through two real-world case studies, the extraction of scientifically meaningful causal insights, and positive feedback from domain experts.

Beyond Shapley: Efficient Computation of Asymmetric Shapley Values

We address the problem of explainability in machine learning models through feature attribution methods. In particular, we consider a variant of Shapley values known as Asymmetric Shapley Values (ASV), which enables the incorporation of causal knowledge into model-agnostic explanations through the use of a causal graph. We show that in certain contexts in which the computation of SHAP is $\#P$-hard, the exact computation of ASV can be done in polynomial time. To extend this algorithmic result, we introduce a notion of equivalence classes over the topological orderings of the underlying causal graph, which is useful to reduce the time to compute ASV. In particular, we present a polynomial-time algorithm (in the number of equivalence classes) to compute it whenever the causal graph is a rooted directed tree. Finally, we develop an algorithm for approximating ASV in arbitrary causal DAGs which relies on a procedure to sample topological orderings uniformly at random. To implement this sampling mechanism we leverage known algorithms as well as simpler alternatives. Our experimental results demonstrate the practical viability of the proposed approach in realistic causal structures.

Structure Over Scale: Schema-Constrained Causal Graphs for RAG

Graph-based retrieval-augmented generation (GraphRAG) grounds answers in structured knowledge, but current systems extract entities and relationships exhaustively, producing graphs whose size and construction cost scale with corpus length rather than with the reasoning a query requires. We introduce HCG-RAG (Hierarchical Causal Graph RAG), which replaces open-ended extraction with schema-constrained causal graphs: an automated pipeline distills a corpus into a fixed, typed vocabulary of causal variables and materializes a compact two-tier graph over it. Our schema-constrained graphs match entity-relation baselines on answer quality at a fraction of the cost: 3-20x fewer nodes, 8x-135x fewer build-time LLM calls than the most LLM-intensive baseline (MS-GraphRAG), and graphs compact enough for a domain expert to audit, correct, and extend. On medical and clinical benchmarks, including a neurologist-validated epilepsy dataset, HCG-RAG matches or exceeds the best entity-relation systems. An ablation isolates the causal graph as a structured retrieval filter, contributing +6 percentage points (pp) over embedding-only retrieval. Across all domains with discoverable hierarchical causal structure, only methods imposing higher-level organization outperform flat entity-relation retrieval, indicating that what is placed in the graph matters more than how many nodes it contains.