Explaining why a language model produces a particular output requires local, input-level explanations. Existing methods uncover global capability circuits (e.g., indirect object identification), but not why the model answers a specific input query in a particular way. We introduce query circuits, which directly trace the information flow inside a model that maps a specific input to the output. Unlike surrogate-based approaches (e.g., sparse autoencoders), query circuits are identified within the model itself, resulting in more faithful and computationally accessible explanations. To make query circuits practical, we address two challenges. First, we introduce Normalized Deviation Faithfulness (NDF), a robust metric to evaluate how well a discovered circuit recovers the model's decision for a specific input, and is broadly applicable to circuit discovery beyond our setting. Second, we develop sampling-based methods to efficiently identify circuits that are sparse yet faithfully describe the model's behavior. Across benchmarks (IOI, arithmetic, MMLU, and ARC), we find that there exist extremely sparse query circuits within the model that can recover much of its performance on single queries. For example, a circuit covering only 1.3% of model connections can recover about 60% of performance on an MMLU questions. Overall, query circuits provide a step towards faithful, scalable explanations of how language models process individual inputs.

Transformer-based language models have achieved significant success; however, their internal mechanisms remain largely opaque due to the complexity of non-linear interactions and high-dimensional operations. While previous studies have demonstrated that these models implicitly embed reasoning trees, humans typically employ various distinct logical reasoning mechanisms to complete the same task. It is still unclear which multi-step reasoning mechanisms are used by language models to solve such tasks. In this paper, we aim to address this question by investigating the mechanistic interpretability of language models, particularly in the context of multi-step reasoning tasks. Specifically, we employ circuit analysis and self-influence functions to evaluate the changing importance of each token throughout the reasoning process, allowing us to map the reasoning paths adopted by the model. We apply this methodology to the GPT-2 model on a prediction task (IOI) and demonstrate that the underlying circuits reveal a human-interpretable reasoning process used by the model.

Understanding the internal mechanisms of transformer-based language models remains challenging. Mechanistic interpretability based on circuit discovery aims to reverse engineer neural networks by analyzing their internal processes at the level of computational subgraphs. In this paper, we revisit existing gradient-based circuit identification methods and find that their performance is either affected by the zero-gradient problem or saturation effects, where edge attribution scores become insensitive to input changes, resulting in noisy and unreliable attribution evaluations for circuit components. To address the saturation effect, we propose Edge Attribution Patching with GradPath (EAP-GP), EAP-GP introduces an integration path, starting from the input and adaptively following the direction of the difference between the gradients of corrupted and clean inputs to avoid the saturated region. This approach enhances attribution reliability and improves the faithfulness of circuit identification. We evaluate EAP-GP on 6 datasets using GPT-2 Small, GPT-2 Medium, and GPT-2 XL. Experimental results demonstrate that EAP-GP outperforms existing methods in circuit faithfulness, achieving improvements up to 17.7%. Comparisons with manually annotated ground-truth circuits demonstrate that EAP-GP achieves precision and recall comparable to or better than previous approaches, highlighting its effectiveness in identifying accurate circuits.

Many recent language model (LM) interpretability studies have adopted the circuits framework, which aims to find the minimal computational subgraph, or circuit, that explains LM behavior on a given task. Most studies determine which edges belong in a LM's circuit by performing causal interventions on each edge independently, but this scales poorly with model size. Edge attribution patching (EAP), gradient-based approximation to interventions, has emerged as a scalable but imperfect solution to this problem. In this paper, we introduce a new method - EAP with integrated gradients (EAP-IG) - that aims to better maintain a core property of circuits: faithfulness. A circuit is faithful if all model edges outside the circuit can be ablated without changing the model's performance on the task; faithfulness is what justifies studying circuits, rather than the full model. Our experiments demonstrate that circuits found using EAP are less faithful than those found using EAP-IG, even though both have high node overlap with circuits found previously using causal interventions. We conclude more generally that when using circuits to compare the mechanisms models use to solve tasks, faithfulness, not overlap, is what should be measured.