# Slaying the Hydra: Interaction-Aware Circuit Discovery in Language Models

arXiv: https://arxiv.org/abs/2610.04017 · HTML: https://mlsanity.com/paper/2610.04017/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 19 of 19)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [The Hydra Effect: Emergent Self-repair in Language Model Computations](https://mlsanity.com/paper/2307.15771/) (2023)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [Causal Analysis of Syntactic Agreement Mechanisms in Neural Language Models](https://mlsanity.com/paper/2106.06087/) (2021)
- [A Mechanistic Interpretation of Arithmetic Reasoning in Language Models using Causal Mediation Analysis](https://mlsanity.com/paper/2305.15054/) (2023)
- [Reparameterizable Subset Sampling via Continuous Relaxations](https://mlsanity.com/paper/1901.10517/) (2019)
- [Missed Causes and Ambiguous Effects: Counterfactuals Pose Challenges for Interpreting Neural Networks](https://mlsanity.com/paper/2407.04690/) (2024)
- [The Curse of Multiple Mediators: Hidden Interaction Effects in Activation Patching](https://mlsanity.com/paper/2606.27510/) (2026)
- [Rethinking Circuit Completeness in Language Models: AND, OR, and ADDER Gates](https://mlsanity.com/paper/2505.10039/) (2025)
- [Conditional Co-Ablation: Recovering Self-Repair Backups in Transformer Circuits](https://mlsanity.com/paper/2607.01940/) (2026)
- [A Computationally Feasible Framework for Causal Probabilistic Explanation](https://mlsanity.com/paper/2609.04177/) (2026)
- [Matryoshka attribution: Learning to attribute language model outputs to representations and weights](https://mlsanity.com/paper/2609.25518/) (2026)

## Abstract (arXiv)

Localizing behavior to individual components of a language model is a central goal of mechanistic interpretability. However, scoring components one at a time misses context-dependent effects: a primary component can inhibit the activation of a backup, leading to issues with ranking components. Actual causality studies the structure of such interactions via witnesses: variables that provide contextual information to resolve interaction terms. However, estimation with witnesses typically requires combinatorial enumeration and is infeasible in practice. We introduce the witness-integrated set effect (WISE), a family of causal estimands that build on the witness mechanism while taking expectations over sets of causes and witnesses to remain computationally feasible. Building on this approach, we introduce JuntaLearner, a gradient-based circuit discovery method that learns to rank components by their causal impact across varying-sized sets of components and witnesses. Alongside faithfulness metrics, we introduce measures of necessity and task specificity, and the circuit recognition score (CRS) to summarize each metric across circuit sizes while emphasizing effects achieved by small circuits. Across tasks and models of increasing size, JuntaLearner achieves higher mean CRS compared to attribution baselines on all metrics. Since its cost does not grow with the number of candidate components, JuntaLearner scales to large models while accounting for set-level interactions and avoiding first-order approximations.