# Beyond Importance: Interchange-Sobol Sensitivity Reveals Task-Specific Content Channels in Transformer Components

arXiv: https://arxiv.org/abs/2606.20678 · HTML: https://mlsanity.com/paper/2606.20678/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet](https://mlsanity.com/paper/2605.29358/) (2026)
- [AtP*: An efficient and scalable method for localizing LLM behaviour to components](https://mlsanity.com/paper/2403.00745/) (2024)
- [The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?](https://mlsanity.com/paper/2507.08802/) (2025)
- [Circuit Insights: Towards Interpretability Beyond Activations](https://mlsanity.com/paper/2510.14936/) (2025)
- [Extracting Interpretable Task-Specific Circuits from Large Language Models for Faster Inference](https://mlsanity.com/paper/2412.15750/) (2024)

## Built on by (most cited first, 3 of 3)

- [A Theory of Conditional Collapse under Low-Rank Weight-Space Ablations: I. The Single-Block Theory and Synthetic Validation](https://mlsanity.com/paper/2608.03620/) (2026)
- [Cross-Layer Interaction under Weight-Space Ablation: A Closed-Form Attention Jacobian Bound and a Test on a Real Pretrained Model](https://mlsanity.com/paper/2608.03629/) (2026)
- [Local Gains and Fixed-Assignment Set Losses in Shared Set Decoders](https://mlsanity.com/paper/2608.14717/) (2026)

## Abstract (arXiv)

Mechanistic interpretability methods summarize a transformer component by a single importance score, conflating two distinct roles: a component may matter because it transports task-relevant content, or because the forward computation degrades when its contribution is removed. We introduce Interchange-Group Sobol Decomposition (IGSD), a paired-intervention framework that compares matched activation replacement with zero ablation on the same component, estimates two Sobol-style variance indices, and uses their signed difference to separate the two roles, with intervention validity monitored by a symmetric off-manifold diagnostic widehatST>1. In factual recall, IGSD identifies an early-layer content channel in both GPT-2 small and Qwen2.5-1.5B that standard importance methods underestimate. A controlled subject and relation donor design shows that the early channel transports relation-frame content while late attention transports subject-retrieval content, refining at head granularity to the known AttnL9H8 head. Late-layer clamping confirms that the early signal is expressed through downstream transformations rather than residual pass-through. These results show that replacement and deletion are not interchangeable controls and their divergence provides a practical statistical diagnostic for content transport in transformer components.