# Mechanistic Tomography: Designed Measurement for Control-Oriented Interpretability

arXiv: https://arxiv.org/abs/2608.19338 · HTML: https://mlsanity.com/paper/2608.19338/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders](https://mlsanity.com/paper/2501.17148/) (2025)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [The Hydra Effect: Emergent Self-repair in Language Model Computations](https://mlsanity.com/paper/2307.15771/) (2023)
- [Analyzing the Generalization and Reliability of Steering Vectors](https://mlsanity.com/paper/2407.12404/) (2024)
- [Tracr: Compiled Transformers as a Laboratory for Interpretability](https://mlsanity.com/paper/2301.05062/) (2023)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)
- [Sparse Autoencoders Do Not Find Canonical Units of Analysis](https://mlsanity.com/paper/2502.04878/) (2025)
- [Transformers represent belief state geometry in their residual stream](https://mlsanity.com/paper/2405.15943/) (2024)
- [Copy Suppression: Comprehensively Understanding an Attention Head](https://mlsanity.com/paper/2310.04625/) (2023)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [Towards Unifying Interpretability and Control: Evaluation via Intervention](https://mlsanity.com/paper/2411.04430/) (2024)
- [New Algorithms for Learning Incoherent and Overcomplete Dictionaries](https://mlsanity.com/paper/1308.6273/) (2013)
- [ProxySPEX: Inference-Efficient Interpretability via Sparse Feature Interactions in LLMs](https://mlsanity.com/paper/2505.17495/) (2025)
- [Activation Steering with a Feedback Controller](https://mlsanity.com/paper/2510.04309/) (2025)
- [The Bayesian Geometry of Transformer Attention](https://mlsanity.com/paper/2512.22471/) (2025)
- [SPEX: Scaling Feature Interaction Explanations for LLMs](https://mlsanity.com/paper/2502.13870/) (2025)
- [Interpretability Can Be Actionable](https://mlsanity.com/paper/2605.11161/) (2026)
- [Gradient Dynamics of Attention: How Cross-Entropy Sculpts Bayesian Manifolds](https://mlsanity.com/paper/2512.22473/) (2025)
- [Geometric Scaling of Bayesian Inference in LLMs](https://mlsanity.com/paper/2512.23752/) (2025)

## Built on by (most cited first, 2 of 2)

- [ObserverBench: Testing Mechanistic Estimates for Intervention and Control](https://mlsanity.com/paper/2609.03026/) (2026)
- [Structure is not mechanism: high-gain gated-FFN rows across text and genomic foundation models](https://mlsanity.com/paper/2609.17599/) (2026)

## Abstract (arXiv)

Mechanistic interpretability seeks quantities that models do not expose directly: represented states, component effects, interactions, and responses to interventions. Patching, gradients, Hessian-vector products, and subset interventions provide different measurements under different access assumptions and may target different quantities. We formulate their shared measurement structure as mechanistic tomography: designed measurement for recovering internal mechanisms and intervention effects. For a chosen basis and intervention family, measurements take the form y = Ax + w, where A describes the interventions, x is the target map, and w contains nonlinear response, sampling error, and basis misspecification. This language gives a practical procedure: start with the least costly measurements, test on held-out interventions at the intended scale, calibrate simple mismatch, and expand the measurement family when structured residuals remain. Control provides a demanding validation setting because an estimate that guides an intervention acts as an observer. In a two-HMM model, control error rises with observer error, while target improvement can hide nuisance-state movement. Under forward-only access, sparse aggregate measurements recover a finite-effect map with fewer interventions than coordinate patching. With gradient access, finite probes improve a local attribution map. Lifted measurements and Hessian-vector products recover interactions missed by first-order maps, while Tracr shows that the required family depends on the basis. On GPT-2-small IOI, the Name Mover-Negative Name Mover interaction is the largest held-out predictive term among three tested cross-group pairs. On Qwen-2.5-7B, finite calibration makes an additive refusal-response map adequate, so held-out error does not support pairwise lifting.