# Patterning: The Dual of Interpretability

arXiv: https://arxiv.org/abs/2601.13548 · HTML: https://mlsanity.com/paper/2601.13548/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 20 Jan 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)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Transformer visualization via dictionary learning: contextualized embedding as a linear superposition of transformer factors](https://mlsanity.com/paper/2103.15949/) (2021)
- [The Local Learning Coefficient: A Singularity-Aware Complexity Measure](https://mlsanity.com/paper/2308.12108/) (2023)
- [Is SGD a Bayesian sampler? Well, almost](https://mlsanity.com/paper/2006.15191/) (2020)
- [Deep Learning is Singular, and That's Good](https://mlsanity.com/paper/2010.11560/) (2020)
- [Loss Landscape Degeneracy and Stagewise Development in Transformers](https://mlsanity.com/paper/2402.02364/) (2024)
- [Differentiation and Specialization of Attention Heads via the Refined Local Learning Coefficient](https://mlsanity.com/paper/2410.02984/) (2024)
- [Bayesian Influence Functions for Hessian-Free Data Attribution](https://mlsanity.com/paper/2509.26544/) (2025)
- [Structural Inference: Interpreting Small Language Models with Susceptibilities](https://mlsanity.com/paper/2504.18274/) (2025)
- [Can Interpretation Predict Behavior on Unseen Data?](https://mlsanity.com/paper/2507.06445/) (2025)
- [Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theory](https://mlsanity.com/paper/2510.12077/) (2025)
- [Stagewise Reinforcement Learning and the Geometry of the Regret Landscape](https://mlsanity.com/paper/2601.07524/) (2026)

## Built on by (most cited first, 7 of 7)

- [Infusion: Shaping Model Behavior by Editing Training Data via Influence Functions](https://mlsanity.com/paper/2602.09987/) (2026)
- [Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning](https://mlsanity.com/paper/2605.07980/) (2026)
- [Linear Response Estimators for Singular Statistical Models](https://mlsanity.com/paper/2605.07970/) (2026)
- [Interpreting Reinforcement Learning Agents with Susceptibilities](https://mlsanity.com/paper/2605.08007/) (2026)
- [Gradient Atoms: Unsupervised Discovery, Attribution and Steering of Model Behaviors via Sparse Decomposition of Training Gradients](https://mlsanity.com/paper/2603.14665/) (2026)
- [Patterning in Practice: Debiasing Reward Models with Susceptibilities](https://mlsanity.com/paper/2609.00699/) (2026)
- [Verifier Errors in RLVR: Reward Hacking, Limits of Feedback, and Selective Control](https://mlsanity.com/paper/2609.35677/) (2026)

## Abstract (arXiv)

Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization, determine what training data produces it. Our approach is based on susceptibilities, which measure how posterior expectation values of observables respond to infinitesimal shifts in the data distribution. Inverting this linear response relationship yields the data intervention that steers the model toward a target internal configuration. We demonstrate patterning in a small language model, showing that re-weighting training data along principal susceptibility directions can accelerate or delay the formation of structure, such as the induction circuit. In a synthetic parentheses balancing task where multiple algorithms achieve perfect training accuracy, we show that patterning can select which algorithm the model learns by targeting the local learning coefficient of each solution. These results establish that the same mathematical framework used to read internal structure can be inverted to write it.