# LAWFUL: Law-Aligned Witness for Faithful Use of Latents

arXiv: https://arxiv.org/abs/2607.28672 · HTML: https://mlsanity.com/paper/2607.28672/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 25 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [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)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)
- [Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching](https://mlsanity.com/paper/2311.17030/) (2023)
- [What Has a Foundation Model Found? Using Inductive Bias to Probe for World Models](https://mlsanity.com/paper/2507.06952/) (2025)
- [The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?](https://mlsanity.com/paper/2507.08802/) (2025)
- [Interpretability Illusions in the Generalization of Simplified Models](https://mlsanity.com/paper/2312.03656/) (2023)
- [Evaluating the Robustness of Interpretability Methods through Explanation Invariance and Equivariance](https://mlsanity.com/paper/2304.06715/) (2023)
- [Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees](https://mlsanity.com/paper/2602.16823/) (2026)
- [From Kepler to Newton: Inductive Biases Guide Learned World Models in Transformers](https://mlsanity.com/paper/2602.06923/) (2026)
- [Actionable Interpretability Must Be Defined in Terms of Symmetries](https://mlsanity.com/paper/2601.12913/) (2026)
- [What Physics do Data-Driven MoCap-to-Radar Models Learn?](https://mlsanity.com/paper/2605.00018/) (2026)

## Abstract (arXiv)

When a neural network predicts a physical system accurately, has it learned the governing law as formal, structured knowledge, and if so, does the network's internal computation actually use that representation throughout the law's domain of validity? We identify four interpretability gaps that limit answering these questions for em physics laws over continuous variables: the absence of a coverage-aware causal-consistency measure over continuous counterfactuals; of a domain-of-validity test for the identified circuit; of a verification of the law's invariants and forbidden behaviors; and of a quantification of how a derived physical quantity flows through the circuit. We develop a foundational framework, LAWFUL, that closes the first two and lays groundwork for the remaining two, and illustrate it on the Mocap2Radar transformer, validating whether it learns and internally uses the Doppler frequency law f(t) = frac2 v(t)λ from motion-capture and radar data in which neither f(t) nor v(t) appears.