mlsanityData to 7 Oct 2026

LAWFUL: Law-Aligned Witness for Faithful Use of Latents

arXiv 2607.28672 ↗First posted 26 Jul 2026cs.LG cs.AIcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 22 of its 25 references that are in the map. First posted on arXiv 26 Jul 2026.

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22 of 25 references.

References · 22

  1. 2016Understanding intermediate layers using linear classifier probescited by 1,279
  2. 2022Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 smallcited by 1,130
  3. 2021Probing Classifiers: Promises, Shortcomings, and Advancescited by 831
  4. 2023Progress measures for grokking via mechanistic interpretabilitycited by 822
  5. 2023Towards Automated Circuit Discovery for Mechanistic Interpretabilitycited by 700
  6. 2019Designing and Interpreting Probes with Control Taskscited by 608
  7. 2024Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Modelscited by 412
  8. 2023LEACE: Perfect linear concept erasure in closed formcited by 254
  9. 2023Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representationscited by 197
  10. 2023Attribution Patching Outperforms Automated Circuit Discoverycited by 196
  11. 2023Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretabilitycited by 194
  12. 2024How to use and interpret activation patchingcited by 191
10 more
  1. 2023Interpretability at Scale: Identifying Causal Mechanisms in Alpacacited by 102
  2. 2023Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patchingcited by 75
  3. 2025What Has a Foundation Model Found? Using Inductive Bias to Probe for World Modelscited by 46
  4. 2025The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?cited by 34
  5. 2023Interpretability Illusions in the Generalization of Simplified Modelscited by 24
  6. 2023Evaluating the Robustness of Interpretability Methods through Explanation Invariance and Equivariancecited by 13
  7. 2026Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guaranteescited by 10
  8. 2026From Kepler to Newton: Inductive Biases Guide Learned World Models in Transformerscited by 6
  9. 2026Actionable Interpretability Must Be Defined in Terms of Symmetriescited by 4
  10. 2026What Physics do Data-Driven MoCap-to-Radar Models Learn?cited by 1

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