LAWFUL: Law-Aligned Witness for Faithful Use of Latents
arXiv:2607.28672v1 Announce Type: new Abstract: 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 $f(t) = \frac{2 v(t)}{\lambda}$ from motion-capture and radar data in which neither $f(t)$ nor $v(t)$ appears.
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[Submitted on 26 Jul 2026]
Title:LAWFUL: Law-Aligned Witness for Faithful Use of Latents
View a PDF of the paper titled LAWFUL: Law-Aligned Witness for Faithful Use of Latents, by Kevin Chen and 2 other authors
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Abstract: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 $f(t) = \frac{2 v(t)}{\lambda}$ from motion-capture and radar data in which neither $f(t)$ nor $v(t)$ appears.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2607.28672 [cs.LG]
(or arXiv:2607.28672v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.28672
arXiv-issued DOI via DataCite
Submission history
From: Kevin Chen [view email] [v1] Sun, 26 Jul 2026 01:32:45 UTC (527 KB)
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