LAWFUL: Law-Aligned Witness for Faithful Use of Latents
For interpretability researchers, this provides a foundational method to verify if networks encode formal laws, but it is an initial step with limited scope.
The paper introduces LAWFUL, a framework to test whether neural networks learn and use formal physics laws internally, addressing interpretability gaps like coverage-aware causal consistency and domain-of-validity testing. Applied to a Mocap2Radar transformer, it validates whether the network uses the Doppler frequency law, finding evidence of internal use.
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 $f(t) = \frac{2 v(t)}λ$ from motion-capture and radar data in which neither $f(t)$ nor $v(t)$ appears.