LAWFUL: Law-Aligned Witness for Faithful Use of Latents

The paper introduces LAWFUL, a framework for testing whether a neural network has learned and actually uses a formal physical law over continuous variables, rather than merely producing accurate predictions. It targets four interpretability gaps: coverage-aware causal consistency over continuous counterfactuals, circuit validity across the law’s domain, verification of invariants and forbidden behaviors, and tracing derived quantities through the circuit. The framework currently closes the first two gaps and establishes groundwork for the others. Its demonstration uses a Mocap2Radar Transformer trained without explicit velocity or frequency inputs, testing the Doppler relation f(t)=2v(t)/λ.