LAWFUL Framework Interprets AI's Understanding of Physics Laws

When neural networks accurately predict physical systems, it's often unclear if they have truly learned the underlying governing laws as structured knowledge, or if they merely mimic observed patterns. Furthermore, it's difficult to ascertain if the network's internal computations consistently apply this learned law across its entire domain of validity. This research identifies four key interpretability gaps that hinder answering these questions for physics laws involving continuous variables. These gaps include the lack of a measure for coverage-aware causal-consistency over continuous counterfactuals, a robust test for the domain of validity of an identified circuit, verification of a law's invariants and forbidden behaviors, and quantification of how derived physical quantities flow through the circuit. To address these challenges, the researchers developed LAWFUL (Law-Aligned Witness for Faithful Use of Latents), a foundational framework. LAWFUL closes the first two interpretability gaps and lays groundwork for the others. The framework was demonstrated on a Mocap2Radar transformer model, validating whether it learned and internally utilized the Doppler frequency law, even though neither frequency nor velocity explicitly appeared in the input data. This work represents a significant step towards more transparent and trustworthy AI in scientific applications.