LAWFUL: Law-Aligned Witness for Faithful Use of Latents

2026-07-25

AI Summary

This work addresses the ongoing challenge of determining whether neural networks genuinely learn and internally utilize physical laws in continuous-variable settings, particularly with respect to causal consistency and domain validity. To this end, the authors propose LAWFUL, a novel framework that introduces, for the first time, coverage-aware causal consistency metrics and circuit-based effective domain testing for continuous physical laws. By integrating counterfactual reasoning, circuit analysis, invariance validation, and information flow tracing, the framework verifies the internal use of the Doppler shift law $f(t) = \frac{2v(t)}{\lambda}$ within a Mocap2Radar Transformer. Experimental results demonstrate that the model faithfully and consistently encodes and applies this physical principle—even without explicit supervision on velocity or frequency—thereby bridging a critical gap in the physical interpretability of neural networks.

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 $f(t) = \frac{2 v(t)}λ$ from motion-capture and radar data in which neither $f(t)$ nor $v(t)$ appears.

Problem

• interpretability
• physics laws
• neural networks
• causal consistency
• domain of validity

Innovation

• LAWFUL
• causal-consistency
• domain-of-validity
• physics laws
• interpretable AI