Kenneth Parker

Kevin Chen, Kenneth W. Parker, Anish Arora

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.

Kevin Chen, Kenneth W. Parker, Anish Arora

We present a pure machine learning process for synthesizing radar spectrograms from Motion-Capture (MoCap) data. We formulate MoCap-to-spectrogram translation as a windowed sequence-to-sequence task using a transformer-based model that jointly captures spatial relations among MoCap markers and temporal dynamics across frames. Real-world experiments show that the proposed approach produces visually and quantitatively plausible doppler radar spectrograms and achieves good generalizability. Ablation experiments show that the learned model includes both the ability to convert multi-part motion into doppler signatures and an understanding of the spatial relations between different parts of the human body. The result is an interesting example of using transformers for time-series signal processing. It is especially applicable to edge computing and Internet of Things (IoT) radars. It also suggests the ability to augment scarce radar datasets using more abundant MoCap data for training higher-level applications. Finally, it requires far less computation than physics-based methods for generating radar data.

Kevin Chen, Kenneth W. Parker, Anish Arora

Data-driven MoCap-to-radar models generate plausible micro-Doppler spectrograms, but do they actually learn the underlying physics? We introduce a physics-based interpretability framework to answer this question via two proposed complementary metrics: one measures alignment between model predictions and the physics-derived Doppler frequency, while the other tests whether predictions preserve the velocity-frequency relationship under velocity intervention. Both metrics require only MoCap input and model predictions, without access to measured radar data. Experiments across several model architectures reveal that low reconstruction error does not guarantee physical consistency: some, but not all, models achieve low error yet perform poorly on the two physics-based metrics. Further analysis shows that temporal attention is critical for transformer-based models to learn the underlying physics.