RePs: Learning Representations from Known Response Laws

Existing augmentation-based self-supervised learning uses transformations to create new views, but often leaves their predictable effects on measurable signal properties unused. Our key insight is that when these effects follow known response laws, augmentation can generate not only new views but also new supervision: an existing measurement can be analytically transformed into the expected measurement of each augmented view. We introduce RePs (Response-law Privileged Supervision), which learns measurement-relevant representations by predicting these targets from augmented signals alone, without additional annotation. We test RePs across three distinct response structures and signal domains: temporal scaling in physiological signals, pitch translation in music, and spatial rotation in multichannel audio. RePs outperforms measurement-free baselines in frozen-feature response prediction across all three domains, reducing spatial angular error from $69.0^{\circ }$ to $20.2^{\circ }$. With only 10% downstream labels, its ECG representation leads four released encoders on four of five clinical tasks. Controlled ablations further show that direct response supervision yields lower nonlinear readout error than separately predicting source measurements and transformations, supporting known response laws as a source of supervision for representation learning.