Learning with Category-Equivariant Architectures for Human Activity Recognition

TL;DR

The paper addresses robust HAR from inertial sensors under structural distribution shifts such as time phase, pose, and calibration gain drift. It introduces CatEquiv, a category-equivariant neural network whose linear core implements a natural transformation between data and feature mappings over a symmetry category. Key architectural components include circular time convolutions, per-sensor RMS/log-RMS normalization, axis-shared filters with invariant readout, and sensor-shared multi-scale branches that preserve the category symmetry. Experiments on UCI-HAR show CatEquiv outperforms baseline CNNs under composite out-of-distribution perturbations, demonstrating improved invariance and generalization without increasing model capacity.

Abstract

We propose CatEquiv, a category-equivariant neural network for Human Activity Recognition (HAR) from inertial sensors that systematically encodes temporal, amplitude, and structural symmetries. We introduce a symmetry category that jointly represents cyclic time shifts, positive gain scalings, and the sensor-hierarchy poset, capturing the categorical symmetry structure of the data. CatEquiv achieves equivariance with respect to the categorical symmetry product. On UCI-HAR under out-of-distribution perturbations, CatEquiv attains markedly higher robustness compared with circularly padded CNNs and plain CNNs. These results demonstrate that enforcing categorical symmetries yields strong invariance and generalization without additional model capacity.

Theorems & Definitions (10)

• lemma 1: Normalization robustness with floor
• proof
• proposition 1: Readout and $C_T$ invariance
• proof
• lemma 2: GN–$C_T$ commutation
• proof
• proposition 2: Naturality on $P$ <=> no cross-sensor mixing
• proof
• proposition 3: Naturality of the linear core over $\mathcal{C}_3$
• proof