# Learning with Category-Equivariant Architectures for Human Activity Recognition

arXiv: https://arxiv.org/abs/2511.01139 · HTML: https://mlsanity.com/paper/2511.01139/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Equivariance Through Parameter-Sharing](https://mlsanity.com/paper/1702.08389/) (2017)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)

## Built on by (most cited first, 3 of 3)

- [Categorical Equivariant Deep Learning: Category-Equivariant Neural Networks and Universal Approximation Theorems](https://mlsanity.com/paper/2511.18417/) (2025)
- [Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networks](https://mlsanity.com/paper/2607.03798/) (2026)
- [Capturing Cardiac Cyclicity through Phase-Equivariant Self-Supervised Learning](https://mlsanity.com/paper/2608.21147/) (2026)

## Abstract (arXiv)

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.