# Generalization Bounds for Equivariant Networks on Markov Data

arXiv: https://arxiv.org/abs/2503.00292 · HTML: https://mlsanity.com/paper/2503.00292/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 1 Mar 2025.

## Builds on (most cited first, 30 of 30)

- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [Provably Strict Generalisation Benefit for Equivariant Models](https://mlsanity.com/paper/2102.10333/) (2021)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [On the Benefits of Invariance in Neural Networks](https://mlsanity.com/paper/2005.00178/) (2020)
- [Sample Efficient Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2202.09468/) (2022)
- [TAX-Pose: Task-Specific Cross-Pose Estimation for Robot Manipulation](https://mlsanity.com/paper/2211.09325/) (2022)
- [Equivariant Transporter Network](https://mlsanity.com/paper/2202.09400/) (2022)
- [Generalization Error of Invariant Classifiers](https://mlsanity.com/paper/1610.04574/) (2016)
- [Provably Strict Generalisation Benefit for Invariance in Kernel Methods](https://mlsanity.com/paper/2106.02346/) (2021)
- [Stability Analysis and Generalization Bounds of Adversarial Training](https://mlsanity.com/paper/2210.00960/) (2022)
- [PDE-based Group Equivariant Convolutional Neural Networks](https://mlsanity.com/paper/2001.09046/) (2020)
- [SEIL: Simulation-augmented Equivariant Imitation Learning](https://mlsanity.com/paper/2211.00194/) (2022)
- [Understanding the Generalization Benefit of Model Invariance from a Data Perspective](https://mlsanity.com/paper/2111.05529/) (2021)
- [A PAC-Bayesian Generalization Bound for Equivariant Networks](https://mlsanity.com/paper/2210.13150/) (2022)
- [Equivariant Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/2408.14336/) (2024)
- [Generalization Error Bounds on Deep Learning with Markov Datasets](https://mlsanity.com/paper/2201.11059/) (2021)
- [PAC-Bayesian Spectrally-Normalized Bounds for Adversarially Robust Generalization](https://mlsanity.com/paper/2310.06182/) (2023)
- [Deep Neural Network for 3D Surface Segmentation based on Contour Tree Hierarchy](https://mlsanity.com/paper/2008.11269/) (2020)
- [A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging](https://mlsanity.com/paper/2110.10580/) (2021)
- [Deep neural network surrogates for non-smooth quantities of interest in shape uncertainty quantification](https://mlsanity.com/paper/2101.07023/) (2021)

## Abstract (arXiv)

Equivariant neural networks play a pivotal role in analyzing datasets with symmetry properties, particularly in complex data structures. However, integrating equivariance with Markov properties presents notable challenges due to the inherent dependencies within such data. Previous research has primarily concentrated on establishing generalization bounds under the assumption of independently and identically distributed data, frequently neglecting the influence of Markov dependencies. In this study, we investigate the impact of Markov properties on generalization performance alongside the role of equivariance within this context. We begin by applying a new McDiarmid's inequality to derive a generalization bound for neural networks trained on Markov datasets, using Rademacher complexity as a central measure of model capacity. Subsequently, we utilize group theory to compute the covering number under equivariant constraints, enabling us to obtain an upper bound on the Rademacher complexity based on this covering number. This bound provides practical insights into selecting low-dimensional irreducible representations, enhancing generalization performance for fixed-width equivariant neural networks.