# Regularizing Towards Permutation Invariance in Recurrent Models

arXiv: https://arxiv.org/abs/2010.13055 · HTML: https://mlsanity.com/paper/2010.13055/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2020.

## Built on by (most cited first, 13 of 13)

- [Learnable Commutative Monoids for Graph Neural Networks](https://mlsanity.com/paper/2212.08541/) (2022)
- [Set-based Neural Network Encoding Without Weight Tying](https://mlsanity.com/paper/2305.16625/) (2023)
- [Learning Graph Search Heuristics](https://mlsanity.com/paper/2212.03978/) (2022)
- [Permutation-Invariant Tabular Data Synthesis](https://mlsanity.com/paper/2211.09286/) (2022)
- [Impartial Games: A Challenge for Reinforcement Learning](https://mlsanity.com/paper/2205.12787/) (2022)
- [Overcoming Order in Autoregressive Graph Generation](https://mlsanity.com/paper/2402.03387/) (2024)
- [Sequential Signal Mixing Aggregation for Message Passing Graph Neural Networks](https://mlsanity.com/paper/2409.19414/) (2024)
- [Causal Deepsets for Off-policy Evaluation under Spatial or Spatio-temporal Interferences](https://mlsanity.com/paper/2407.17910/) (2024)
- [The Impossibility of Inverse Permutation Learning in Transformer Models](https://mlsanity.com/paper/2509.24125/) (2025)
- [Iteratively Refined Early Interaction Alignment for Subgraph Matching based Graph Retrieval](https://mlsanity.com/paper/2510.22538/) (2025)
- [Exploring Parity Challenges in Reinforcement Learning through Curriculum Learning with Noisy Labels](https://mlsanity.com/paper/2312.05379/) (2023)
- [Information Topology](https://mlsanity.com/paper/2210.03850/) (2022)
- [What is Intelligence? A Cycle Closure Perspective](https://mlsanity.com/paper/2404.05484/) (2024)

## Abstract (arXiv)

In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recurrent architectures. We implement this idea via a novel form of stochastic regularization. Existing solutions mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design. Our approach of enforcing permutation invariance via regularization gives rise to models which are textitsemi permutation invariant (e.g. invariant to some permutations and not to others). We show that our method outperforms other permutation invariant approaches on synthetic and real world datasets.