# On the Effectiveness of Equivariant Regularization for Robust Online Continual Learning

arXiv: https://arxiv.org/abs/2305.03648 · HTML: https://mlsanity.com/paper/2305.03648/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 53 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [Co2L: Contrastive Continual Learning](https://mlsanity.com/paper/2106.14413/) (2021)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)
- [Using Hindsight to Anchor Past Knowledge in Continual Learning](https://mlsanity.com/paper/2002.08165/) (2020)
- [Self-Supervised Models are Continual Learners](https://mlsanity.com/paper/2112.04215/) (2021)
- [Towards Robust Evaluations of Continual Learning](https://mlsanity.com/paper/1805.09733/) (2018)
- [Continual Prototype Evolution: Learning Online from Non-Stationary Data Streams](https://mlsanity.com/paper/2009.00919/) (2020)
- [Adversarial Continual Learning](https://mlsanity.com/paper/2003.09553/) (2020)
- [Boosting Few-Shot Visual Learning with Self-Supervision](https://mlsanity.com/paper/1906.05186/) (2019)

## Built on by (most cited first, 2 of 2)

- [On Understanding of the Dynamics of Model Capacity in Continual Learning](https://mlsanity.com/paper/2508.08052/) (2025)
- [An Attention-based Representation Distillation Baseline for Multi-Label Continual Learning](https://mlsanity.com/paper/2407.14249/) (2024)

## Abstract (arXiv)

Humans can learn incrementally, whereas neural networks forget previously acquired information catastrophically. Continual Learning (CL) approaches seek to bridge this gap by facilitating the transfer of knowledge to both previous tasks (backward transfer) and future ones (forward transfer) during training. Recent research has shown that self-supervision can produce versatile models that can generalize well to diverse downstream tasks. However, contrastive self-supervised learning (CSSL), a popular self-supervision technique, has limited effectiveness in online CL (OCL). OCL only permits one iteration of the input dataset, and CSSL's low sample efficiency hinders its use on the input data-stream. In this work, we propose Continual Learning via Equivariant Regularization (CLER), an OCL approach that leverages equivariant tasks for self-supervision, avoiding CSSL's limitations. Our method represents the first attempt at combining equivariant knowledge with CL and can be easily integrated with existing OCL methods. Extensive ablations shed light on how equivariant pretext tasks affect the network's information flow and its impact on CL dynamics.