# Latent Spectral Regularization for Continual Learning

arXiv: https://arxiv.org/abs/2301.03345 · HTML: https://mlsanity.com/paper/2301.03345/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 66 references that are in the map.
- First posted on arXiv 9 Jan 2023.

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [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)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (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)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [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)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Rainbow Memory: Continual Learning with a Memory of Diverse Samples](https://mlsanity.com/paper/2103.17230/) (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)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Using Hindsight to Anchor Past Knowledge in Continual Learning](https://mlsanity.com/paper/2002.08165/) (2020)
- [Towards Robust Evaluations of Continual Learning](https://mlsanity.com/paper/1805.09733/) (2018)
- [Supervised Contrastive Replay: Revisiting the Nearest Class Mean Classifier in Online Class-Incremental Continual Learning](https://mlsanity.com/paper/2103.13885/) (2021)
- [SS-IL: Separated Softmax for Incremental Learning](https://mlsanity.com/paper/2003.13947/) (2020)

## Built on by (most cited first, 6 of 6)

- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [Wake-Sleep Consolidated Learning](https://mlsanity.com/paper/2401.08623/) (2023)
- [Class incremental learning with probability dampening and cascaded gated classifier](https://mlsanity.com/paper/2402.01262/) (2024)
- [Adaptive Model Ensemble for Continual Learning](https://mlsanity.com/paper/2509.19819/) (2025)
- [Dream2Learn: Structured Generative Dreaming for Continual Learning](https://mlsanity.com/paper/2603.01935/) (2026)
- [CRMA: A Spectrally-Bounded Backbone for Modular Continual Fine-Tuning of LLMs](https://mlsanity.com/paper/2606.00382/) (2026)

## Abstract (arXiv)

While biological intelligence grows organically as new knowledge is gathered throughout life, Artificial Neural Networks forget catastrophically whenever they face a changing training data distribution. Rehearsal-based Continual Learning (CL) approaches have been established as a versatile and reliable solution to overcome this limitation; however, sudden input disruptions and memory constraints are known to alter the consistency of their predictions. We study this phenomenon by investigating the geometric characteristics of the learner's latent space and find that replayed data points of different classes increasingly mix up, interfering with classification. Hence, we propose a geometric regularizer that enforces weak requirements on the Laplacian spectrum of the latent space, promoting a partitioning behavior. Our proposal, called Continual Spectral Regularizer for Incremental Learning (CaSpeR-IL), can be easily combined with any rehearsal-based CL approach and improves the performance of SOTA methods on standard benchmarks.