# Integral Continual Learning Along the Tangent Vector Field of Tasks

arXiv: https://arxiv.org/abs/2211.13108 · HTML: https://mlsanity.com/paper/2211.13108/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 75 references that are in the map.
- First posted on arXiv 23 Nov 2022.

## Builds on (most cited first, 30 of 59)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [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)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (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)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [End-to-End Incremental Learning](https://mlsanity.com/paper/1807.09536/) (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)
- [Expert Gate: Lifelong Learning with a Network of Experts](https://mlsanity.com/paper/1611.06194/) (2016)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [DER: Dynamically Expandable Representation for Class Incremental Learning](https://mlsanity.com/paper/2103.16788/) (2021)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [On Tiny Episodic Memories in Continual Learning](https://mlsanity.com/paper/1902.10486/) (2019)

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

- [Tangent Model Composition for Ensembling and Continual Fine-tuning](https://mlsanity.com/paper/2307.08114/) (2023)
- [Tangent Transformers for Composition, Privacy and Removal](https://mlsanity.com/paper/2307.08122/) (2023)
- [RADIN: Souping on a Budget](https://mlsanity.com/paper/2401.17790/) (2024)

## Abstract (arXiv)

We propose a lightweight continual learning method which incorporates information from specialized datasets incrementally, by integrating it along the vector field of "generalist" models. The tangent plane to the specialist model acts as a generalist guide and avoids the kind of over-fitting that leads to catastrophic forgetting, while exploiting the convexity of the optimization landscape in the tangent plane. It maintains a small fixed-size memory buffer, as low as 0.4% of the source datasets, which is updated by simple resampling. Our method achieves strong performance across various buffer sizes for different datasets. Specifically, in the class-incremental setting we outperform the existing methods that do not require distillation by an average of 18.77% and 28.48%, for Seq-CIFAR-10 and Seq-TinyImageNet respectively. Our method can easily be used in conjunction with existing replay-based continual learning methods. When memory buffer constraints are relaxed to allow storage of metadata such as logits, we attain an error reduction of 17.84% towards the paragon performance on Seq-CIFAR-10.