# Elastic Multi-Gradient Descent for Parallel Continual Learning

arXiv: https://arxiv.org/abs/2401.01054 · HTML: https://mlsanity.com/paper/2401.01054/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 105 references that are in the map.
- First posted on arXiv 2 Jan 2024.

## Builds on (most cited first, 30 of 57)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [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)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [PathNet: Evolution Channels Gradient Descent in Super Neural Networks](https://mlsanity.com/paper/1701.08734/) (2017)
- [Multi-Task Deep Neural Networks for Natural Language Understanding](https://mlsanity.com/paper/1901.11504/) (2019)
- [DyTox: Transformers for Continual Learning with DYnamic TOken eXpansion](https://mlsanity.com/paper/2111.11326/) (2021)
- [Rainbow Memory: Continual Learning with a Memory of Diverse Samples](https://mlsanity.com/paper/2103.17230/) (2021)
- [Learning without Memorizing](https://mlsanity.com/paper/1811.08051/) (2018)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Learning Multi-Domain Convolutional Neural Networks for Visual Tracking](https://mlsanity.com/paper/1510.07945/) (2015)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [Multi-task Self-Supervised Visual Learning](https://mlsanity.com/paper/1708.07860/) (2017)

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

- [Confidence Self-Calibration for Multi-Label Class-Incremental Learning](https://mlsanity.com/paper/2403.12559/) (2024)
- [Controllable Continual Test-Time Adaptation](https://mlsanity.com/paper/2405.14602/) (2024)

## Abstract (arXiv)

The goal of Continual Learning (CL) is to continuously learn from new data streams and accomplish the corresponding tasks. Previously studied CL assumes that data are given in sequence nose-to-tail for different tasks, thus indeed belonging to Serial Continual Learning (SCL). This paper studies the novel paradigm of Parallel Continual Learning (PCL) in dynamic multi-task scenarios, where a diverse set of tasks is encountered at different time points. PCL presents challenges due to the training of an unspecified number of tasks with varying learning progress, leading to the difficulty of guaranteeing effective model updates for all encountered tasks. In our previous conference work, we focused on measuring and reducing the discrepancy among gradients in a multi-objective optimization problem, which, however, may still contain negative transfers in every model update. To address this issue, in the dynamic multi-objective optimization problem, we introduce task-specific elastic factors to adjust the descent direction towards the Pareto front. The proposed method, called Elastic Multi-Gradient Descent (EMGD), ensures that each update follows an appropriate Pareto descent direction, minimizing any negative impact on previously learned tasks. To balance the training between old and new tasks, we also propose a memory editing mechanism guided by the gradient computed using EMGD. This editing process updates the stored data points, reducing interference in the Pareto descent direction from previous tasks. Experiments on public datasets validate the effectiveness of our EMGD in the PCL setting.