# On the Convergence of Continual Learning with Adaptive Methods

Source: [On the Convergence of Continual Learning with Adaptive Methods](<https://www.sota2.com/research/paper/68fa72ec1e209131cea5942f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T02:37:39.153Z

Authors: Seungyub Han, Yeongmo Kim, Taehyun Cho, Jungwoo Lee

Published: 2024-04-08T14:28:27.000Z

## Abstract

One of the objectives of continual learning is to prevent catastrophic forgetting in learning multiple tasks sequentially, and the existing solutions have been driven by the conceptualization of the plasticity-stability dilemma. However, the convergence of continual learning for each sequential task is less studied so far. In this paper, we provide a convergence analysis of memory-based continual learning with stochastic gradient descent and empirical evidence that training current tasks causes the cumulative degradation of previous tasks. We propose an adaptive method for nonconvex continual learning (NCCL), which adjusts step sizes of both previous and current tasks with the gradients. The proposed method can achieve the same convergence rate as the SGD method when the catastrophic forgetting term which we define in the paper is suppressed at each iteration. Further, we demonstrate that the proposed algorithm improves the performance of continual learning over existing methods for several image classification tasks.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on PMNIST Domain-Incremental (test)](<https://www.sota2.com/research/sota/image-classification-on-pmnist-domain-incremental-test.md>): Image Classification; PMNIST Domain-Incremental (test); Accuracy: 61.93.

- [Task-Incremental Learning on Split-CIFAR100 M = 5k (test)](<https://www.sota2.com/research/sota/task-incremental-learning-on-split-cifar100-m-5k-test.md>): Task-Incremental Learning; Split-CIFAR100 M = 5k (test); Accuracy: 50.79.

- [Task-Incremental Learning on Split-CIFAR10 M = 1k (test)](<https://www.sota2.com/research/sota/task-incremental-learning-on-split-cifar10-m-1k-test.md>): Task-Incremental Learning; Split-CIFAR10 M = 1k (test); Accuracy: 71.9.

- [Task-Incremental Learning on Split-TinyImageNet M = 5k (test)](<https://www.sota2.com/research/sota/task-incremental-learning-on-split-tinyimagenet-m-5k-test.md>): Task-Incremental Learning; Split-TinyImageNet M = 5k (test); Accuracy: 30.15.

- [Task-incremental learning on Split Tiny-ImageNet (test)](<https://www.sota2.com/research/sota/task-incremental-learning-on-split-tiny-imagenet-test.md>): Task-Incremental Learning; Split Tiny-ImageNet (test); Average Accuracy (A\_T): 19.64.

- [Task-incremental learning on CIFAR-10 Split (test)](<https://www.sota2.com/research/sota/task-incremental-learning-on-cifar-10-split-test.md>): Task-Incremental Learning; CIFAR-10 Split (test); Average Accuracy: 72.99.

- [Task-incremental learning on Split CIFAR-100 (test)](<https://www.sota2.com/research/sota/task-incremental-learning-on-split-cifar-100-test.md>): Task-Incremental Learning; Split CIFAR-100 (test); Average Accuracy (A\_T): 29.2.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2404.05555>)

[PDF](<https://arxiv.org/pdf/2404.05555.pdf>)