# TS-ACL: Closed-Form Solution for Time Series-oriented Continual Learning

arXiv: https://arxiv.org/abs/2410.15954 · HTML: https://mlsanity.com/paper/2410.15954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 21 Oct 2024.

## Builds on (most cited first, 20 of 20)

- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (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)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [HIVE-COTE 2.0: a new meta ensemble for time series classification](https://mlsanity.com/paper/2104.07551/) (2021)
- [Deep Learning for Time Series Classification and Extrinsic Regression: A Current Survey](https://mlsanity.com/paper/2302.02515/) (2023)
- [DS-AL: A Dual-Stream Analytic Learning for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2403.17503/) (2024)
- [Open Access Dataset for Electromyography based Multi-code Biometric Authentication](https://mlsanity.com/paper/2201.01051/) (2022)
- [FastICARL: Fast Incremental Classifier and Representation Learning with Efficient Budget Allocation in Audio Sensing Applications](https://mlsanity.com/paper/2106.07268/) (2021)
- [Class-incremental Learning for Time Series: Benchmark and Evaluation](https://mlsanity.com/paper/2402.12035/) (2024)

## Built on by (most cited first, 1 of 1)

- [APFL: Analytic Personalized Federated Learning via Dual-Stream Least Squares](https://mlsanity.com/paper/2508.10732/) (2025)

## Abstract (arXiv)

Time series classification underpins critical applications such as healthcare diagnostics and gesture-driven interactive systems in multimedia scenarios. However, time series class-incremental learning (TSCIL) faces two major challenges: catastrophic forgetting and intra-class variations. Catastrophic forgetting occurs because gradient-based parameter update strategies inevitably erase past knowledge. And unlike images, time series data exhibits subject-specific patterns, also known as intra-class variations, which refer to differences in patterns observed within the same class. While exemplar-based methods fail to cover diverse variation with limited samples, existing exemplar-free methods lack explicit mechanisms to handle intra-class variations. To address these two challenges, we propose TS-ACL, which leverages a gradient-free closed-form solution to avoid the catastrophic forgetting problem inherent in gradient-based optimization methods while simultaneously learning global distributions to resolve intra-class variations. Additionally, it provides privacy protection and efficiency. Extensive experiments on five benchmark datasets covering various sensor modalities and tasks demonstrate that TS-ACL achieves performance close to joint training on four datasets, outperforming existing methods and establishing a new state-of-the-art (SOTA) for TSCIL.