# GACL: Exemplar-Free Generalized Analytic Continual Learning

arXiv: https://arxiv.org/abs/2403.15706 · HTML: https://mlsanity.com/paper/2403.15706/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 23 Mar 2024.

## Builds on (most cited first, 8 of 8)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [ImageNet-21K Pretraining for the Masses](https://mlsanity.com/paper/2104.10972/) (2021)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Less-forgetting Learning in Deep Neural Networks](https://mlsanity.com/paper/1607.00122/) (2016)
- [Online Continual Learning on Class Incremental Blurry Task Configuration with Anytime Inference](https://mlsanity.com/paper/2110.10031/) (2021)
- [ACIL: Analytic Class-Incremental Learning with Absolute Memorization and Privacy Protection](https://mlsanity.com/paper/2205.14922/) (2022)
- [Analytic Learning of Convolutional Neural Network For Pattern Recognition](https://mlsanity.com/paper/2202.06504/) (2022)

## Built on by (most cited first, 22 of 22)

- [Mixture of Noise for Pre-Trained Model-Based Class-Incremental Learning](https://mlsanity.com/paper/2509.16738/) (2025)
- [AFL: A Single-Round Analytic Approach for Federated Learning with Pre-trained Models](https://mlsanity.com/paper/2405.16240/) (2024)
- [AIR: Analytic Imbalance Rectifier for Continual Learning](https://mlsanity.com/paper/2408.10349/) (2024)
- [Semantic Shift Estimation via Dual-Projection and Classifier Reconstruction for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2503.05423/) (2025)
- [AnaCP: Toward Upper-Bound Continual Learning via Analytic Contrastive Projection](https://mlsanity.com/paper/2511.13880/) (2025)
- [Online Analytic Exemplar-Free Continual Learning with Large Models for Imbalanced Autonomous Driving Task](https://mlsanity.com/paper/2405.17779/) (2024)
- [Achieving Upper Bound Accuracy of Joint Training in Continual Learning](https://mlsanity.com/paper/2502.12388/) (2025)
- [Autoencoder-Based Hybrid Replay for Class-Incremental Learning](https://mlsanity.com/paper/2505.05926/) (2025)
- [Towards Efficient and Exact Forgetting Services in Pre-Trained-Model-based Continual Learning](https://mlsanity.com/paper/2505.12239/) (2025)
- [L3A: Label-Augmented Analytic Adaptation for Multi-Label Class Incremental Learning](https://mlsanity.com/paper/2506.00816/) (2025)
- [APFL: Analytic Personalized Federated Learning via Dual-Stream Least Squares](https://mlsanity.com/paper/2508.10732/) (2025)
- [FlyPrompt: Brain-Inspired Random-Expanded Routing with Temporal-Ensemble Experts for General Continual Learning](https://mlsanity.com/paper/2602.01976/) (2026)
- [Analytic Drift Resister for Non-Exemplar Continual Graph Learning](https://mlsanity.com/paper/2604.02633/) (2026)
- [Learning After Model Deployment](https://mlsanity.com/paper/2510.17160/) (2025)
- [CaMiT: A Time-Aware Car Model Dataset for Classification and Generation](https://mlsanity.com/paper/2510.17626/) (2025)
- [Analytic Incremental Learning For Sound Source Localization With Imbalance Rectification](https://mlsanity.com/paper/2601.18335/) (2026)
- [MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound](https://mlsanity.com/paper/2605.11617/) (2026)
- [Online Continual Learning with Dynamic Label Hierarchies](https://mlsanity.com/paper/2605.11742/) (2026)
- [Non-Forgetting Knowledge Allocation with Bi-level Competition for Class-Incremental Learning](https://mlsanity.com/paper/2605.29592/) (2026)
- [Accurate and Resource-Efficient Federated Continual Learning](https://mlsanity.com/paper/2606.11480/) (2026)
- [Spectral-Aware Analytic Class-Incremental Learning for Long-Tailed Distributions](https://mlsanity.com/paper/2607.22931/) (2026)
- [SPARCL: Spectral Partitioned Analytic Continual Learning](https://mlsanity.com/paper/2608.21307/) (2026)

## Abstract (arXiv)

Class incremental learning (CIL) trains a network on sequential tasks with separated categories in each task but suffers from catastrophic forgetting, where models quickly lose previously learned knowledge when acquiring new tasks. The generalized CIL (GCIL) aims to address the CIL problem in a more real-world scenario, where incoming data have mixed data categories and unknown sample size distribution. Existing attempts for the GCIL either have poor performance or invade data privacy by saving exemplars. In this paper, we propose a new exemplar-free GCIL technique named generalized analytic continual learning (GACL). The GACL adopts analytic learning (a gradient-free training technique) and delivers an analytical (i.e., closed-form) solution to the GCIL scenario. This solution is derived via decomposing the incoming data into exposed and unexposed classes, thereby attaining a weight-invariant property, a rare yet valuable property supporting an equivalence between incremental learning and its joint training. Such an equivalence is crucial in GCIL settings as data distributions among different tasks no longer pose challenges to adopting our GACL. Theoretically, this equivalence property is validated through matrix analysis tools. Empirically, we conduct extensive experiments where, compared with existing GCIL methods, our GACL exhibits a consistently leading performance across various datasets and GCIL settings. Source code is available at https://github.com/CHEN-YIZHU/GACL.