# KAC: Kolmogorov-Arnold Classifier for Continual Learning

arXiv: https://arxiv.org/abs/2503.21076 · HTML: https://mlsanity.com/paper/2503.21076/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 60 references that are in the map.
- First posted on arXiv 27 Mar 2025.

## Builds on (most cited first, 30 of 39)

- [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)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [DyTox: Transformers for Continual Learning with DYnamic TOken eXpansion](https://mlsanity.com/paper/2111.11326/) (2021)
- [S-Prompts Learning with Pre-trained Transformers: An Occam's Razor for Domain Incremental Learning](https://mlsanity.com/paper/2207.12819/) (2022)
- [Semantic Drift Compensation for Class-Incremental Learning](https://mlsanity.com/paper/2004.00440/) (2020)
- [SLCA: Slow Learner with Classifier Alignment for Continual Learning on a Pre-trained Model](https://mlsanity.com/paper/2303.05118/) (2023)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [A Unified Continual Learning Framework with General Parameter-Efficient Tuning](https://mlsanity.com/paper/2303.10070/) (2023)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Hierarchical Decomposition of Prompt-Based Continual Learning: Rethinking Obscured Sub-optimality](https://mlsanity.com/paper/2310.07234/) (2023)
- [Expandable Subspace Ensemble for Pre-Trained Model-Based Class-Incremental Learning](https://mlsanity.com/paper/2403.12030/) (2024)
- [Class-Incremental Learning by Knowledge Distillation with Adaptive Feature Consolidation](https://mlsanity.com/paper/2204.00895/) (2022)
- [A Comprehensive Study of Class Incremental Learning Algorithms for Visual Tasks](https://mlsanity.com/paper/2011.01844/) (2020)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [FeCAM: Exploiting the Heterogeneity of Class Distributions in Exemplar-Free Continual Learning](https://mlsanity.com/paper/2309.14062/) (2023)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics](https://mlsanity.com/paper/2407.04192/) (2024)
- [Consistent Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2403.08568/) (2024)
- [Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem](https://mlsanity.com/paper/1906.11945/) (2019)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)

## Built on by (most cited first, 4 of 4)

- [Improving Memory Efficiency for Training KANs via Meta Learning](https://mlsanity.com/paper/2506.07549/) (2025)
- [Unifying Locality of KANs and Feature Drift Compensation Projection for Data-free Replay based Continual Face Forgery Detection](https://mlsanity.com/paper/2508.03189/) (2025)
- [BRAIN: Bias-Mitigation Continual Learning Approach to Vision-Brain Understanding](https://mlsanity.com/paper/2508.18187/) (2025)
- [Core-KAN: Continuous Vision Kernels with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2608.19817/) (2026)

## Abstract (arXiv)

Continual learning requires models to train continuously across consecutive tasks without forgetting. Most existing methods utilize linear classifiers, which struggle to maintain a stable classification space while learning new tasks. Inspired by the success of Kolmogorov-Arnold Networks (KAN) in preserving learning stability during simple continual regression tasks, we set out to explore their potential in more complex continual learning scenarios. In this paper, we introduce the Kolmogorov-Arnold Classifier (KAC), a novel classifier developed for continual learning based on the KAN structure. We delve into the impact of KAN's spline functions and introduce Radial Basis Functions (RBF) for improved compatibility with continual learning. We replace linear classifiers with KAC in several recent approaches and conduct experiments across various continual learning benchmarks, all of which demonstrate performance improvements, highlighting the effectiveness and robustness of KAC in continual learning. The code is available at https://github.com/Ethanhuhuhu/KAC.