用可学习的多项式函数改进自编码器，提升特征表示能力。
KAE: Kolmogorov-Arnold Auto-Encoder for Representation Learning
- 用KAN替代传统MLP，让激活函数可学习
- 在多个任务中降低重建误差，提升特征质量
- 适合需要高精度表征的图像检索与去噪场景
Kolmogorov-Arnold Network（KAN）作为多层感知机（MLP）的替代方案，通过在边上的可学习激活函数实现了更高的精度和可解释性。本文提出Kolmogorov-Arnold自编码器（KAE），将KAN与自编码器（AE）结合，用于增强检索、分类和去噪任务中的表示学习。利用KAN层中的灵活多项式函数，KAE能够捕捉复杂的数据模式与非线性关系。在基准数据集上的实验表明，相较于标准自编码器和其他KAN变体，KAE显著提升了潜在表示质量，降低了重构误差，并在下游任务中取得更优性能。结果表明KAE在表示学习中具有广泛应用潜力。代码已开源。
原文摘要 · Abstract (English)
The Kolmogorov-Arnold Network (KAN) has recently gained attention as an alternative to traditional multi-layer perceptrons (MLPs), offering improved accuracy and interpretability by employing learnable activation functions on edges. In this paper, we introduce the Kolmogorov-Arnold Auto-Encoder (KAE), which integrates KAN with autoencoders (AEs) to enhance representation learning for retrieval, classification, and denoising tasks. Leveraging the flexible polynomial functions in KAN layers, KAE captures complex data patterns and non-linear relationships. Experiments on benchmark datasets demonstrate that KAE improves latent representation quality, reduces reconstruction errors, and achieves superior performance in downstream tasks such as retrieval, classification, and denoising, compared to standard autoencoders and other KAN variants. These results suggest KAE's potential as a useful tool for representation learning. Our code is available at \url{https://github.com/SciYu/KAE/}.
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