# Nonlinear Factor Decomposition via Kolmogorov-Arnold Networks: A Spectral Approach to Asset Return Analysis

arXiv: https://arxiv.org/abs/2603.28257 · HTML: https://mlsanity.com/paper/2603.28257/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [KAN based Autoencoders for Factor Models](https://mlsanity.com/paper/2408.02694/) (2024)
- [KAE: Kolmogorov-Arnold Auto-Encoder for Representation Learning](https://mlsanity.com/paper/2501.00420/) (2024)

## Abstract (arXiv)

KAN-PCA is an autoencoder that uses a KAN as encoder and a linear map as decoder. It generalizes classical PCA by replacing linear projections with learned B-spline functions on each edge. The motivation is to capture more variance than classical PCA, which becomes inefficient during market crises when the linear assumption breaks down and correlations between assets change dramatically. We prove that if the spline activations are forced to be linear, KAN-PCA yields exactly the same results as classical PCA, establishing PCA as a special case. Experiments on 20 S&P 500 stocks (2015-2024) show that KAN-PCA achieves a reconstruction R^2 of 66.57%, compared to 62.99% for classical PCA with the same 3 factors, while matching PCA out-of-sample after correcting for data leakage in the training procedure.