Nonlinear Factor Decomposition via Kolmogorov-Arnold Networks: A Spectral Approach to Asset Return Analysis
arXiv:2603.28257v2 Announce Type: replace-cross Abstract: 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 specia
This research builds on recent advancements in Kolmogorov-Arnold Networks (KANs) and applies them to a critical problem in financial modeling, addressing known limitations of traditional PCA during market volatility.
Sophisticated financial institutions and quantitative funds rely heavily on robust models for risk management and asset allocation, especially in volatile periods. KAN-PCA could offer a significant advantage by providing more accurate and adaptive factor decomposition.
Current linear dimensionality reduction techniques in finance, often inadequate during crises, could be superseded by nonlinear, more resilient methods, potentially leading to better predictive models and risk assessments.
- · Quantitative hedge funds
- · High-frequency trading firms
- · Financial AI/ML researchers
- · AI model developers
- · Traditional linear PCA-based models
- · Financial institutions relying solely on linear risk models
- · Analysts without advanced AI/ML skills
Financial models for risk management and asset allocation become more robust, especially during periods of market stress.
Adoption of KAN-PCA and similar nonlinear techniques could lead to a competitive advantage for early implementers, creating new alpha opportunities.
The increased sophistication of financial AI may necessitate new regulatory frameworks to manage unforeseen systemic risks from complex, non-interpretable models.
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Read at arXiv cs.LG