Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting

2026-04-25

AI Summary

Standard Kolmogorov–Arnold Networks (KANs) mitigate spectral bias but reintroduce a preference for low-frequency components in time series forecasting due to the temporal autocorrelation among input variables. This work is the first to identify autocorrelation as the key mechanism underlying the reemergence of spectral bias in KANs and proposes preprocessing inputs with the Discrete Cosine Transform (DCT) to reduce such correlation. Theoretical analysis and empirical experiments demonstrate that DCT preprocessing substantially attenuates the low-frequency bias of KANs, effectively restoring their spectral neutrality. This approach offers a novel perspective for modeling time series with improved frequency fidelity.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Existing theory suggests that Kolmogorov-Arnold Networks (KANs) can overcome the spectral bias commonly observed in neural networks under the assumption that inputs are statistically independent. However, this assumption does not hold in time series forecasting (TSF), where inputs are lagged observations with strong temporal autocorrelation. Through theoretical analysis and empirical validation, we obtain an unexpected finding: temporal autocorrelation reintroduces spectral bias in KANs, and the bias becomes increasingly pronounced as the degree of autocorrelation increases. This suggests that standard KANs may face substantial difficulties in TSF with strongly autocorrelated inputs. To address this problem, we introduce the Discrete Cosine Transform (DCT) to reduce the correlations among the network inputs. As expected, experimental results reveal that DCT preprocessing substantially reduces the observed low-frequency preference in TSF. This result also corroborates that the spectral bias of KANs in TSF tasks is indeed induced by the autocorrelation among input variables.

Problem

• spectral bias
• Kolmogorov-Arnold Networks
• time series forecasting
• autocorrelation
• temporal dependence

Innovation

• Kolmogorov-Arnold Networks
• spectral bias
• temporal autocorrelation
• time series forecasting
• Discrete Cosine Transform