Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting

Chen Zeng; Jiahui Wang; Qiao Wang

cs.LGApr 26, 2026

Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting

Authors: Chen Zeng, Jiahui Wang, Qiao Wang

Organizations: School of Information Science and Engineering, Southeast University, Nanjing, China · School of Economics and Management, Southeast University, Nanjing, China · both the School of Information Science and Engineering and the School of Economics and Management, Southeast University, Nanjing, China

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.

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Nov 23, 2025 · cs.LGJ/K move · Enter open · S save

KAN vs LSTM Performance in Time Series Forecasting

Tabish Ali Rather, S M Mahmudul Hasan Joy, Nadezda Sukhorukova, Federico Frascoli

Department of Mathematics, Swinburne University of Technology, Hawthorn, 3122, Victoria, Australia.

This study presents a controlled comparison of baseline Kolmogorov-Arnold Networks (KAN), implemented via PyKAN, and Long Short-Term Memory (LSTM) networks for the forecasting of stochastic, non-stationary financial time series. The two architectures are assessed in terms of predictive accuracy, computational efficiency, and interpretability, with accuracy measured by the Root Mean Square Error (RMSE) in normalised feature space. Under a direct multi-output forecasting protocol, LSTM attains clearly superior accuracy across all tested prediction horizons, consistent with its well-established effectiveness for sequential data modelling. Baseline KAN, although offering theoretical interpretability through the Kolmogorov-Arnold representation theorem, exhibits substantially higher error rates and limited practical applicability for time series forecasting in its standard form. Several specialised temporal variants -- including Temporal KAN and Time-Frequency KAN -- have since been proposed to address these sequential modelling limitations, but they lie outside the scope of the present study. KAN is observed to converge faster during training under the configurations tested, although direct runtime comparisons are constrained by methodological factors. These findings support the adoption of LSTM for accuracy-critical financial forecasting and establish an empirical baseline for standard KAN on stochastic sequential data, motivating further investigation of temporally-aware KAN architectures. The study benchmarks baseline KAN against baseline LSTM only; the results do not extend to specialised KAN variants designed for sequential data, nor to the broader family of temporal models.

Multivariate Forecasting Kolmogorov-Arnold Networks Bidirectional Long Short-Term Memory Non-Stationarity Long-Term Memory

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Abstract

Explore similar work

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