自相关性在KANs时间序列预测中重新引入频谱偏置
Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting
AI总结：
研究发现自相关性在KANs中重新引入频谱偏置，通过理论分析和实验验证，提出用DCT预处理减少输入相关性以提升时间序列预测性能。
摘要：
现有理论表明Kolmogorov-Arnold网络(KANs)能在输入统计独立的假设下克服神经网络常见的频谱偏置。然而在时间序列预测(TSF)中，输入为滞后观测具有强时间自相关性，这一假设不成立。通过理论分析和实证验证，发现时间自相关性在KANs中重新引入频谱偏置，且自相关程度越高偏置越显著。这表明标准KANs在强自相关输入的TSF任务中可能面临重大困难。为解决此问题，引入离散余弦变换(DCT)以减少网络输入间的相关性。实验结果表明，DCT预处理显著降低了TSF中的低频偏好。此结果也证实了KANs在TSF任务中的频谱偏置确实由输入变量间的自相关性引起。
英文摘要：
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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