FENet: Functional Embedding Neural Network for Change-Point Detection in Functional Time Series

Detecting abnormal changes in server operational data is an important task in modern computing systems, as unexpected shifts in traffic, workload, or performance metrics may indicate service degradation, abnormal access patterns, system failures, or potential security risks. However, server monitoring data are often naturally observed as functional time series, with complex temporal patterns, high dimensionality, and heterogeneous structures, making traditional change-point detection methods difficult to apply reliably in practice. To address this problem, we propose a general change-point detection framework based on a Functional Embedding Neural Network (FENet), designed to provide robust detection across different data types and structural conditions without relying on strong prior assumptions. The proposed method is motivated by the connection between the classical functional CUSUM (FCUSUM) statistic and neural network representations, which allows FENet to learn effective detection rules directly from data while retaining useful statistical intuition. We provide theoretical analysis to formalize this connection and study key properties of the proposed approach. Extensive simulation studies show that FENet achieves competitive performance compared with existing methods and remains robust under limited training data and distributional mismatch between training and test settings. We further apply FENet to real-world server operational metrics, demonstrating its practical value in detecting and localizing abnormal changes in complex server monitoring systems.