OliO: ODE-based Linear Transition Operator for Self-Supervised Time Series Forecasting· OliO: 基于ODE的线性转换算子

Self-supervised representation learning has advanced time series forecasting by capturing robust features from unlabeled data. However, existing contrastive and masking-based methods often struggle to explicitly model the underlying temporal flow, either by treating time lag as noise or by disrupting the inherent temporal dynamics essential for forecasting. To address these limitations, we propose OliO (**O**DE-based **Li**near Transition **O**perator), a plug-and-play self-supervised learning method that learns bidirectional temporal flows as a continuous and structurally consistent dynamical system. OliO introduces a transition operator derived from linear Ordinary Differential Equations (ODEs) to align latent representations across arbitrary time shifts. By imposing a strictly upper tri