Learning What to Transfer? Self-Supervised Disentanglement of Transferable Semantics for Source-Free Multivariate Time Series Domain Adaptation

We consider source-free domain adaptation (SFDA), which transfers a source-trained model to an unlabeled target domain without retaining source samples. For multivariate time series (MTS), target self-supervision can reveal temporal, spectral, and channel-relation structure, but consistency within the target domain does not necessarily imply relevance to the source task. Without source data for direct verification, indiscriminately transferring such structure may retain target-specific variation at the expense of task-relevant semantics. We propose self-supervised transferable semantic disentanglement (STSD) for source-free MTS domain adaptation. During source training, we decompose temporal, spectral, and channel-relation views into a shared semantic representation and view-specific components, and calibrate normalized classifier directions as persistent class anchors. We then use the frozen anchors to form a source semantic scatter operator and disagreement among unlabeled target views to form a target self-supervised variation operator. STSD solves a generalized spectral problem whose leading eigenspace preserves source class separation while suppressing target cross-view disagreement. The resulting eigenspace induces complementary transferable and target-local projectors, so semantic disentanglement follows from the geometry of the construction rather than from an auxiliary decoupling loss. Target prototypes are matched with the frozen source anchors only in the transferable subspace through entropic optimal transport. The target encoder is finally updated with a single semantic objective, while the spectral subspace and transport plan are refreshed from the current target representations. Extensive experiments on three standard MTS benchmarks demonstrate the effectiveness and superiority of STSD. The code is publicly available at https://github.com/Sky-byte-box/STSD_Code.