Beyond Wasserstein Proximity: Finding Better Transfer Sources

The goal of domain adaptation is to make predictions for unlabeled samples from a target domain with the help of labeled samples from a different but related source domain. The performance of domain adaptation methods is highly influenced by the choice of source domain and pre-trained feature extractor. However, the selection of source data and pre-trained model is not trivial due to the absence of a labeled validation set for the target domain and the large number of available pre-trained models. In this work, we propose PAS, a novel score designed to estimate the transferability of a source domain set and a pre-trained feature extractor to a target classification task before actually performing domain adaptation. PAS leverages the generalization power of pre-trained models and assesses source-target compatibility based on the pre-trained feature embeddings. We integrate PAS into a framework that indicates the most relevant pre-trained model and source domain among multiple candidates, thus improving target accuracy while reducing the computational overhead. Extensive experiments on image classification benchmarks demonstrate that PAS correlates strongly with actual target accuracy and consistently guides the selection of the best-performing pre-trained model and source domain for adaptation.

Synthetic pretraining under distribution shift requires deciding what synthetic data to use. A natural criterion is to match the spectral predictability $Ω$ of the source to the target, but is $Ω$ sufficient? We test this hypothesis, which we call predictability-aware pretraining, across three architectures (LSTM, PatchTST, TCN) and three seeds. Under ideal synthetic-to-synthetic conditions, $Ω$-matched pretraining can outperform even an oracle baseline (+46.8% MSE reduction, LSTM), though the benefit is already architecture-dependent. On the real-world ETTm1 benchmark, however, this relationship does not hold: sine-plus-noise pretraining at matched $Ω$ yields only a marginal mean improvement +2.3% averaged over all three architectures, up to +65.5% on individual channels), whereas $Ω$ matched chaotic ODE trajectories systematically degrade performance -13.2%). The two sources agree on the direction of transfer for only 53% of configurations across all three architectures (Pearson r=-0.02), indicating that $Ω$ carries little information about which source will transfer beneficially. We further observe an architecture-dependent asymmetry in the response to the direction of the $Ω$ gap. We conclude that $Ω$ matching can help in controlled settings but is not sufficient to predict transfer across sources, and we discuss additional signal properties that a source-selection criterion may need to consider.

Time series foundation models (TSFMs) are pretrained on heterogeneous collections containing billions of observations, yet their training windows are typically sampled without estimating whether they provide useful learning signal. We introduce a static data-selection framework that scores each window with a reference forecaster and retains an intermediate interval within every source dataset. Specifically, we connect forecasting loss to optimization difficulty by showing that normalized squared loss controls the per-sample gradient norm under a local Jacobian condition. We then define a reference loss score and apply dataset-stratified selection to preserve the diversity of samples. Across various TSFM architectures, our method outperforms random selection by an absolute margin and even improves both relative MASE and CRPS over full-data pretraining by retaining fewer candidate pretraining windows. Further analyses show strong cross-scale and cross-architecture score correlations, indicating that a small reference model can often select data for larger targets, provided that the reference and target share compatible difficulty orderings.