Unsupervised Post-Training of Foundation Models: A Survey

Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.

Foundation models are typically trained in stages: pretraining, midtraining, supervised fine-tuning (SFT), and reinforcement learning (RL), with changes in both data and learning algorithms. We show that this algorithmic separation is not fundamental. By deriving suitable RL objectives as maximum-likelihood fitting to model-generated target distributions, we place all of these stages under a single likelihood-based training algorithm, unified training. This perspective turns the foundation-model training lifecycle into a problem of choosing which data to train on, in what proportions, and when, with conventional staged training as a special case. We instantiate this framework in a unified training system that mixes static data and RL generations within a single trainer. Across controlled and real-world experiments, unified training improves the accuracy-compute tradeoff and task coverage while preserving broader capabilities, and provides a stronger starting point for continual learning. This work lays the groundwork for a unified science of foundation-model training, connecting mathematical principles, training infrastructure, and the development of model capabilities.

Source-free universal domain adaptation (SF-UniDA) adapts a pre-trained source model to an unlabeled target domain under both covariate and label shifts, without access to source data. However, existing SF-UniDA methods rely on inefficient techniques such as threshold tuning and clustering. Foundation models (FMs), known for their generalization and zero-shot capabilities, remain underexplored in SF-UniDA. In this paper, we propose a framework that leverages foundation models (LFM) for SF-UniDA. We use a vision-language model (VLM) to compute similarities between target samples and text labels, including those for unknown classes generated by prompting a large language model. The label shift type is determined by analyzing the coefficient of variation of a similarity-based sample-level score. Unknown samples are identified using a binary Gaussian mixture model fitted to another similarity-based metric. Under a consensus strategy, the pseudo-labels generated by the VLM are refined by the target model initialized with the pre-trained source model, integrating knowledge from both the source domain and foundation models. Finally, these refined pseudo-labels are used to train the target model. Extensive experiments across all possible label shifts and multiple benchmarks demonstrate the effectiveness and superiority of our proposed LFM framework. Our code is available at https://github.com/iamjingli/LFM.