Progressive Alignment of Recommender Foundation Model through Multi-Phase Post-Training

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.

We study the problem of optimal continual fine-tuning for a pre-trained Foundation Model deployed at a resource-limited device. At each time slot, a new batch of training data arrives, and the controller is faced with two options: either use the data to fine-tune the model and incur a compute cost, or do not fine-tune the model and discard the data. After the decision, the performance of the current model is measured in terms of an application-specific performance metric such as classification accuracy. Our objective is to learn an optimal policy that determines \emph{when to fine-tune the model} on a single task (e.g., sentiment analysis), under a finite compute budget. We formulate this online decision-making problem as a constrained Markov Decision Process, where the system state captures three essential aspects: (\textit{i}) model's performance, (\textit{ii}) computational budget, and (\textit{iii}) data distribution relevance to historic data encountered up to that point. The transition to the next state is stochastic and therefore, we propose a reinforcement learning-based method to solve this problem, namely the \emph{actor-critic} algorithm. We also consider the special case where the performance of fine-tuning for a given model can be predicted or estimated prior to decision; in this case the problem becomes a Dynamic Programming one. Experiments with a large pre-trained model on a widely-used text classification dataset demonstrate that our method consistently outperforms fine-tuning approaches with the same compute budget by more than $4\%$ in terms of accuracy and achieves $97\%$ of full-parameter fine-tuning accuracy while requiring only $25\%$ of the fine-tuning steps.

Knowledge distillation (KD) transfers a single scalar prediction from a large foundation model (FM) to compact vertical models (VMs), suffering from diminishing transfer ratio -- the fraction of FM improvement captured by the VM -- as a single scalar cannot convey the rich intermediate knowledge that larger FMs learn. To address this bottleneck, we propose LoopFM (Learning frOm HistOrical RePresentations of FM), a framework that opens a high-bandwidth transfer channel by structuring FM intermediate embeddings as input features (e.g., user history sequence) for downstream VMs, without requiring real-time FM inference at serving and architectural coupling between FM and VM. We provide a theoretical framework for LoopFM with a gain decomposition and transfer-ratio analysis. On three public benchmarks, LoopFM demonstrates strong AUC improvements (e.g., 6%+ on TaobaoAd) and complementary knowledge transfer capability with KD. On industrial-scale systems (billions of examples, trillion-parameter FMs), LoopFM approximately doubles the knowledge transfer ratio on top of KD, delivering a +0.5% conversion improvement in the first half after its initial launch, and +1.03% and +1.22% conversion improvement from two individual launches in the subsequent half.