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This research introduces ORCA, a novel method for adapting Time Series Foundation Models in black-box environments where direct parameter access is unavailable. By leveraging the context of predictive errors rather than relying on gradient backpropagation, the approach enables effective online adaptation across multiple state-of-the-art models and datasets. This work addresses a critical gap as foundation models increasingly shift toward closed-source API services, offering a viable path for continuous learning without white-box access.
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Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models

arXiv2 min read

arXiv:2606.14222v2 Announce Type: replace Abstract: The rapid evolution of Time Series Foundation Models (TSFMs) has advanced zero-shot forecasting across diverse domains. Inspired by the current form of Large Language Models, future TSFMs may be offered as commercialized, closed-source API services. However, many existing online adaptation methods still rely on white-box access for parameter fine-tuning or gradient backpropagation. This paradigm mismatch raises a question: In black-box online adaptation for TSFMs, what should we learn? We answer this with an insight: the predictive errors of the base model are conditioned on both the input and output of the base model (i.e., the context of errors). To validate this insight, we propose ORCA (Online Residual Contextual Adaptation). We conduct extensive experiments across 5 state-of-the-art TSFMs and 8 datasets to demonstrate the effectiveness of our approach. Furthermore, through ablation studies, we quantitatively analyze the impact of different adapter learning hypotheses on the final adaptation performance in black-box online adaptation. Code available at https://github.com/Fifthky/ORCA.

Abstract:The rapid evolution of Time Series Foundation Models (TSFMs) has advanced zero-shot forecasting across diverse domains. Inspired by the current form of Large Language Models, future TSFMs may be offered as commercialized, closed-source API services. However, many existing online adaptation methods still rely on white-box access for parameter fine-tuning or gradient backpropagation. This paradigm mismatch raises a question: In black-box online adaptation for TSFMs, what should we learn? We answer this with an insight: the predictive errors of the base model are conditioned on both the input and output of the base model (i.e., the context of errors). To validate this insight, we propose ORCA (Online Residual Contextual Adaptation). We conduct extensive experiments across 5 state-of-the-art TSFMs and 8 datasets to demonstrate the effectiveness of our approach. Furthermore, through ablation studies, we quantitatively analyze the impact of different adapter learning hypotheses on the final adaptation performance in black-box online adaptation. Code available at this https URL.

Machine Learning (cs.LG)

arXiv:2606.14222 [cs.LG]

(or arXiv:2606.14222v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.14222 Focus to learn more arXiv-issued DOI via DataCite

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