A model-agnostic online certificate-driven calibration framework keeps convolutional, attention-based, and LLM forecasters more stable and accurate under covariate and concept shift

It proposes a model-agnostic online martingale PAC-Bayesian framework that yields finite-sample certificates under temporal dependence and distribution shift. Standard PAC-Bayesian domain adaptation analyses rely on independent sampling and distributional stability, assumptions violated in time series by serial dependence and nonstationary shift; the framework replaces independent-sample concentration with martingale concentration that adapts to loss scale and predictable variation. The abstract-level text presents the framework design and certificate construction and identifies the assumption gap it targets; theorem forms, sample sizes, and numerical values are not given in the text.

It uses the certificate as a surrogate regularizer for online calibration by training a gated residual Bayesian head on a fixed forecasting backbone, reverting to the backbone prediction when the gate is closed. It turns a computable certificate from an analysis tool into a training signal, decoupling the calibration module from the backbone so it applies to convolutional, attention-based, and LLM-based forecasters. The text describes the gated residual head and the reversion mechanism, which is method-design-level evidence.

Online calibration combines a source risk anchor, a posterior-shift penalty, and a time-adaptive mismatch term computed from target windows observed before forecasting. It combines source risk, posterior shift, and target-window mismatch signals into an online update and follows a predict-then-update protocol in which outcomes become available only after forecasting and are used to update subsequent predictions. The text explicitly lists the three components and the protocol order, but gives no weights or ablation results.

Experiments across convolutional, attention-based, and large language model-based forecasters show improved stability and accuracy under covariate and concept shift. Validation across three backbone families indicates the method is not tied to a specific model structure, supporting its model-agnostic claim. The abstract reports cross-backbone experimental conclusions but provides no datasets, metric values, or statistical significance information.

The framework targets time series forecasting where deployment dynamics differ from training conditions, applying to online settings with covariate shift, concept shift, and serial dependence under a predict-then-update protocol in which outcomes become available only after forecasting. Its model-agnostic design means it can pair with fixed convolutional, attention-based, and large language model-based forecasting backbones, calibrating via a gated residual Bayesian head that reverts to the backbone prediction when the gate is closed. The certificate decomposes into a source risk term, a source-to-target mismatch term, and a complexity term, and uses martingale concentration that adapts to loss scale and predictable variation, making it suited to online forecasting tasks that need finite-sample reliability statements.

The text is abstract-level information and does not give the concrete form of the theorems, sample sizes, dataset names, evaluation metric values, or ablation results, so how tight the certificate is at practical sequence lengths and shift intensities, the individual contribution of the three calibration signals, and which shift patterns the gating mechanism handles best remain open questions that require the full text. The magnitude and statistical significance of improvements across convolutional, attention-based, and LLM backbones are also not quantified in the text.