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Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models

NeurIPS 2026 · Time series › Foundation models for time series · approach: Time series foundation models · 0 citations (OpenAlex)

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Proposes ORCA, a black-box online residual adapter for frozen time series foundation models that learns error context from inputs and base predictions, with a Bayesian loss and Boltzmann router, improving five TSFMs on eight datasets.

Problem

Online adaptation of time series foundation models when only black-box API access is available (no gradients or weights), so the adapter can only apply output-side residual corrections under concept drift.

Approach

Learn the conditional error distribution given both the input context and the base model prediction using a linear residual adapter, trained with a predictive-space Bayesian loss anchored to a prior snapshot, and fused with the base output via an EMA-error Boltzmann softmax router.

Key results

• ORCA reduces MSE for 90% of 40 dataset-model aggregates, averaging -6.3% across 8 datasets and 5 TSFMs (best Moirai-2 at -7.7%, Chronos-2 -5.4%).
• Largest single-configuration reduction is 21.2% (Weather, Moirai-2 at one horizon averaged), with maximum degradation capped at 3.3%.
• Removing the Boltzmann Router drops the average MSE drop from 6.51% to 5.23% on six-dataset ablation.

Surprising findings

• Learning the historical error sequence alone degrades performance (average -0.7%), and adding past errors to the input+prediction context slightly lowers the gain from 6.5% to 6.1%.
• Adapted white-box and grey-box methods (DSOF, TAFAS, SOLID) fail when forced into the black-box contract, per the authors.

Limitations

• As a post-hoc corrector, performance depends on the base model giving reasonable forecasts.
• Evaluated only on standard benchmarks with deterministic MSE; probabilistic metrics and abrupt structural shifts are not tested.
• Local smoothing costs and directed regularization remain open; synchronous training causes a 2-3.5 s pause per cycle.

Experimental setup

Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Exchange Weather Traffic

Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Exchange Weather Traffic

Metrics: MSE

Baselines: ELF delta-Adapter (Ada-Y) DSOF (adapted) TAFAS (adapted) SOLID (adapted) Ridge Regression ETS

Builds on: delta-Adapter ELF DSOF TAFAS SOLID DLinear

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