A two-stage method estimates uncertainty with foundation models
HIFI: A Highly Efficient Framework for Statistical Inference with Foundation Models · arXiv:2610.34550
In plain words
The paper introduces HIFI, a two-stage way to use a foundation model to estimate an average outcome for a particular input and show uncertainty around that estimate.
HIFI adapts the model once using a larger sample. It then uses a separate, smaller sample to fit many lightweight estimates of the remaining error.
In synthetic image and text tasks, its intervals were closer to the intended 95% coverage than intervals from direct resampling at the same total sample size.
The research
How can researchers put a useful confidence interval around a foundation model's estimate of an average outcome at a particular input, when resampling requires many costly fits and does not itself remove systematic estimation error? The paper develops a two-stage approach to address both parts of that problem.
HIFI adapts a foundation model once, then fits residuals on a separate sample to estimate uncertainty around a conditional mean.
The authors ask how to build confidence intervals for a conditional mean when repeated resampling fits are costly and can leave systematic estimation error uncorrected.
HIFI separates the work: it adapts the model once on a larger sample, then uses an independent sample to estimate residual uncertainty.
At the same total sample size, HIFI's 95% intervals contained the true conditional mean or probability at rates closer to 95% than direct resampling, which was strongly conservative. Estimated training computation was also lower across the tested configurations. This supports the approach in the evaluated settings.
The matched-sample results come from synthetic image and text tasks using four tested backbones and LoRA. The authors note that parameter-efficient tuning can depend on the task and that repeated Stage 2 fits may still be costly for very large models.
What the evidence shows
- The inference problem
HIFI is a two-stage framework for estimating a population conditional mean at a fixed input and giving a confidence interval for that estimate with a foundation model.
The paper addresses a tension in resampling: repeated model fits can be expensive, while resampling alone does not correct systematic estimation error that can undermine the interval.
- Split the two tasks
HIFI divides labeled data into two independent samples. It adapts the pretrained model once on the larger first sample, then uses the second sample to fit lightweight estimators of the remaining residual.
Because the first-stage estimate is held fixed, the second-stage fits focus on residual variation rather than relearning the full task.
- Evidence at equal sample size
The authors compared HIFI with direct resampling using the same total sample size and the same pretrained backbone within each pair. Across three vision backbones and one text backbone on synthetic tasks, HIFI's nominal 95% intervals had empirical coverage closer to 95%, while direct resampling was strongly conservative. HIFI also had lower estimated training computation in these tested configurations.
- Check the adaptation sample
A separate text-task diagnostic held the second-stage sample fixed while varying how much data HIFI used for its initial adaptation. Larger first-stage samples reduced mean absolute bias and moved coverage toward 95%.
At the largest tested size, intervals were shorter than direct-resampling intervals, but coverage remained slightly below nominal. This result is specific to that synthetic task and backbone.
Deep
- Original paper authors
- Po-Wei Chen, Shan Yu, Chunlin Li
- Submitted to arXiv
- License
- arXiv non-exclusive