HIFI: A Highly Efficient Framework for Statistical Inference with Foundation Models

Po-Wei Chen, Shan Yu, Chunlin Li

Foundation models provide powerful representations for unstructured data, such as text and images, and parameter-efficient fine-tuning (PEFT) makes their adaptation to downstream tasks increasingly practical. For neural estimators that lack a tractable sampling distribution, resampling-based procedures offer a flexible route to statistical inference, but they often require hundreds of model fits, making them computationally prohibitive at foundation-model scale. We introduce HIFI, a two-stage fine-tuning framework for statistical inference on parameters such as conditional means. Stage 1 adapts a foundation model once on a larger sample, capturing the complex structure of the data and controlling estimation bias through a single fit. Stage 2 applies a resampling inference procedure to a smaller independent sample, concurrently fitting multiple lightweight PEFT estimators to the residual to quantify estimation variability without relearning the full task. HIFI accommodates a broad class of resampling procedures, including ensemble subsampling and the nonparametric bootstrap. Across vision and text experiments, HIFI scales to pretrained models ranging from tens of millions to more…