# General Synthetic-Powered Inference

arXiv: https://arxiv.org/abs/2509.20345 · HTML: https://mlsanity.com/paper/2509.20345/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 70 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 30 of 31)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Interpreting CLIP's Image Representation via Text-Based Decomposition](https://mlsanity.com/paper/2310.05916/) (2023)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [An introduction to domain adaptation and transfer learning](https://mlsanity.com/paper/1812.11806/) (2018)
- [AutoEval Done Right: Using Synthetic Data for Model Evaluation](https://mlsanity.com/paper/2403.07008/) (2024)
- [Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model](https://mlsanity.com/paper/1506.00691/) (2015)
- [Generalized Resilience and Robust Statistics](https://mlsanity.com/paper/1909.08755/) (2019)
- [Predictions as Surrogates: Revisiting Surrogate Outcomes in the Age of AI](https://mlsanity.com/paper/2501.09731/) (2025)
- [Prediction-Powered Ranking of Large Language Models](https://mlsanity.com/paper/2402.17826/) (2024)
- [Combining Observational and Experimental Datasets Using Shrinkage Estimators](https://mlsanity.com/paper/2002.06708/) (2020)
- [Adaptive Combination of Randomized and Observational Data](https://mlsanity.com/paper/2111.15012/) (2021)
- [Transductive conformal inference with adaptive scores](https://mlsanity.com/paper/2310.18108/) (2023)
- [Robust Conformal Outlier Detection under Contaminated Reference Data](https://mlsanity.com/paper/2502.04807/) (2025)
- [Efficient Randomized Experiments Using Foundation Models](https://mlsanity.com/paper/2502.04262/) (2025)
- [Robust W-GAN-Based Estimation Under Wasserstein Contamination](https://mlsanity.com/paper/2101.07969/) (2021)
- [Reliable Confidence Intervals for Information Retrieval Evaluation Using Generative A.I](https://mlsanity.com/paper/2407.02464/) (2024)
- [Synthetic-Powered Predictive Inference](https://mlsanity.com/paper/2505.13432/) (2025)
- [Batch Predictive Inference](https://mlsanity.com/paper/2409.13990/) (2024)
- [Valid Inference with Imperfect Synthetic Data](https://mlsanity.com/paper/2508.06635/) (2025)
- [The Real Deal Behind the Artificial Appeal: Inferential Utility of Tabular Synthetic Data](https://mlsanity.com/paper/2312.07837/) (2023)
- [GLM Inference with AI-Generated Synthetic Data Using Misspecified Linear Regression](https://mlsanity.com/paper/2503.21968/) (2025)
- [Optimal Multiple Testing Under a Gaussian Prior on the Effect Sizes](https://mlsanity.com/paper/1504.02935/) (2015)
- [Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shift](https://mlsanity.com/paper/2306.16406/) (2023)

## Built on by (most cited first, 6 of 6)

- [Same Scores, Different Decisions: Evaluating JEV and Language Models for Legal Document Understanding](https://mlsanity.com/paper/2609.27678/) (2026)
- [Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective](https://mlsanity.com/paper/2512.05267/) (2025)
- [Synthetic-Powered Multiple Testing with FDR Control](https://mlsanity.com/paper/2602.16690/) (2026)
- [Confounding-Valid Conformal Inference for Counterfactual KPIs in Wireless Networks](https://mlsanity.com/paper/2609.05073/) (2026)
- [Learning a Size-Weight Frontier for Synthetic-Augmented Inference](https://mlsanity.com/paper/2608.28576/) (2026)
- [Statistical attribute alignment for black-box generative AI via output post-processing](https://mlsanity.com/paper/2609.31607/) (2026)

## Abstract (arXiv)

The rapid proliferation of high-quality synthetic data -- generated by advanced AI models or collected as auxiliary data from related tasks -- presents both opportunities and challenges for statistical inference. This paper introduces a GEneral Synthetic-Powered Inference (GESPI) framework that wraps around a broad class of statistical inference procedures to safely enhance sample efficiency by combining synthetic and real data. Our framework leverages high-quality synthetic data to boost statistical power, yet adaptively defaults to the standard method using only real data when synthetic data are of low quality. The error rate of our method remains below a user-specified bound without any distributional assumptions on the synthetic data, and decreases as the quality of the synthetic data improves. This flexibility enables seamless integration with conformal prediction, risk control, hypothesis testing, and multiple testing procedures, all without modifying the base inference method. We demonstrate the benefits of our method on challenging tasks with limited labeled data, including AlphaFold protein structure prediction, and comparing large reasoning models on complex math problems.