# How Much Data Is Enough? Uniform Convergence Bounds for Generative & Vision-Language Models under Low-Dimensional Structure

arXiv: https://arxiv.org/abs/2512.23109 · HTML: https://mlsanity.com/paper/2512.23109/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 28 Dec 2025.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 9 of 9)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MedCLIP: Contrastive Learning from Unpaired Medical Images and Text](https://mlsanity.com/paper/2210.10163/) (2022)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Making the Most of Text Semantics to Improve Biomedical Vision--Language Processing](https://mlsanity.com/paper/2204.09817/) (2022)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Evaluating model calibration in classification](https://mlsanity.com/paper/1902.06977/) (2019)
- [Generalization Guarantees for Neural Networks via Harnessing the Low-rank Structure of the Jacobian](https://mlsanity.com/paper/1906.05392/) (2019)
- [Generalization Bounds For Unsupervised and Semi-Supervised Learning With Autoencoders](https://mlsanity.com/paper/1902.01449/) (2019)

## Abstract (arXiv)

Modern generative and vision-language models (VLMs) are increasingly used in scientific and medical decision support, where predicted probabilities must be both accurate and well calibrated. Despite strong empirical results with moderate data, it remains unclear when such predictions generalize uniformly across inputs, classes, or subpopulations, rather than only on average-a critical issue in biomedicine, where rare conditions and specific groups can exhibit large errors even when overall loss is low. We study this question from a finite-sample perspective and ask: under what structural assumptions can generative and VLM-based predictors achieve uniformly accurate and calibrated behavior with practical sample sizes? Rather than analyzing arbitrary parameterizations, we focus on induced families of classifiers obtained by varying prompts or semantic embeddings within a restricted representation space. When model outputs depend smoothly on a low-dimensional semantic representation-an assumption supported by spectral structure in text and joint image-text embeddings-classical uniform convergence tools yield meaningful non-asymptotic guarantees. Our main results give finite-sample uniform convergence bounds for accuracy and calibration functionals of VLM-induced classifiers under Lipschitz stability with respect to prompt embeddings. The implied sample complexity depends on intrinsic/effective dimension, not ambient embedding dimension, and we further derive spectrum-dependent bounds that make explicit how eigenvalue decay governs data requirements. We conclude with implications for data-limited biomedical modeling, including when current dataset sizes can support uniformly reliable predictions and why average calibration metrics may miss worst-case miscalibration.