# From Theory to Decision Rule: Calibrating the Noisy-Label Crossover for Vision-Language Model Weak Supervision Across Three Medical-Imaging Benchmarks

arXiv: https://arxiv.org/abs/2605.24771 · HTML: https://mlsanity.com/paper/2605.24771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical vision-language models, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 7 of its 9 references that are in the map.
- First posted on arXiv 23 May 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Medical vision-language models](https://mlsanity.com/mllm/medical-vision-language-models/)

## Builds on (most cited first, 7 of 7)

- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [BiomedCLIP: a multimodal biomedical foundation model pretrained from fifteen million scientific image-text pairs](https://mlsanity.com/paper/2303.00915/) (2023)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [VLM-CPL: Consensus Pseudo Labels from Vision-Language Models for Annotation-Free Pathological Image Classification](https://mlsanity.com/paper/2403.15836/) (2024)

## Abstract (arXiv)

Classical noisy-label theory predicts that downstream performance under weak supervision is bounded above by the labeler's accuracy, implying a sharp crossover: once a gold-trained classifier matches the labeler, weak labels stop helping and start hurting. The prediction is theoretical; what is missing is a benchmark calibration that turns it into an instance-level statement for modern foundation-model labelers. We provide such a calibration for BiomedCLIP-generated weak labels on three medical-imaging benchmarks (PCAM, ISIC, NIH-CXR) and six downstream architectures spanning an 11x parameter range. The crossover predicted by theory appears at ng~100 on PCAM, 20-50 on ISIC, and 250-500 on NIH-CXR; weak labels above the crossover degrade AUC by up to -0.10. The location is architecture-invariant for four of five pretrained architectures, and a within-family DenseNet sweep (2.5x parameters, identical pretraining) supports the view that the labeler, not the student, is the dominant constraint. The calibration in turn produces a decision rule operable from 10-20 gold labels: compare gold-only AUC to VLM accuracy on the user's gold set. A structured-vs-random noise sign flip on NIH-CXR shows that the rate-only formulation of the bound is incomplete and identifies a concrete refinement (label-space projection) that future benchmarks can be designed to test.