# Discriminative Span as a Predictor of Synthetic Data Utility via Classifier Reconstruction

arXiv: https://arxiv.org/abs/2605.09697 · HTML: https://mlsanity.com/paper/2605.09697/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Model collapse from synthetic data, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 10 May 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Model collapse from synthetic data](https://mlsanity.com/synth/model-collapse-from-synthetic-data/)

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

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Diverse Image-to-Image Translation via Disentangled Representations](https://mlsanity.com/paper/1808.00948/) (2018)
- [Deep MR to CT Synthesis using Unpaired Data](https://mlsanity.com/paper/1708.01155/) (2017)
- [Generative AI for Synthetic Data Across Multiple Medical Modalities: A Systematic Review of Recent Developments and Challenges](https://mlsanity.com/paper/2407.00116/) (2024)
- [VecGAN: Image-to-Image Translation with Interpretable Latent Directions](https://mlsanity.com/paper/2207.03411/) (2022)
- [SliderGAN: Synthesizing Expressive Face Images by Sliding 3D Blendshape Parameters](https://mlsanity.com/paper/1908.09638/) (2019)
- [Synthetic Data in Radiological Imaging: Current State and Future Outlook](https://mlsanity.com/paper/2407.01561/) (2024)
- [DC-cycleGAN: Bidirectional CT-to-MR Synthesis from Unpaired Data](https://mlsanity.com/paper/2211.01293/) (2022)

## Abstract (arXiv)

In many real-world computer vision applications, including medical imaging and industrial inspection, binary classification tasks are characterized by a severe scarcity of positive samples. A widely adopted solution is to generate synthetic positive data using image-to-image transformations applied to negative samples. However, a fundamental challenge remains: how can we reliably assess whether such synthetic data will improve downstream model performance? In this work, we propose a geometry-driven metric that predicts the utility of synthetic data without requiring model training. Our approach operates in the embedding space of a pre-trained foundation model and represents the dataset through difference vectors between samples. We evaluate whether the weight vector of a linear classifier can be expressed within the subspace spanned by these variations by measuring the relative projection error. Intuitively, if the variations induced by synthetic data capture task-relevant directions, their span can approximate the classifier, resulting in low projection error. Conversely, poor synthetic data fails to span these directions, leading to higher error. Across multiple datasets and architectures, we show that this metric exhibits strong correlation with downstream classification performance of CNNs trained on mixtures of real negative and synthetic positive data. These findings suggest that the proposed metric serves as a practical and informative tool for evaluating synthetic data quality in data-scarce settings.