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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.08764 |
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| _version_ | 1866909029596397568 |
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| author | Dhinagar, Nikhil J. Chhatbar, Vidhi Jagad, Chirag Senthilkumar, Pavithra Thomopoulos, Sophia I. Khan, Mahir H. Liew, Sook-Lei Group, the ENIGMA-Stroke Recovery Working Thompson, Paul M. |
| author_facet | Dhinagar, Nikhil J. Chhatbar, Vidhi Jagad, Chirag Senthilkumar, Pavithra Thomopoulos, Sophia I. Khan, Mahir H. Liew, Sook-Lei Group, the ENIGMA-Stroke Recovery Working Thompson, Paul M. |
| contents | Deep vision models degrade sharply in low-data regimes, particularly in medical imaging where labeled samples are scarce. We show this arises not merely from overfitting but from a geometric failure: finite-sample noise corrupts the embedding covariance, collapsing the eigengap and limiting the number of recoverable signal-bearing modes. We develop a spectral theory of finite-sample representation learning that quantifies the recoverable dimension K(N), the number of eigenmodes that can be stably estimated from N samples. Using perturbation theory and concentration bounds, we show that only modes with eigenvalues above the noise floor $\|\hatΣ - Σ\|_{\mathrm{op}} \sim \sqrt{D/N}$ are reliable, yielding a truncated Mahalanobis energy that governs classification performance. Under a power-law spectral model, this energy can be approximated by a truncated Riemann zeta function, linking eigenvalue decay to data efficiency and AUC. Within this framework, multimodal learning acts as spectral stabilization: vision-language models impose low-rank constraints that suppress noise-dominated directions and preserve the eigengap, increasing K(N) under data scarcity. Across MNIST and multi-disease neuroimaging, we show that multimodal training maintains more stable modes and improves class separation, even when unimodal models achieve comparable few-shot accuracy. These results identify spectral collapse as a fundamental bottleneck in low-data learning. We use truncated Mahalanobis energy and K(N) to diagnose encoder quality, and introduce zeta-based spectral filtering as a principled approach to improve data efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Anchoring the Eigengap: Cross-Modal Spectral Stabilization for Sample-Efficient Representation Learning Dhinagar, Nikhil J. Chhatbar, Vidhi Jagad, Chirag Senthilkumar, Pavithra Thomopoulos, Sophia I. Khan, Mahir H. Liew, Sook-Lei Group, the ENIGMA-Stroke Recovery Working Thompson, Paul M. Machine Learning Computer Vision and Pattern Recognition Image and Video Processing Deep vision models degrade sharply in low-data regimes, particularly in medical imaging where labeled samples are scarce. We show this arises not merely from overfitting but from a geometric failure: finite-sample noise corrupts the embedding covariance, collapsing the eigengap and limiting the number of recoverable signal-bearing modes. We develop a spectral theory of finite-sample representation learning that quantifies the recoverable dimension K(N), the number of eigenmodes that can be stably estimated from N samples. Using perturbation theory and concentration bounds, we show that only modes with eigenvalues above the noise floor $\|\hatΣ - Σ\|_{\mathrm{op}} \sim \sqrt{D/N}$ are reliable, yielding a truncated Mahalanobis energy that governs classification performance. Under a power-law spectral model, this energy can be approximated by a truncated Riemann zeta function, linking eigenvalue decay to data efficiency and AUC. Within this framework, multimodal learning acts as spectral stabilization: vision-language models impose low-rank constraints that suppress noise-dominated directions and preserve the eigengap, increasing K(N) under data scarcity. Across MNIST and multi-disease neuroimaging, we show that multimodal training maintains more stable modes and improves class separation, even when unimodal models achieve comparable few-shot accuracy. These results identify spectral collapse as a fundamental bottleneck in low-data learning. We use truncated Mahalanobis energy and K(N) to diagnose encoder quality, and introduce zeta-based spectral filtering as a principled approach to improve data efficiency. |
| title | Anchoring the Eigengap: Cross-Modal Spectral Stabilization for Sample-Efficient Representation Learning |
| topic | Machine Learning Computer Vision and Pattern Recognition Image and Video Processing |
| url | https://arxiv.org/abs/2605.08764 |