Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity
arXiv:2511.02496v2 Announce Type: replace Abstract: We study latent geometry as an explicit component of representation quality in data-scarce learning. For an encoder (\phi), we define (Q_{\beta,\gamma}(\phi)=I(\phi(X);Y)-\beta\mathcal C(\phi)-\gamma d_{\mathrm{int}}(\phi)), combining task-relevant information with penalties for curvature and intrinsic latent dimension. Thus geometry becomes part of the bottleneck criterion, not only a post hoc diagnostic. Under smooth-manifold, loss-transfer, and estimator-concentration assumptions, we derive non-asymptotic low-label generalization bounds wh
The paper focuses on representation learning under data scarcity, a critical challenge given the increasing cost of high-quality labeled data and the push towards more efficient AI systems.
This research introduces a novel theoretical framework for improving AI model generalization in data-scarce environments by explicitly incorporating geometric considerations into the information bottleneck.
The explicit inclusion of latent geometry in representation quality promises more robust and data-efficient machine learning, potentially reducing the need for massive datasets in some applications.
- · AI researchers
- · Companies with limited proprietary datasets
- · Edge AI developers
- · Massive data aggregators (potentially, over time)
Improved model efficiency and generalization in scenarios with scarce training data.
Reduced barriers to entry for AI development in specialized or data-poor domains.
Shift in AI development paradigms away from purely data-driven brute force to more geometrically informed and data-efficient approaches.
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Read at arXiv cs.LG