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Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity
We study latent geometry as an explicit component of representation quality in data-scarce learning. For an encoder (ϕ), we define (Q_{β,γ}(ϕ)=I(ϕ(X);Y)-β\mathcal C(ϕ)-γd_{\mathrm{int}}(ϕ)), combining task-relevant information with penalties for curvature and intrinsic latent dimension. Thus geometr
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