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Exact Degeneracy Under Balanced k-Shot Sampling:Consequences for Small-Sample Discriminant Analysis on LLM Embeddings

arXiv · AI, language, vision and robotics · article · Sep 9, 2026 · UTC

Balanced k-shot sampling draws exactly k labeled examples per class. We show that it induces an exact, provable degeneracy in a family of small-sample discriminant estimators. Under balanced sampling, the within-class scatter operator of Kernelized Linear Principal Component Discriminant Analysis (KLPCDA) is not merely rank-deficient but exactly a scaled orthogonal projector. We derive the consequences in closed form: two of KLPCDA's seven variants have every signal eigenvalue exactly equal, so their eigenvector selection criterion is provably indifferent rather than ill-conditioned, and a thi

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