Detection and Classification in Latent Spaces: High-Dimensional Analysis and Validation

Foundation models produce high-dimensional latent representations in which suitably designed statistical decision rules can be effective yet analytically tractable. We study such detectors in the high-dimensional regime, where latent dimension and training sample size grow proportionally. For linear and quadratic statistics, we derive explicit large-deviation characterizations of false-alarm and miss-detection performance under the Neyman--Pearson paradigm, and show how the binary analysis extends to multi-class classification. The resulting error probabilities and corresponding decay rates exhibit non-monotonic dependence on the shape parameter, including double-descent and, in some regimes, multiple-descent. Experiments on vision, text, and audio datasets using modern foundation models show close agreement between theoretical predictions and empirical performance. In particular, the proposed framework allows us to set a prescribed false-alarm level and accurately predict the corresponding miss-detection probability. Overall, our results provide a theoretically grounded and interpretable framework with competitive empirical performance across different modalities.