A particle-based probabilistic CBF framework derives finite-sample safety certificates for Gaussian state estimation uncertainty by showing that barrier increments remain sub-Gaussian under Lipschitz control-affine dynamics.
Vershynin,High-Dimensional Probability: An Introduction with Applications in Data Science
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Finite-sample noise collapses the eigengap in representation covariances limiting recoverable modes K(N); multimodal learning stabilizes it via low-rank constraints, yielding better class separation quantified by truncated Mahalanobis energy approximated with a zeta function.
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Probabilistic Control Barrier Functions for Systems with State Estimation Uncertainty using Sub-Gaussian Concentration
A particle-based probabilistic CBF framework derives finite-sample safety certificates for Gaussian state estimation uncertainty by showing that barrier increments remain sub-Gaussian under Lipschitz control-affine dynamics.
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Anchoring the Eigengap: Cross-Modal Spectral Stabilization for Sample-Efficient Representation Learning
Finite-sample noise collapses the eigengap in representation covariances limiting recoverable modes K(N); multimodal learning stabilizes it via low-rank constraints, yielding better class separation quantified by truncated Mahalanobis energy approximated with a zeta function.