Distributional Stability of Tangent-Linearized Gaussian Inference on Smooth Manifolds

• URL: http://arxiv.org/abs/2602.19179v1
• Date: Sun, 22 Feb 2026 13:18:45 GMT
• Title: Distributional Stability of Tangent-Linearized Gaussian Inference on Smooth Manifolds
• Abstract summary: We derive explicit non-asymptotic $W$ stability bounds for projection marginalization and surface-measure conditioning.<n>The bounds separate local second-order geometric distortion from nonlocal tail leakage.<n>Experiments validate the predicted calibration transition near $sqrt||_mathrmop/Rapprox 1/6$ and indicate that normal-direction uncertainty is the dominant failure mode when locality breaks.
• Score: 3.632189127068905
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian inference on smooth manifolds is central to robotics, but exact marginalization and conditioning are generally non-Gaussian and geometry-dependent. We study tangent-linearized Gaussian inference and derive explicit non-asymptotic $W_2$ stability bounds for projection marginalization and surface-measure conditioning. The bounds separate local second-order geometric distortion from nonlocal tail leakage and, for Gaussian inputs, yield closed-form diagnostics from $(μ,Σ)$ and curvature/reach surrogates. Circle and planar-pushing experiments validate the predicted calibration transition near $\sqrt{\|Σ\|_{\mathrm{op}}}/R\approx 1/6$ and indicate that normal-direction uncertainty is the dominant failure mode when locality breaks. These diagnostics provide practical triggers for switching from single-chart linearization to multi-chart or sample-based manifold inference.

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