Distributional Stability of Tangent-Linearized Gaussian Inference on Smooth Manifolds
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915965181100032 |
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| author | Seo, Junghoon Lee, Hakjin Sim, Jaehoon |
| author_facet | Seo, Junghoon Lee, Hakjin Sim, Jaehoon |
| contents | 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. Code and Jupyter notebooks are available at https://github.com/mikigom/StabilityTLGaussian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributional Stability of Tangent-Linearized Gaussian Inference on Smooth Manifolds Seo, Junghoon Lee, Hakjin Sim, Jaehoon Robotics Systems and Control 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. Code and Jupyter notebooks are available at https://github.com/mikigom/StabilityTLGaussian. |
| title | Distributional Stability of Tangent-Linearized Gaussian Inference on Smooth Manifolds |
| topic | Robotics Systems and Control |
| url | https://arxiv.org/abs/2602.19179 |