Robust Sequential Tracking via Bounded Information Geometry and Non-Parametric Field Actions

• URL: http://arxiv.org/abs/2603.13613v1
• Date: Fri, 13 Mar 2026 21:40:44 GMT
• Title: Robust Sequential Tracking via Bounded Information Geometry and Non-Parametric Field Actions
• Abstract summary: Empirical benchmarks across three domains--LiDAR maneuvering target tracking, high-frequency cryptocurrency order flow, and quantum state tomography--demonstrate that this information geometry analytically truncates outliers.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Standard sequential inference architectures are compromised by a normalizability crisis when confronted with extreme, structured outliers. By operating on unbounded parameter spaces, state-of-the-art estimators lack the intrinsic geometry required to appropriately sever anomalies, resulting in unbounded covariance inflation and mean divergence. This paper resolves this structural failure by analyzing the abstraction sequence of inference at the meta-prior level (S_2). We demonstrate that extremizing the action over an infinite-dimensional space requires a non-parametric field anchored by a pre-prior, as a uniform volume element mathematically does not exist. By utilizing strictly invariant Delta (or ν) Information Separations on the statistical manifold, we physically truncate the infinite tails of the spatial distribution. When evaluated as a Radon-Nikodym derivative against the base measure, the active parameter space compresses into a strictly finite, normalizable probability droplet. Empirical benchmarks across three domains--LiDAR maneuvering target tracking, high-frequency cryptocurrency order flow, and quantum state tomography--demonstrate that this bounded information geometry analytically truncates outliers, ensuring robust estimation without relying on infinite-tailed distributional assumptions.

Related papers

• Computer-assisted global regularity across nonlinear families of three-dimensional periodic Navier-Stokes flows [0.0]
  I develop a computer-assisted framework that establishes global regularity for three-dimensional periodic Navier-Stokes flows.<n>The method retains the complete nonlinear residual before spectral truncation and controls the evolution until decay guarantees regularity for all subsequent times.<n>An ensemble of 4,096 configurations, supplemented by 1,600 refinement trajectories and public turbulence data, connects the mathematical observables to spectral transfer and vortex geometry.
  arXiv  Detail & Related papers  (2026-09-14T18:02:50Z)
• Fitting Unknown Number of Hyperplanes with Manifold Optimization [57.48093263119306]
  Fitting unknown number of linearplanes to data is a fundamental yet challenging problem in machine learning.<n>Existing approaches often struggle with optimum optima or lack geometric consistency.
  arXiv  Detail & Related papers  (2026-05-27T14:02:20Z)
• Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data [45.85698554568285]
  We find necessary and sufficient conditions for deciding when an observed distribution is compatible with a memoryless sequential quantum process in a fixed direction.<n>We then specialize to the two-qubit Pauli setting, where the problem remains non-tomographic but becomes explicitly tractable.
  arXiv  Detail & Related papers  (2026-05-06T07:16:29Z)
• A Mean Curvature Approach to Boundary Detection: Geometric Insights for Unsupervised Learning [52.452902154360565]
  We introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning.<n>MCBP explicitly models the intrinsic curvature of the data manifold and computes pointwise mean curvature without requiring principled manifold parametrization.<n>Experiments on synthetic and real-world datasets demonstrate that MCBP consistently improves clustering performance.
  arXiv  Detail & Related papers  (2026-05-05T20:19:09Z)
• Statistical-Geometric Degeneracy in UAV Search: A Physics-Aware Asymmetric Filtering Approach [23.49656058107753]
  Post-disaster survivor localization using Unmanned Aerial Vehicles (UAVs) faces a fundamental physical challenge.<n>Unlike standard Gaussian noise, signal reflection from debris introduces strictly non-negative ranging biases.<n>Existing robust estimators, typically designed with symmetric loss functions, implicitly rely on the assumption of error symmetry.<n>We propose a physically-grounded solution, the AsymmetricHuberEKF, which explicitly incorporates the non-negative physical prior of NLOS biases.
  arXiv  Detail & Related papers  (2026-02-11T08:33:56Z)
• Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits [72.0643009153473]
  We show that expressive variational ansatze enter a Haar-like universality class in which both observable expectation values and parameter gradients concentrate exponentially with system size.<n>As a consequence, the hypothesis class induced by such circuits collapses with high probability to a narrow family of near-constant functions.<n>We further show that this collapse is not unavoidable: tensor-structured VQCs, including tensor-network-based and tensor-hypernetwork parameterizations, lie outside the Haar-like universality class.
  arXiv  Detail & Related papers  (2026-01-05T08:04:33Z)
• ARGUS: Adaptive Rotation-Invariant Geometric Unsupervised System [0.0]
  This paper introduces Argus, a framework that reconceptualizes drift detection as tracking local statistics over a fixed spatial partition of the data manifold.<n> Voronoi tessellations over canonical orthonormal frames yield drift metrics that are invariant to transformations.<n>A graph-theoretic characterization of drift propagation is developed that distinguishes coherent distributional shifts from isolated perturbations.
  arXiv  Detail & Related papers  (2026-01-03T22:39:20Z)
• An approach to Fisher-Rao metric for infinite dimensional non-parametric information geometry [0.6138671548064355]
  Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier"<n>This paper introduces a novel framework to resolve the intractability with an Orthogonal Decomposition of the Tangent Space.<n>By defining the Information Capture Ratio, we provide a rigorous method for estimating intrinsic dimensionality in high-dimensional data.
  arXiv  Detail & Related papers  (2025-12-25T00:18:41Z)
• Learning Eigenstructures of Unstructured Data Manifolds [47.81117132002129]
  We introduce a novel framework that learns a spectral basis for shape and manifold analysis from unstructured data.<n>By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines.
  arXiv  Detail & Related papers  (2025-11-30T22:06:49Z)
• Manifold Percolation: from generative model to Reinforce learning [0.26905021039717986]
  Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution.<n>We propose that continuum percolation is uniquely suited to this support analysis, as the sampling process effectively projects high-dimensional density estimation onto a geometric counting problem on the support.
  arXiv  Detail & Related papers  (2025-11-25T17:12:42Z)
• Intrinsic Bayesian Cramér-Rao Bound with an Application to Covariance Matrix Estimation [49.67011673289242]
  This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a smooth manifold. It induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure.
  arXiv  Detail & Related papers  (2023-11-08T15:17:13Z)
• Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computation [52.73824786627612]
  This paper establishes new convergence results for textitgeodesic strongly monotone games.<n>Our key result shows that RGD attains last-iterate linear convergence in a textitgeometry-agnostic fashion.<n>Overall, this paper presents the first geometry-agnostic last-iterate convergence analysis for games beyond the Euclidean settings.
  arXiv  Detail & Related papers  (2023-06-29T01:20:44Z)
• A Unifying and Canonical Description of Measure-Preserving Diffusions [60.59592461429012]
  A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework. We develop a geometric theory that improves and generalises this construction to any manifold.
  arXiv  Detail & Related papers  (2021-05-06T17:36:55Z)
• Log-Likelihood Ratio Minimizing Flows: Towards Robust and Quantifiable Neural Distribution Alignment [52.02794488304448]
  We propose a new distribution alignment method based on a log-likelihood ratio statistic and normalizing flows. We experimentally verify that minimizing the resulting objective results in domain alignment that preserves the local structure of input domains.
  arXiv  Detail & Related papers  (2020-03-26T22:10:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.