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.
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 W2 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 ∥Σ∥op/R≈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.
We study Bayesian optimization (BO) through the lens of information geometry. Pulling back the Fisher information metric through the surrogate posterior map yields a local sensitivity tensor on the input space, which leads to an upper bound on the gradient of reparameterizable acquisition functions. This view explains vanishing-gradient behavior in high-dimensional BO and provides a common interpretation of heuristics such as RAASP and dimension-scaled lengthscales. Building on this analysis, we propose FITR, a trust-region-based BO method that replaces lengthscale-based scaling by local pullback-Fisher weights. FITR is not restricted to GP kernels with explicit lengthscales. On GP benchmarks with an SE kernel, experiments show competitive performance using FITR. The proposed method also easily generalizes to non-isotropic surrogates, although the gains are more task-dependent in that setting.
Saksham Kiroriwal, Julius Pfrommer, Jürgen Beyerer
Cognitive Industrial Systems, Fraunhofer IOSB, Karlsruhe, Germany · Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Multiobject tracking (MOT) is a fundamental capability in autonomous navigation, radar and sonar systems, as well as 6G integrated sensing-and-communication (ISAC) networks. In this paper, we propose a neural-enhanced track-before-detect (TkBD) framework that operates directly on complex-valued raw signals and learns a latent representation of unmodeled propagation effects during runtime. We introduce an environment-dependent latent intensity variable that characterizes the signal power of each object in the shared propagation environment. The probability density function of this intensity variable is represented by a normalizing flow and trained online in an unsupervised manner within the sequential Bayesian inference procedure. The learning objective is derived from a variational Bayes formulation by maximizing the evidence lower bound (ELBO), thereby accounting for the uncertainties inherent in the Bayesian TkBD problem. To enable scalable inference, we make use of a recently introduced Bayesian TkBD framework that combines belief propagation, which avoids high-dimensional operations, with sequential Monte Carlo methods for efficient low-dimensional updates.