mailitics

Tag: geometric

  • Geometric structures and deviations on James’ symmetric positive-definite matrix bicone domain

    Geometric structures and deviations on James’ symmetric positive-definite matrix bicone domain arXiv:2603.02483v1 Announce Type: new Abstract: Symmetric positive-definite (SPD) matrix datasets play a central role across numerous scientific disciplines, including signal processing, statistics, finance, computer vision, information theory, and machine learning among others. The set of SPD matrices forms a cone which can be viewed…

  • A Geometric Method to Spot Hallucinations Without an LLM Judge

    A Geometric Method to Spot Hallucinations Without an LLM Judge Imagine a flock of birds in flight. There’s no leader. No central command. Each bird aligns with its neighbors—matching direction, adjusting speed, maintaining coherence through purely local coordination. The result is global order emerging from local consistency. Now imagine one bird flying with the same…

  • Geometric Calibration and Neutral Zones for Uncertainty-Aware Multi-Class Classification

    Geometric Calibration and Neutral Zones for Uncertainty-Aware Multi-Class Classification arXiv:2511.20960v1 Announce Type: new Abstract: Modern artificial intelligence systems make critical decisions yet often fail silently when uncertain. We develop a geometric framework for post-hoc calibration of neural network probability outputs, treating probability vectors as points on the $(c-1)$-dimensional probability simplex equipped with the Fisher–Rao metric.…

  • CP$^2$: Leveraging Geometry for Conformal Prediction via Canonicalization

    CP$^2$: Leveraging Geometry for Conformal Prediction via Canonicalization arXiv:2506.16189v1 Announce Type: new Abstract: We study the problem of conformal prediction (CP) under geometric data shifts, where data samples are susceptible to transformations such as rotations or flips. While CP endows prediction models with post-hoc uncertainty quantification and formal coverage guarantees, their practicality breaks under distribution…

  • Categorical and geometric methods in statistical, manifold, and machine learning

    Categorical and geometric methods in statistical, manifold, and machine learning arXiv:2505.03862v1 Announce Type: new Abstract: We present and discuss applications of the category of probabilistic morphisms, initially developed in cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics,…