Beyond the Simplex: Balanced Prototype Geometry for Scorer-Agnostic Open-Set Recognition

• URL: http://arxiv.org/abs/2606.01883v1
• Date: Mon, 01 Jun 2026 08:28:24 GMT
• Title: Beyond the Simplex: Balanced Prototype Geometry for Scorer-Agnostic Open-Set Recognition
• Abstract summary: We give a theoretical account of simplex-ratio OSR that holds in every embedding dimension, including d C-1.<n>We show that the prototypes attain one-distance symmetry, behaving like a regular simplex, if and only if d >= C-1.<n>We further show the false-ratio rate decays exponentially in d under natural isotropy assumptions.
• Score: 2.9506547907695997
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Open-set recognition (OSR) requires a classifier to reject inputs from unseen classes which is essential in safety-critical settings such as medical imaging. Simplex based methods, which fix class prototypes at the vertices of a regular simplex and then reject via a distance-ratio score, perform well empirically but lack theoretical justification, and existing analysis applies only when the embedding dimension d is at least C-1, which is the regime in which a regular simplex exists. We give a theoretical account of simplex-ratio OSR that holds in every embedding dimension, including d < C-1. Our analysis centers on balanced equal-norm codes: prototype configurations with equal lengths and zero sum, which exist for all d >= 2 and include the regular simplex as a special case. For these codes we show that an auxiliary squared ratio score has sublevel sets that are exact unions of Euclidean balls, which in turn bracket the acceptance region of the operational score; and we prove a sharp dichotomy: the prototypes attain one-distance symmetry, behaving like a regular simplex, if and only if d >= C-1, with controlled degradation governed by an explicit defect parameter below that threshold. We further show the false-acceptance rate decays exponentially in d under natural isotropy assumptions, and that the operational score is globally Lipschitz with compact acceptance regions. Empirically, we study balanced prototype geometry as both an analytic tool and a representation-learning prior, rather than as a stand-alone state-of-the-art detector. Across CIFAR and MedMNIST open-set splits, the geometry provides useful structure, but OSR performance remains strongly dependent on the scoring rule: raw ratio scores typically underperform nearest-neighbor and logit-based alternatives.

Related papers

• Scaling-Score Conformal Prediction for Multi-Target Regression [0.42970700836450476]
  Multi-target regression requires a model to simultaneously predict several related outputs.<n>We propose the scaling-score conformal method, which is model-agnostic (requires only component-wise absolute residuals)
  arXiv  Detail & Related papers  (2026-09-15T12:23:57Z)
• Anchored Regularized Direct Least Squares (ARDLS): Integrating Established Prioritization Operators for Priority Elicitation in the Analytic Hierarchy Process [0.0]
  This paper introduces the Anchored Regularized Direct Least Squares (ARDLS)<n>ARDLS uniquely determined established operators, such as normalization techniques, the Eigenvector method, Singular Value Decomposition, Cosine Maximization, and the.<n>The proposed ARDLS may be the guarantee for the ADL applied to many application domains.
  arXiv  Detail & Related papers  (2026-08-21T14:57:41Z)
• Structuring Semantic Embeddings for Principle Evaluation: A Prototype-Guided Contrastive Learning Approach [58.15427952222424]
  General-purpose text embeddings are widely deployed for such tasks, but broad semantic similarity can place semantically similar yet task-distinct examples.<n>We introduce Prototype-Guided Contrastive Learning (PGCL), a prototype-guided geometric regularization module built on top of frozen text embeddings.
  arXiv  Detail & Related papers  (2026-08-15T13:19:25Z)
• Entanglement Quantification via Symmetric Extensions: A Resource Theory Hierarchy [3.662037602213926]
  We introduce a hierarchy of entanglement measures Ek based on k-symmetric PPT extensions.<n>Each Ek, defined via a minimal eigenvalue shift, is faithful, convex, and monotone under free operations.<n>The hierarchy strictly refines PPT-robustness at k = 1, detects bound entanglement at k = 2, and converges exactly to the separability measure as k -> infinity.
  arXiv  Detail & Related papers  (2026-07-18T20:39:35Z)
• Precise sample covariance spectral norm error -- an RDT view [2.538209532048867]
  We develop a generic framework based on Random Duality Theory (RDT)<n>We establish complementary lower bounds by introducing a novel bilinear-quadratic RDT lower-bounding mechanism.<n>Our theoretical results are supplemented with numerical evaluations and simulations.
  arXiv  Detail & Related papers  (2026-07-16T01:16:31Z)
• Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments [17.990911601858482]
  We introduce Diffused Geodesic Moments (DGM), a seed-conditioned descriptor that computes sparse implicit heat responses.<n>DGM is used both as a practical non-spectral baseline and as an instrument for isolating protocol effects.
  arXiv  Detail & Related papers  (2026-05-27T19:00:41Z)
• Regularized Online RLHF with Generalized Bilinear Preferences [68.44113000390544]
  We consider the problem of contextual online RLHF with general preferences.<n>We adopt the Generalized Bilinear Preference Model to capture preferences via low-rank, skew-symmetric matrices.<n>We prove that the dual gap of the greedy policy is bounded by the square of the estimation error.
  arXiv  Detail & Related papers  (2026-02-26T15:27:53Z)
• RANSAC Scoring Functions: Analysis and Reality Check [0.0]
  We revisit the problem of assigning a score (a quality of fit) to candidate geometric models.<n>We show that a threshold-based parameterization leads to a unified view of likelihood-based and robust M-estimators.
  arXiv  Detail & Related papers  (2025-12-22T20:08:46Z)
• Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations [121.39938773554523]
  The Area Under the ROC Curve (AUC) is a pivotal evaluation metric in real-world scenarios with both class imbalance and decision constraints.<n>We present two simple instance-wise minimax reformulations to close the approximation gap of PAUC optimization.<n>The resulting algorithms enjoy a linear per-iteration computational complexity w.r.t. the sample size and a convergence rate of $O(-2/3)$ for typical one-way and two-way PAUCs.
  arXiv  Detail & Related papers  (2025-12-01T02:52:33Z)
• Geometric Calibration and Neutral Zones for Uncertainty-Aware Multi-Class Classification [0.0]
  This work bridges information geometry and statistical learning, offering formal guarantees for uncertainty-aware classification in applications requiring rigorous validation.<n> Empirical validation on Adeno-Associated Virus classification demonstrates that the two-stage framework captures 72.5% of errors while deferring 34.5% of samples, reducing automated decision error rates from 16.8% to 6.9%.
  arXiv  Detail & Related papers  (2025-11-26T01:29:49Z)
• 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)
• Asymptotically Unbiased Instance-wise Regularized Partial AUC Optimization: Theory and Algorithm [101.44676036551537]
  One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC) measures the average performance of a binary classifier. Most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllable. We present a simpler reformulation of the PAUC problem via distributional robust optimization AUC.
  arXiv  Detail & Related papers  (2022-10-08T08:26:22Z)
• Generalized Orthogonal Procrustes Problem under Arbitrary Adversaries [1.0152838128195467]
  We study the semidefinite relaxation (SDR) and an iterative method named generalized power method (GPM) to find the least squares estimator.<n>In addition, we analyze the low-rank factorization algorithm and show the corresponding optimization landscape is free of spurious local minimizers.
  arXiv  Detail & Related papers  (2021-06-29T15:19:25Z)
• Making Affine Correspondences Work in Camera Geometry Computation [62.7633180470428]
  Local features provide region-to-region rather than point-to-point correspondences. We propose guidelines for effective use of region-to-region matches in the course of a full model estimation pipeline. Experiments show that affine solvers can achieve accuracy comparable to point-based solvers at faster run-times.
  arXiv  Detail & Related papers  (2020-07-20T12:07:48Z)

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.