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Fisher-Rao Sensitivity for Out-of-Distribution Detection in Deep Neural Networks

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Deep LearningOut-Of Distribution DetectionInformation Geometry
Abstract:

Deep neural networks often remain overconfident on Out-of-Distribution (OoD) inputs. We revisit this problem through Riemannian information geometry. We model the network's predictions as a statistical manifold and find that OoD inputs exhibit higher local Fisher-Rao sensitivity. By quantifying this sensitivity with the trace of the Fisher Information Matrix (FIM), we derive a unifying geometric connection between two common OoD signals: feature magnitude and output uncertainty. Analyzing the limitations of this multiplicative form, we extend our analysis using a product manifold construction. This provides a theoretical framework for the robust additive scores used in state-of-the-art (SOTA) detectors and motivates our final, competitive method.

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Overview

Overall Novelty Assessment

The paper proposes a Riemannian information geometry framework for OOD detection, connecting feature magnitude and output uncertainty through Fisher-Rao sensitivity and the Fisher Information Matrix trace. It resides in the 'Curvature and Fisher Information Methods' leaf under 'Detection Methods Based on Gradient and Curvature', sharing this leaf with only one sibling paper. This places the work in a relatively sparse research direction within the broader taxonomy, which encompasses fifty papers across diverse detection paradigms including output-based, feature-based, and domain-specific approaches.

The taxonomy reveals neighboring branches focused on gradient-based detection and broader feature-space methods. While gradient-based approaches use first-order sensitivity, this work leverages second-order curvature information, positioning it at the intersection of geometric analysis and practical detection. The product manifold construction bridges theoretical geometry with additive scoring mechanisms common in state-of-the-art detectors, connecting to output-space methods that use softmax probabilities and feature-space techniques employing distance metrics. This cross-branch positioning suggests the work synthesizes insights from multiple detection paradigms rather than operating in isolation.

Among twelve candidates examined, the competitive post-hoc detector contribution shows one refutable candidate from ten examined, while the product manifold construction found no refutations among two candidates. The geometric connection contribution was not tested against prior work in this limited search. The statistics indicate moderate prior work overlap for the detector component, but the theoretical contributions around Fisher-Rao sensitivity and product manifolds appear less directly challenged within this candidate pool. The search scope remains constrained to top-K semantic matches, leaving open whether broader literature contains additional overlapping work.

Based on the limited search of twelve candidates, the theoretical framework connecting Fisher geometry to OOD detection appears relatively novel within the examined literature, while the final detector method encounters some prior work. The sparse population of the curvature-based leaf and the cross-branch synthesis suggest the work occupies a less crowded niche, though the restricted search scope prevents definitive claims about field-wide novelty.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
12
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: Out-of-distribution detection in deep neural networks. The field has evolved into a rich landscape organized around several complementary perspectives. Detection Methods Based on Output Space exploit softmax scores and energy-based formulations, while Detection Methods Based on Feature Space leverage learned representations and distance metrics such as those in Deep Nearest Neighbors[1]. Detection Methods Based on Gradient and Curvature examine second-order information and sensitivity measures, including approaches like Sketching Curvature[12]. Statistical and Hypothesis Testing Frameworks provide principled testing procedures, and Robustness and Adversarial Considerations address the interplay between adversarial robustness and OOD detection, as explored in Robust OOD Detection[2]. Domain-Specific OOD Detection Applications tailor methods to specialized settings such as medical imaging, time-series data, and IoT systems, while Distribution Shift and Generalization Analysis investigates how models behave under covariate and label shifts. Empirical Evaluation and Benchmarking Studies systematically compare methods, Unified Frameworks and Survey Literature synthesize the field, and Anomaly Detection in Specialized Data Modalities extends techniques to graphs, videos, and other non-standard inputs. Recent work has intensified around understanding the theoretical underpinnings of detection scores and the practical trade-offs between computational cost and detection accuracy. Fisher-Rao Sensitivity[0] sits within the Curvature and Fisher Information Methods branch, emphasizing geometric and information-theoretic perspectives on model sensitivity to distributional shifts. This approach contrasts with simpler output-based methods like Learning Confidence[4] and complements feature-space techniques such as those in OOD Not All[3], which examines nuanced distinctions among OOD types. By leveraging curvature information, Fisher-Rao Sensitivity[0] offers a principled alternative to gradient-based methods like Gradients Distributional Shifts[50], aiming to capture richer geometric structure in the parameter space. Open questions remain about scalability and the interplay between curvature-based detection and adversarial robustness, themes that continue to drive innovation across multiple branches of this taxonomy.

Claimed Contributions

Geometric connection between feature magnitude and output uncertainty via Fisher-Rao sensitivity

The authors establish a theoretical link showing that the Fisher Information Matrix trace for the final layer decomposes into a product of feature magnitude and output uncertainty. This provides a geometric foundation connecting information geometry to common OoD detection signals.

0 retrieved papers
Product manifold construction for additive OoD score

The authors develop a product manifold framework that decouples uncertainty and feature-space signals, yielding an additive OoD detection score. This construction provides theoretical justification for additive compositions used in state-of-the-art methods and addresses limitations of multiplicative formulations.

2 retrieved papers
Competitive post-hoc OoD detector requiring no training modifications

The authors introduce a practical OoD detection method that operates post-hoc without requiring model retraining, OoD data exposure, or inference-time modifications. The method achieves competitive performance on standard benchmarks while using only a single forward pass.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Geometric connection between feature magnitude and output uncertainty via Fisher-Rao sensitivity

The authors establish a theoretical link showing that the Fisher Information Matrix trace for the final layer decomposes into a product of feature magnitude and output uncertainty. This provides a geometric foundation connecting information geometry to common OoD detection signals.

Contribution

Product manifold construction for additive OoD score

The authors develop a product manifold framework that decouples uncertainty and feature-space signals, yielding an additive OoD detection score. This construction provides theoretical justification for additive compositions used in state-of-the-art methods and addresses limitations of multiplicative formulations.

Contribution

Competitive post-hoc OoD detector requiring no training modifications

The authors introduce a practical OoD detection method that operates post-hoc without requiring model retraining, OoD data exposure, or inference-time modifications. The method achieves competitive performance on standard benchmarks while using only a single forward pass.

Table of Contents