Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.39591

Structural Limits of the Information-Theoretic Uncertainty Decomposition

Jakob Lønborg Christensen·Christian F. Baumgartner·Morten Rieger Hannemose·Anders Bjorholm Dahl·Vedrana Andersen Dahl
View original source ↗Read source document ↗Export metadata ↓

Abstract

Uncertainty estimation in machine learning typically decomposes uncertainty into aleatoric uncertainty (AU) and epistemic uncertainty (EU) using the standard information-theoretic framework. However, in practice, two critical issues arise: entanglement (AU and EU are highly correlated) and epistemic collapse (EU magnitude shrinks with increasing model capacity). We analyze this framework on a functional level and discover that significant portions of the assumed AU, EU range are infeasible in finite settings, and cannot be attained with any class probabilities. We characterize how this infeasible region scales with the number of classes and Monte Carlo samples $N$ (e.g., from ensembles with $N$ members), revealing it is bounded by $\text{AU} \leq \log(2)/N$. Crucially, the infeasible region's boundary helps explain epistemic collapse: when model confidence is high, $\text{AU} > \text{EU}$ is guaranteed by this fundamental structural limitation. Our findings show that increasing ensemble size mitigates epistemic collapse by reducing the infeasible area. Lastly, we caution against interpreting AU and EU as independent quantities in low AU regimes, since we show they are coupled when $\text{AU} \leq \log(2)/N$.

Explore related subjects

cs.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jakob Lønborg Christensen, Christian F. Baumgartner, Morten Rieger Hannemose, Anders Bjorholm Dahl, Vedrana Andersen Dahl. 2026-09-30. Structural Limits of the Information-Theoretic Uncertainty Decomposition. https://arxiv.org/abs/2609.39591

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Long-Tailed 3D Detection via Multi-Modal Fusion

Contemporary autonomous vehicle (AV) benchmarks have significantly advanced multimodal (LiDAR+RGB) 3D detection. However, despite the naturally long-tailed distribution of object classes, existing benchmarking protocols primarily focus on frequent categories (e.g., pedestrian and car), largely overlooking rare but safety-critical classes such as stroller and emergency vehicle. In practice, reliable detection of both common and rare classes is essential for safe autonomous driving. We formalize this problem as Long-Tailed 3D Detection (LT3D), where evaluation encompasses all annotated classes, including rare ones. To address LT3D, we introduce hierarchical losses that promote feature sharing across classes, diagnostic metrics that assign partial credit to semantically reasonable mistakes with respect to the semantic hierarchy (e.g., confusing a child with an adult), and a multimodal late-fusion (MMLF) framework to fuse detections. In particular, we show that rare-class accuracy benefits substantially from MMLF of independently trained uni-modal LiDAR and RGB detectors. Because of the modular design, unlike prevailing end-to-end trained multi-modal detectors that require paired LiDAR-RGB data, MMLF enables the use of advanced unimodal detectors that are trained on large-scale uni-modal datasets with sufficient data for rare classes. Lastly, we examine three fundamental design choices in MMLF, including the RGB detector representation (2D vs. 3D), cross-modal association (3D vs. image plane), and fusion strategy. We find that 2D RGB detectors recognize rare classes more reliably than 3D RGB detectors, image-plane association is more robust to depth estimation errors, and probabilistic score-calibrated fusion consistently yields the best performance. Extensive experiments on nuScenes and Argoverse2 demonstrate substantial improvements of MMLF, establishing a new state of the art.

cs.CV↗
arXiv2026

DiDA: Video Object Segmentation with Distillation Learning of Deformable Attention

Video object segmentation is a fundamental research problem in computer vision. Recent techniques have often applied attention mechanism to object representation learning from video sequences. However, due to temporal changes in the video data, attention maps may not well align with the objects of interest across video frames, causing accumulated errors in long-term video processing. In addition, existing techniques have utilised complex architectures, requiring highly computational complexity and hence limiting the ability to integrate video object segmentation into low-powered devices. To address these issues, we propose DiDA, a new method for video object segmentation based on Distillation Learning of Deformable Attention. Specifically, we devise a lightweight architecture for video object segmentation that is effectively adapted to temporal changes. This is enabled by deformable attention mechanism, where the keys and values capturing the memory of a video sequence in the attention module have flexible locations updated across frames. The learnt object representations are thus adaptive to both the spatial and temporal dimensions. We train the proposed architecture using a new knowledge distillation paradigm where deformable attention maps are integrated into the distillation loss. We qualitatively and quantitatively evaluate our method and compare it with existing methods on benchmark datasets including DAVIS 2016/2017 and YouTube-VOS 2018/2019. Experimental results verify the superiority of our method via its achieved state-of-the-art performance on YouTube-VOS18 dataset and optimal memory usage. Project page and code: https://github.com/quangtrungtruong/DiDA.

cs.CV↗
arXiv2026

Towards Formal Verification of Deep Neural Networks for Object Detection

Deep neural networks (DNNs) are widely used in real-world computer vision applications, yet they remain vulnerable to errors and adversarial attacks. Formal verification offers a systematic approach to identify and mitigate these vulnerabilities, enhancing model robustness and reliability. While most existing verification methods focus on image classification models, this work extends formal verification to the more complex domain of object detection models. We propose a formulation for verifying the robustness of such models and demonstrate how state-of-the-art verification tools, originally developed for classification, can be adapted for this purpose. Through a comprehensive evaluation, we highlight the ability of formal verification to uncover vulnerabilities in object detection models, and derive formal robustness guarantees, underscoring the potential and need to further extend verification efforts in this domain. This work lays the foundation for further research into formal verification of object detection models across a broader range of computer vision applications. Our source code is publicly available online.

cs.CV↗