David Brellmann

Joseph Hoche, David Brellmann, Gianni Franchi

Uncertainty quantification (UQ) remains a critical challenge in Large Vision Language Models (LVLMs) for reliable predictions and real-world deployment. However, most existing methods are adapted from the LLM literature and primarily focus on the language modality, leaving the contribution of visual information to LVLM uncertainty largely underexplored. In this paper, we investigate how LVLMs process visual information and whether this process can be used to improve uncertainty estimation. By analyzing hidden representations after the integration of visual features during the generation process, we observe that high-confidence predictions rely more heavily on visual content than uncertain ones. Building on this insight, we propose Visual-Grounded Token UQ (VIG-TUQ), a training-free framework that explicitly incorporates visual grounding into uncertainty estimation by weighting token-level language uncertainty with visual grounding scores. We evaluate VIG-TUQ on multiple datasets and across diverse LVLM architectures, including early-fusion, late-fusion, and native-fusion models. Results indicate that our method often improves upon existing token-level uncertainty approaches. Code and data will be made available upon acceptance.

Joseph Hoche, Andrei Bursuc, David Brellmann et al.

Large Vision-Language Models (LVLMs) often produce plausible but unreliable outputs, making robust uncertainty estimation essential. Recent work on semantic uncertainty estimates relies on external models to cluster multiple sampled responses and measure their semantic consistency. However, these clustering methods are often fragile, highly sensitive to minor phrasing variations, and can incorrectly group or separate semantically similar answers, leading to unreliable uncertainty estimates. We propose Semantic Gaussian Process Uncertainty (SGPU), a Bayesian framework that quantifies semantic uncertainty by analyzing the geometric structure of answer embeddings, avoiding brittle clustering. SGPU maps generated answers into a dense semantic space, computes the Gram matrix of their embeddings, and summarizes their semantic configuration via the eigenspectrum. This spectral representation is then fed into a Gaussian Process Classifier that learns to map patterns of semantic consistency to predictive uncertainty, and that can be applied in both black-box and white-box settings. Across six LLMs and LVLMs on eight datasets spanning VQA, image classification, and textual QA, SGPU consistently achieves state-of-the-art calibration (ECE) and discriminative (AUROC, AUARC) performance. We further show that SGPU transfers across models and modalities, indicating that its spectral representation captures general patterns of semantic uncertainty.

David Brellmann, Eloïse Berthier, David Filliat et al.

Temporal Difference (TD) algorithms are widely used in Deep Reinforcement Learning (RL). Their performance is heavily influenced by the size of the neural network. While in supervised learning, the regime of over-parameterization and its benefits are well understood, the situation in RL is much less clear. In this paper, we present a theoretical analysis of the influence of network size and $l_2$-regularization on performance. We identify the ratio between the number of parameters and the number of visited states as a crucial factor and define over-parameterization as the regime when it is larger than one. Furthermore, we observe a double descent phenomenon, i.e., a sudden drop in performance around the parameter/state ratio of one. Leveraging random features and the lazy training regime, we study the regularized Least-Square Temporal Difference (LSTD) algorithm in an asymptotic regime, as both the number of parameters and states go to infinity, maintaining a constant ratio. We derive deterministic limits of both the empirical and the true Mean-Squared Bellman Error (MSBE) that feature correction terms responsible for the double descent. Correction terms vanish when the $l_2$-regularization is increased or the number of unvisited states goes to zero. Numerical experiments with synthetic and small real-world environments closely match the theoretical predictions.

Mouïn Ben Ammar, David Brellmann, Arturo Mendoza et al.

Out-of-distribution (OOD) detection is essential for ensuring the reliability and safety of machine learning systems. In recent years, it has received increasing attention, particularly through post-hoc detection and training-based methods. In this paper, we focus on post-hoc OOD detection, which enables identifying OOD samples without altering the model's training procedure or objective. Our primary goal is to investigate the relationship between model capacity and its OOD detection performance. Specifically, we aim to answer the following question: Does the Double Descent phenomenon manifest in post-hoc OOD detection? This question is crucial, as it can reveal whether overparameterization, which is already known to benefit generalization, can also enhance OOD detection. Despite the growing interest in these topics by the classic supervised machine learning community, this intersection remains unexplored for OOD detection. We empirically demonstrate that the Double Descent effect does indeed appear in post-hoc OOD detection. Furthermore, we provide theoretical insights to explain why this phenomenon emerges in such setting. Finally, we show that the overparameterized regime does not yield superior results consistently, and we propose a method to identify the optimal regime for OOD detection based on our observations.