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Precisecharacterizationofthepriorpredictive distributionofdeepReLUnetworks

Neural Information Processing Systems

Whiletheoretical results havebeen obtained for their heavy-tailedness, the full characterization of the prior predictive distribution (i.e. its density, CDF andmoments), remained unknownpriortothiswork.




Flow Matching for Robust Simulation-Based Inference under Model Misspecification

Ruhlmann, Pierre-Louis, Rodrigues, Pedro L. C., Arbel, Michael, Forbes, Florence

arXiv.org Machine Learning

Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data. A persistent challenge, however, is model misspecification: simulators are only approximations of reality, and mismatches between simulated and real data can yield biased or overconfident posteriors. We address this issue by introducing Flow Matching Corrected Posterior Estimation (FMCPE), a framework that leverages the flow matching paradigm to refine simulation-trained posterior estimators using a small set of real calibration samples. Our approach proceeds in two stages: first, a posterior approximator is trained on abundant simulated data; second, flow matching transports its predictions toward the true posterior supported by real observations, without requiring explicit knowledge of the misspecification. This design enables FMCPE to combine the scalability of SBI with robustness to distributional shift. Across synthetic benchmarks and real-world datasets, we show that our proposal consistently mitigates the effects of misspecification, delivering improved inference accuracy and uncertainty calibration compared to standard SBI baselines, while remaining computationally efficient.



Explainable Graph Neural Networks: Understanding Brain Connectivity and Biomarkers in Dementia

Tewari, Niharika, Le, Nguyen Linh Dan, Liu, Mujie, Ren, Jing, Xu, Ziqi, Sarwar, Tabinda, Baths, Veeky, Xia, Feng

arXiv.org Artificial Intelligence

Dementia is a progressive neurodegenerative disorder with multiple etiologies, including Alzheimer's disease, Parkinson's disease, frontotemporal dementia, and vascular dementia. Its clinical and biological heterogeneity makes diagnosis and subtype differentiation highly challenging. Graph Neural Networks (GNNs) have recently shown strong potential in modeling brain connectivity, but their limited robustness, data scarcity, and lack of interpretability constrain clinical adoption. Explainable Graph Neural Networks (XGNNs) have emerged to address these barriers by combining graph-based learning with interpretability, enabling the identification of disease-relevant biomarkers, analysis of brain network disruptions, and provision of transparent insights for clinicians. This paper presents the first comprehensive review dedicated to XGNNs in dementia research. We examine their applications across Alzheimer's disease, Parkinson's disease, mild cognitive impairment, and multi-disease diagnosis. A taxonomy of explainability methods tailored for dementia-related tasks is introduced, alongside comparisons of existing models in clinical scenarios. We also highlight challenges such as limited generalizability, underexplored domains, and the integration of Large Language Models (LLMs) for early detection. By outlining both progress and open problems, this review aims to guide future work toward trustworthy, clinically meaningful, and scalable use of XGNNs in dementia research.


Precise characterization of the prior predictive distribution of deep ReLU networks

Neural Information Processing Systems

Recent works on Bayesian neural networks (BNNs) have highlighted the need to better understand the implications of using Gaussian priors in combination with the compositional structure of the network architecture. Similar in spirit to the kind of analysis that has been developed to devise better initialization schemes for neural networks (cf. He-or Xavier initialization), we derive a precise characterization of the prior predictive distribution of finite-width ReLU networks with Gaussian weights. While theoretical results have been obtained for their heavy-tailedness, the full characterization of the prior predictive distribution (i.e. its density, CDF and moments), remained unknown prior to this work. Our analysis, based on the Meijer-G function, allows us to quantify the influence of architectural choices such as the width or depth of the network on the resulting shape of the prior predictive distribution. We also formally connect our results to previous work in the infinite width setting, demonstrating that the moments of the distribution converge to those of a normal log-normal mixture in the infinite depth limit. Finally, our results provide valuable guidance on prior design: for instance, controlling the predictive variance with depth-and width-informed priors on the weights of the network.


Data-Agnostic Augmentations for Unknown Variations: Out-of-Distribution Generalisation in MRI Segmentation

Vaish, Puru, Meister, Felix, Heimann, Tobias, Brune, Christoph, Wolterink, Jelmer M.

arXiv.org Artificial Intelligence

Medical image segmentation models are often trained on curated datasets, leading to performance degradation when deployed in real-world clinical settings due to mismatches between training and test distributions. While data augmentation techniques are widely used to address these challenges, traditional visually consistent augmentation strategies lack the robustness needed for diverse real-world scenarios. In this work, we systematically evaluate alternative augmentation strategies, focusing on MixUp and Auxiliary Fourier Augmentation. These methods mitigate the effects of multiple variations without explicitly targeting specific sources of distribution shifts. We demonstrate how these techniques significantly improve out-of-distribution generalization and robustness to imaging variations across a wide range of transformations in cardiac cine MRI and prostate MRI segmentation. We quantitatively find that these augmentation methods enhance learned feature representations by promoting separability and compactness. Additionally, we highlight how their integration into nnU-Net training pipelines provides an easy-to-implement, effective solution for enhancing the reliability of medical segmentation models in real-world applications.