Deep neural networks (DNNs) frequently fail to generalize to out-of-distribution (OOD) medical images because of variations in scanners and acquisition protocols. Retraining DNN models to address these distribution shifts is often impractical due to the high cost of acquiring and annotating new medical datasets. To address this, we introduce VarDeepPCA, a novel lightweight variational DNN framework designed to restore/refine degraded segmentation maps by leveraging intrinsic geometric priors. Unlike existing approaches that require target-domain data or extensive pre-training, our VarDeepPCA explicitly learns a distribution of valid anatomical geometries using only small in-distribution (ID) datasets. Theoretically, our novel variational learning framework leverages a reinterpretation of the softmax mapping to implicitly perform exact distribution modeling, thereby enabling computationally efficient, sampling-free learning and inference. This also enables VarDeepPCA to provide uncertainty estimates associated with its restored segmentation maps. We empirically validate our framework across 4 distinct clinical applications, using 14 publicly available datasets, involving segmentation of the myocardium, neuroretinal rim, prostate, and fetal head. Comparisons against 15 existing methods demonstrate that VarDeepPCA consistently restores segmentation maps produced by the existing methods on OOD data to (i) significantly improve anatomical plausibility of geometries and clinical utility of the segmentations, and (ii) significantly reduce errors, without needing any more training data than that used by existing methods.

Benchmarks for out-of-distribution (OOD) generalization frequently show a strong positive correlation between in-distribution (ID) and OOD accuracy across models, termed "accuracy-on-the-line." This pattern is often taken to imply that spurious correlations--correlations that improve ID but reduce OOD performance--are rare in practice. We find that this positive correlation is often an artifact of aggregating heterogeneous OOD examples. Using a simple gradient-based method, OODSelect, we identify semantically coherent OOD subsets where accuracy on the line does not hold. Across widely used distribution shift benchmarks, the OODSelect uncovers subsets, sometimes up to over half of the standard OOD set, where higher ID accuracy predicts lower OOD accuracy. Our findings indicate that aggregate metrics can obscure important failure modes of OOD robustness. We release code and the identified subsets to facilitate further research.

Out-of-distribution (OOD) 3D relighting requires novel view synthesis under unseen lighting conditions that differ significantly from the observed images. Existing relighting methods, which assume consistent light source distributions between training and testing, often degrade in OOD scenarios. We introduce MetaGS to tackle this challenge from two perspectives. First, we propose a meta-learning approach to train 3DGaussian splatting, which explicitly promotes learning generalizable Gaussian geometries and appearance attributes across diverse lighting conditions, even with biased training data. Second, we embed fundamental physical priors from the Blinn-Phong reflection model into Gaussian splatting, which enhances the decoupling of shading components and leads to more accurate 3D scene reconstruction. Results on both synthetic and real-world datasets demonstrate the effectiveness of MetaGS in challenging OOD relighting tasks, supporting efficient point-light relighting and generalizing well to unseen environment lighting maps.

We study the tradeoff between sample complexity and round complexity in *on-demand sampling*, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of Multi-Distribution Learning (MDL), we show that the optimal sample complexity of an $r$-round algorithm scales approximately as $dk^{\Theta(1/r)} / \epsilon$. For the general agnostic case, we present an algorithm that achieves near-optimal sample complexity of $\widetilde O((d + k) / \epsilon^2)$ within $\widetilde O(\sqrt{k})$ rounds. Of independent interest, we introduce a new framework, Optimization via On-Demand Sampling (OODS), which abstracts the sample-adaptivity tradeoff and captures most existing MDL algorithms. We establish nearly tight bounds on the round complexity in the OODS setting. The upper bounds directly yield the $\widetilde O(\sqrt{k})$-round algorithm for agnostic MDL, while the lower bounds imply that achieving sub-polynomial round complexity would require fundamentally new techniques that bypass the inherent hardness of OODS.

Uncertainty quantification (UQ) is critical for safety-critical domains like healthcare, yet it is rarely evaluated under realistic out-of-distribution (OOD) conditions. Here, we assessed predictive performance and uncertainty reliability for deep learning-based blood pressure (BP) estimation from photoplethysmography (PPG) signals under both in-distribution (ID) and OOD settings. Using an XResNet1D-50 trained on PulseDB and tested on four external datasets, we compared deep ensembles (DE) and Monte Carlo dropout (MCD) with Gaussian negative log-likelihood (GNLL) and mean squared error (MSE) losses, optionally followed by post-hoc recalibration via conformal prediction (CP), temperature scaling (TS), and isotonic regression (IR). The key findings of our study are as follows: (1) DE provides stronger predictive robustness under domain shift than MCD, an advantage that becomes clear primarily under external shift. (2) Recalibrated GNLL-based methods yield the best uncertainty calibration (e.g., GNLL+DE+CP for systolic blood pressure (SBP), GNLL+DE+TS for diastolic blood pressure (DBP)), while MSE-based uncertainty requires recalibration to become practically useful. (3) Across settings, CP and TS offer the most consistent gains, with IR remaining competitive in several cases. Overall, our results identify DE-based methods as most robust for predictive performance under domain shift, GNLL as strongest for native UQ, and recalibration as essential for making MSE-based uncertainty practical. These findings highlight the need to jointly assess predictive accuracy and calibration on external data for trustworthy cuffless BP estimation

Most existing out-of-distribution (OOD) detection benchmarks classify samples with novel labels as the OOD data. However, some marginal OOD samples actually have close semantic contents to the in-distribution (ID) sample, which makes determining the OOD sample a Sorites Paradox. In this paper, we construct a benchmark named Incremental Shift OOD (IS-OOD) to address the issue, in which we divide the test samples into subsets with different semantic and covariate shift degrees relative to the ID dataset. The data division is achieved through a shift measuring method based on our proposed Language Aligned Image feature Decomposition (LAID). Moreover, we construct a Synthetic Incremental Shift (Syn-IS) dataset that contains high-quality generated images with more diverse covariate contents to complement the IS-OOD benchmark. We evaluate current OOD detection methods on our benchmark and find several important insights: (1) The performance of most OOD detection methods significantly improves as the semantic shift increases; (2) Some methods like GradNorm may have different OOD detection mechanisms as they rely less on semantic shifts to make decisions; (3) Excessive covariate shifts in the image are also likely to be considered as OOD for some methods. Our code and data are released in https://github.com/qqwsad5/IS-OOD.

The significant heterogeneity poses higher requirements foralgorithm robustness.

Alldatausedispublic.] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they werechosen)? A.1 TrainingDetails In our experiments, the classifierfθ is a 8-layer MLP with 128 hidden dimensions per layer.