Soft-argmax operation is commonly adopted in detection-based methods to localize the target position in a differentiable manner. However, training the neural network with soft-argmax makes the shape of the probability map unconstrained. Consequently, the model lacks pixel-wise supervision through the map during training, leading to performance degradation. In this work, we propose sampling-argmax, a differentiable training method that imposes implicit constraints to the shape of the probability map by minimizing the expectation of the localization error. To approximate the expectation, we introduce a continuous formulation of the output distribution and develop a differentiable sampling process. The expectation can be approximated by calculating the average error of all samples drawn from the output distribution. We show that sampling-argmax can seamlessly replace the conventional soft-argmax operation on various localization tasks. Comprehensive experiments demonstrate the effectiveness and flexibility of the proposed method.

Background. Subdural hematoma (SDH) is a common neurosurgical emergency, with increasing incidence in aging populations. Rapid and accurate identification is essential to guide timely intervention, yet existing automated tools focus primarily on detection and provide limited interpretability or spatial localization. There remains a need for transparent, high-performing systems that integrate multimodal clinical and imaging information to support real-time decision-making. Methods. We developed a multimodal deep-learning framework that integrates structured clinical variables, a 3D convolutional neural network trained on CT volumes, and a transformer-enhanced 2D segmentation model for SDH detection and localization. Using 25,315 head CT studies from Hartford HealthCare (2015--2024), of which 3,774 (14.9\%) contained clinician-confirmed SDH, tabular models were trained on demographics, comorbidities, medications, and laboratory results. Imaging models were trained to detect SDH and generate voxel-level probability maps. A greedy ensemble strategy combined complementary predictors. Findings. Clinical variables alone provided modest discriminatory power (AUC 0.75). Convolutional models trained on CT volumes and segmentation-derived maps achieved substantially higher accuracy (AUCs 0.922 and 0.926). The multimodal ensemble integrating all components achieved the best overall performance (AUC 0.9407; 95\% CI, 0.930--0.951) and produced anatomically meaningful localization maps consistent with known SDH patterns. Interpretation. This multimodal, interpretable framework provides rapid and accurate SDH detection and localization, achieving high detection performance and offering transparent, anatomically grounded outputs. Integration into radiology workflows could streamline triage, reduce time to intervention, and improve consistency in SDH management.

We present a learning-based approach to computing solutions for certain NPhard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph convolutional network that is trained to estimate the likelihood, for each vertex in a graph, of whether this vertex is part of the optimal solution.

We present a learning-based approach to computing solutions for certain NPhard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph convolutional network that is trained to estimate the likelihood, for each vertex in a graph, of whether this vertex is part of the optimal solution.

Each mini-batch consists of half 2D and half 3D samples. S7, S8) are used for training and two subjects (S9, S11) for evaluation. The output of the last layer is a per-point probability map for each keypoint. Furthermore, our method is an improvement of existing capabilities but does not introduce a radically new capability in machine learning. Theoretically, the underlying density function cannot be perfectly reconstructed since the proposed basis distributions are fixed.

Soft-argmax operation is commonly adopted in detection-based methods to localize the target position in a differentiable manner.

Scene text detection remains a grand challenge due to the variation in text curvatures, orientations, and aspect ratios.

Context: Predicting human trajectories is crucial for the safety and reliability of autonomous systems, such as automated vehicles and mobile robots. However, rigorously testing the underlying multimodal Human Trajectory Prediction (HTP) models, which typically use multiple input sources (e.g., trajectory history and environment maps) and produce stochastic outputs (multiple possible future paths), presents significant challenges. The primary difficulty lies in the absence of a definitive test oracle, as numerous future trajectories might be plausible for any given scenario. Objectives: This research presents the application of Metamorphic Testing (MT) as a systematic methodology for testing multimodal HTP systems. We address the oracle problem through metamorphic relations (MRs) adapted for the complexities and stochastic nature of HTP. Methods: We present five MRs, targeting transformations of both historical trajectory data and semantic segmentation maps used as an environmental context. These MRs encompass: 1) label-preserving geometric transformations (mirroring, rotation, rescaling) applied to both trajectory and map inputs, where outputs are expected to transform correspondingly. 2) Map-altering transformations (changing semantic class labels, introducing obstacles) with predictable changes in trajectory distributions. We propose probabilistic violation criteria based on distance metrics between probability distributions, such as the Wasserstein or Hellinger distance. Conclusion: This study introduces tool, a MT framework for the oracle-less testing of multimodal, stochastic HTP systems. It allows for assessment of model robustness against input transformations and contextual changes without reliance on ground-truth trajectories.

Predicting the spatio-temporal progression of brain tumors is essential for guiding clinical decisions in neuro-oncology. We propose a hybrid mechanistic learning framework that combines a mathematical tumor growth model with a guided denoising diffusion implicit model (DDIM) to synthesize anatomically feasible future MRIs from preceding scans. The mechanistic model, formulated as a system of ordinary differential equations, captures temporal tumor dynamics including radiotherapy effects and estimates future tumor burden. These estimates condition a gradient-guided DDIM, enabling image synthesis that aligns with both predicted growth and patient anatomy. We train our model on the BraTS adult and pediatric glioma datasets and evaluate on 60 axial slices of in-house longitudinal pediatric diffuse midline glioma (DMG) cases. Our framework generates realistic follow-up scans based on spatial similarity metrics. It also introduces tumor growth probability maps, which capture both clinically relevant extent and directionality of tumor growth as shown by 95th percentile Hausdorff Distance. The method enables biologically informed image generation in data-limited scenarios, offering generative-space-time predictions that account for mechanistic priors.

Each mini-batch consists of half 2D and half 3D samples. S7, S8) are used for training and two subjects (S9, S11) for evaluation. The output of the last layer is a per-point probability map for each keypoint. Furthermore, our method is an improvement of existing capabilities but does not introduce a radically new capability in machine learning. Theoretically, the underlying density function cannot be perfectly reconstructed since the proposed basis distributions are fixed.