In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs) produce predictive uncertainty by propagating uncertainty in neural network (NN) weights and offer the promise of obtaining not only an accurate predictive model but also accurate UQ. However, in practice, obtaining accurate UQ with BNNs is difficult due in part to the approximations used for practical model training and in part to the need to choose a suitable set of hyperparameters; these hyperparameters outnumber those needed for traditional NNs and often have opaque effects on the results. We aim to shed light on the effects of hyperparameter choices for BNNs by performing a global sensitivity analysis of BNN performance under varying hyperparameter settings. Our results indicate that many of the hyperparameters interact with each other to affect both predictive accuracy and UQ. For improved usage of BNNs in real-world applications, we suggest that global sensitivity analysis, or related methods such as Bayesian optimization, should be used to aid in dimensionality reduction and selection of hyperparameters to ensure accurate UQ in BNNs.

We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced Wasserstein (SW) distances. Specifically, we leverage both standard SW distances, which provide lower bounds, and lifted SW distances, which provide upper bounds, as predictors of the true Wasserstein distance. To ensure parsimony, we introduce two linear models: an unconstrained model with a closed-form least-squares solution, and a constrained model that uses only half as many parameters. We show that accurate models can be learned from a small number of distribution pairs. Once estimated, the model can predict the Wasserstein distance for any pair of distributions via a linear combination of SW distances, making it highly efficient. Empirically, we validate our approach on diverse tasks, including Gaussian mixtures, point-cloud classification, and Wasserstein-space visualizations for 3D point clouds. Across various datasets such as MNIST point clouds, ShapeNetV2, MERFISH Cell Niches, and scRNA-seq, our method consistently provides a better approximation of Wasserstein distance than the state-of-the-art Wasserstein embedding model, Wasserstein Wormhole, particularly in low-data regimes. Finally, we demonstrate that our estimator can also accelerate Wormhole training, yielding \textit{RG-Wormhole}.

We develop a new high-dimensional statistical learning model which can take advantage of structured correlation in data even in the presence of randomness. We completely characterize learnability in this model in terms of VCN${}_{k,k}$-dimension (essentially $k$-dependence from Shelah's classification theory). This model suggests a theoretical explanation for the success of certain algorithms in the 2006~Netflix Prize competition.

Existing distribution compression methods reduce dataset size by minimising the Maximum Mean Discrepancy (MMD) between original and compressed sets, but modern datasets are often large in both sample size and dimensionality. We propose Bilateral Distribution Compression (BDC), a two-stage framework that compresses along both axes while preserving the underlying distribution, with overall linear time and memory complexity in dataset size and dimension. Central to BDC is the Decoded MMD (DMMD), which quantifies the discrepancy between the original data and a compressed set decoded from a low-dimensional latent space. BDC proceeds by (i) learning a low-dimensional projection using the Reconstruction MMD (RMMD), and (ii) optimising a latent compressed set with the Encoded MMD (EMMD). We show that this procedure minimises the DMMD, guaranteeing that the compressed set faithfully represents the original distribution. Experiments show that across a variety of scenarios BDC can achieve comparable or superior performance to ambient-space compression at substantially lower cost.

As large language models (LLMs) achieve strong performance on traditional benchmarks, there is an urgent need for more challenging evaluation frameworks that probe deeper aspects of semantic understanding. We introduce SAGE (Semantic Alignment & Generalization Evaluation), a rigorous benchmark designed to assess both embedding models and similarity metrics across five categories: Human Preference Alignment, Transformation Robustness, Information Sensitivity, Clustering Performance, and Retrieval Robustness. Unlike existing benchmarks that focus on isolated capabilities, SAGE evaluates semantic understanding through adversarial conditions, noisy transformations, and nuanced human judgment tasks across 30+ datasets. Our comprehensive evaluation of 9 embedding models and classical metrics reveals significant performance gaps, with no single approach excelling across all dimensions. For instance, while state-of-the-art embedding models like OpenAI's text-embedding-3-large dominate in aligning with human preferences (0.682 vs. 0.591 for the best classical metric), they are significantly outperformed by classical metrics on information sensitivity tasks, where Jaccard Similarity achieves a score of 0.905 compared to the top embedding score of 0.794. SAGE further uncovers critical trade-offs: OpenAI's text-embedding-3-small achieves the highest clustering performance (0.483) but demonstrates extreme brittleness with the lowest robustness score (0.011). SAGE exposes critical limitations in current semantic understanding capabilities and provides a more realistic assessment of model robustness for real-world deployment.

Contrastive language-audio pretraining, which aims to unify multimodal representations in a shared embedding space, serves as a cornerstone for building a wide range of applications, from cross-modal retrieval to cutting-edge multimodal large language models. However, we find that the perpendicular component of the pushing force from negative samples in contrastive learning is a double-edged sword: it contains rich supplementary information from negative samples, yet its unconstrained nature causes optimization trajectory drift and training instability. To address this, we propose Support V ector Regularization (SVR), a method that introduces an auxiliary support vector to control this perpendicular component, aiming to harness its rich information while mitigating the associated trajectory drift. The efficacy of SVR is critically governed by its semantic radius, for which we explore two unsupervised modeling strategies: direct parameterization and an adaptive radius predictor module enhanced with constraints to improve its predicting accuracy. Extensive experimental results demonstrate that our method surpasses widely used baselines like InfoNCE and SigLIP loss across classification, monolingual retrieval, and multilingual retrieval on standard audio-text datasets. Contrastive Language-Audio Pretraining (CLAP) Wu et al. (2023); Ghosh et al. (2025) aims to learn a unified audio-text embedding space by pulling corresponding pairs closer and pushing others apart. This paradigm, which powers applications like cross-modal retrieval Xie et al. (2024) and multimodal LLMs Xue et al. (2024); Lam et al. (2025), has achieved great empirical success. However, standard InfoNCE-based CLAP methods still struggle to learn ideal representations, facing limitations such as poor temporal alignment of audio events Y uan et al. (2024) and inconsistent multilingual alignment Yin et al. (2025). Therefore, achieving optimal alignment between the language and audio representation spaces remains an open challenge. In this paper, we uncover a complex yet overlooked dynamic in the optimization process of standard InfoNCE-based contrastive learning Wu et al. (2021): optimization trajectory drift.

Abstract-- 3D object localisation based on a sequence of camera measurements is essential for safety-critical surveillance tasks, such as drone-based wildfire monitoring. Localisation of objects detected with a camera can typically be solved with dense depth estimation or 3D scene reconstruction. However, in the context of distant objects or tasks limited by the amount of available computational resources, neither solution is feasible. In this paper, we show that the task can be solved using particle filters for both single and multiple target scenarios. The method was studied using a 3D simulation and a drone-based image segmentation sequence with global navigation satellite system (GNSS)-based camera pose estimates. The results showed that a particle filter can be used to solve practical localisation tasks based on camera poses and image segments in these situations where other solutions fail. The particle filter is independent of the detection method, making it flexible for new tasks. The study also demonstrates that drone-based wildfire monitoring can be conducted using the proposed method paired with a pre-existing image segmentation model.

Accurate plant counting provides valuable information for agriculture such as crop yield prediction, plant density assessment, and phenotype quantification. Vision-based approaches are currently the mainstream solution. Prior art typically uses a detection or a regression model to count a specific plant. However, plants have biodiversity, and new cultivars are increasingly bred each year. It is almost impossible to exhaust and build all species-dependent counting models. Inspired by class-agnostic counting (CAC) in computer vision, we argue that it is time to rethink the problem formulation of plant counting, from what plants to count to how to count plants. In contrast to most daily objects with spatial and temporal invariance, plants are dynamic, changing with time and space. Their non-rigid structure often leads to worse performance than counting rigid instances like heads and cars such that current CAC and open-world detection models are suboptimal to count plants. In this work, we inherit the vein of the TasselNet plant counting model and introduce a new extension, TasselNetV4, shifting from species-specific counting to cross-species counting. TasselNetV4 marries the local counting idea of TasselNet with the extract-and-match paradigm in CAC. It builds upon a plain vision transformer and incorporates novel multi-branch box-aware local counters used to enhance cross-scale robustness. Two challenging datasets, PAC-105 and PAC-Somalia, are harvested. Extensive experiments against state-of-the-art CAC models show that TasselNetV4 achieves not only superior counting performance but also high efficiency.Our results indicate that TasselNetV4 emerges to be a vision foundation model for cross-scene, cross-scale, and cross-species plant counting.

Approximately 10\% of newborns require assistance to initiate breathing at birth, and around 5\% need ventilation support. Fetal heart rate (FHR) monitoring plays a crucial role in assessing fetal well-being during prenatal care, enabling the detection of abnormal patterns and supporting timely obstetric interventions to mitigate fetal risks during labor. Applying artificial intelligence (AI) methods to analyze large datasets of continuous FHR monitoring episodes with diverse outcomes may offer novel insights into predicting the risk of needing breathing assistance or interventions. Recent advances in wearable FHR monitors have enabled continuous fetal monitoring without compromising maternal mobility. However, sensor displacement during maternal movement, as well as changes in fetal or maternal position, often lead to signal dropouts, resulting in gaps in the recorded FHR data. Such missing data limits the extraction of meaningful insights and complicates automated (AI-based) analysis. Traditional approaches to handle missing data, such as simple interpolation techniques, often fail to preserve the spectral characteristics of the signals. In this paper, we propose a masked transformer-based autoencoder approach to reconstruct missing FHR signals by capturing both spatial and frequency components of the data. The proposed method demonstrates robustness across varying durations of missing data and can be used for signal inpainting and forecasting. The proposed approach can be applied retrospectively to research datasets to support the development of AI-based risk algorithms. In the future, the proposed method could be integrated into wearable FHR monitoring devices to achieve earlier and more robust risk detection.

Learning from human video demonstrations offers a scalable alternative to teleoperation or kinesthetic teaching, but poses challenges for robot manipulators due to embodiment differences and joint feasibility constraints. We address this problem by proposing the Joint Flow Trajectory Optimization (JFTO) framework for grasp pose generation and object trajectory imitation under the video-based Learning-from-Demonstration (LfD) paradigm. Rather than directly imitating human hand motions, our method treats demonstrations as object-centric guides, balancing three objectives: (i) selecting a feasible grasp pose, (ii) generating object trajectories consistent with demonstrated motions, and (iii) ensuring collision-free execution within robot kinematics. To capture the multimodal nature of demonstrations, we extend flow matching to $\SE(3)$ for probabilistic modeling of object trajectories, enabling density-aware imitation that avoids mode collapse. The resulting optimization integrates grasp similarity, trajectory likelihood, and collision penalties into a unified differentiable objective. We validate our approach in both simulation and real-world experiments across diverse real-world manipulation tasks.