The Hausdorff distance (HD) is a robust measure of set dissimilarity, but computing it exactly on large, high-dimensional datasets is prohibitively expensive. We propose \textbf{ProHD}, a projection-guided approximation algorithm that dramatically accelerates HD computation while maintaining high accuracy. ProHD identifies a small subset of candidate "extreme" points by projecting the data onto a few informative directions (such as the centroid axis and top principal components) and computing the HD on this subset. This approach guarantees an underestimate of the true HD with a bounded additive error and typically achieves results within a few percent of the exact value. In extensive experiments on image, physics, and synthetic datasets (up to two million points in $D=256$), ProHD runs 10--100$\times$ faster than exact algorithms while attaining 5--20$\times$ lower error than random sampling-based approximations. Our method enables practical HD calculations in scenarios like large vector databases and streaming data, where quick and reliable set distance estimation is needed.

Lemma 1.1 implies that sup

Lemma 1. Considering a fixed Only the highest confidence term in the output of the neural network affects the classification result. For the nonlinear part, which is always defined as ReLU, we have, ReLU (a b) null > ReLU ( a) ReLU (b), if a < 0 and b < 0, = ReLU ( a) ReLU (b), if a > 0 or b > 0 . Since each standard Gaussian distribution is i . The results are shown in Table 1. CIFAR-10 is used as the dataset and all the settings are the same as in the main text. For the attack algorithm, multiple iterations in a round of attack are randomly sampled only once.

To reduce the amount of required labeled data for lung disease severity classification from chest X-rays (CXRs) under class imbalance, this study applied deep active learning with a Bayesian Neural Network (BNN) approximation and weighted loss function. This retrospective study collected 2,319 CXRs from 963 patients (mean age, 59.2 $\pm$ 16.6 years; 481 female) at Emory Healthcare affiliated hospitals between January and November 2020. All patients had clinically confirmed COVID-19. Each CXR was independently labeled by 3 to 6 board-certified radiologists as normal, moderate, or severe. A deep neural network with Monte Carlo Dropout was trained using active learning to classify disease severity. Various acquisition functions were used to iteratively select the most informative samples from an unlabeled pool. Performance was evaluated using accuracy, area under the receiver operating characteristic curve (AU ROC), and area under the precision-recall curve (AU PRC). Training time and acquisition time were recorded. Statistical analysis included descriptive metrics and performance comparisons across acquisition strategies. Entropy Sampling achieved 93.7% accuracy (AU ROC, 0.91) in binary classification (normal vs. diseased) using 15.4% of the training data. In the multi-class setting, Mean STD sampling achieved 70.3% accuracy (AU ROC, 0.86) using 23.1% of the labeled data. These methods outperformed more complex and computationally expensive acquisition functions and significantly reduced labeling needs. Deep active learning with BNN approximation and weighted loss effectively reduces labeled data requirements while addressing class imbalance, maintaining or exceeding diagnostic performance.

Lemma 1.1 implies that sup

Although there are highly effective GBDT implementations, their scalability to such problems is still unsatisfactory.

Accurately predicting the geographic ranges of species is crucial for assisting conservation efforts. Traditionally, range maps were manually created by experts. However, species distribution models (SDMs) and, more recently, deep learning-based variants offer a potential automated alternative. Deep learning-based SDMs generate a continuous probability representing the predicted presence of a species at a given location, which must be binarized by setting per-species thresholds to obtain binary range maps. However, selecting appropriate per-species thresholds to binarize these predictions is non-trivial as different species can require distinct thresholds. In this work, we evaluate different approaches for automatically identifying the best thresholds for binarizing range maps using presence-only data. This includes approaches that require the generation of additional pseudo-absence data, along with ones that only require presence data. We also propose an extension of an existing presence-only technique that is more robust to outliers. We perform a detailed evaluation of different thresholding techniques on the tasks of binary range estimation and large-scale fine-grained visual classification, and we demonstrate improved performance over existing pseudo-absence free approaches using our method.

Using the generative nature of a language model to generate task-relevant separators has shown competitive results compared to human-curated prompts like "TL;DR". We demonstrate that even randomly chosen tokens from the vocabulary as separators can achieve near-state-of-the-art performance. We analyse this phenomenon in detail using three different random generation strategies, establishing that the language space is rich with potential good separators, regardless of the underlying language model size. These observations challenge the common assumption that an effective prompt should be human-readable or task-relevant. Experimental results show that using random separators leads to an average 16% relative improvement across nine text classification tasks on seven language models, compared to human-curated separators, and is on par with automatic prompt searching methods.

Contrastive Learning has recently achieved state-of-the-art performance in a wide range of tasks. Many contrastive learning approaches use mined hard negatives to make batches more informative during training but these approaches are inefficient as they increase epoch length proportional to the number of mined negatives and require frequent updates of nearest neighbor indices or mining from recent batches. In this work, we provide an alternative to hard negative mining, Global Contrastive Batch Sampling (GCBS), an efficient approximation to the batch assignment problem that upper bounds the gap between the global and training losses, $\mathcal{L}^{Global} - \mathcal{L}^{Train}$, in contrastive learning settings. Through experimentation we find GCBS improves state-of-the-art performance in sentence embedding and code-search tasks. Additionally, GCBS is easy to implement as it requires only a few additional lines of code, does not maintain external data structures such as nearest neighbor indices, is more computationally efficient than the most minimal hard negative mining approaches, and makes no changes to the model being trained.