Biotic communities vary continuously across space, yet biome maps impose categorical boundaries that compress this variation, particularly at ecotones where transitional communities are ecologically distinct. Could Earth observation (EO) foundation models, which encode spectral, spatial, and temporal information with dense embeddings, convert discrete biome maps into continuous representations that better capture ecological variation? Here, we fit a linear classifier on Clay v1.5 satellite image embeddings to predict biome labels from a categorical map. The softmax output yields a continuous probability vector whose dimensions correspond to named biome classes. We evaluate this approach using six Brazilian biomes, 1.3 million embeddings, and 10,015 withheld forest inventory plots spanning 4,672 plant species. The continuous biome representation outperforms discrete biome labels for predicting species occurrence (mean per-species AUC 0.618 vs. 0.570 across 10 spatial cross-validation folds). Decomposing this gain shows that continuity in the graded probability output, rather than label reassignment, accounts for the improvement; the pattern holds across all distances from biome boundaries. The raw 1024-dimensional embedding remains the strongest predictor we tested (mean AUC 0.646 vs. 0.618), but the continuous representation recovers most of the embedding's gain over discrete labels. This simple approach provides a probabilistic replacement for categorical map labels, preserving their meaning while encoding graded variation that discrete maps suppress.

To keep experiments uniform, for all datasets (STL-10, CIFAR-10, and CIFAR-100) we used a train/val/test partitioning. In our experiments we compared FED with four baselines. For all baselines we tried different learning rates [0.1, 0.01, 0.001] and batch sizes [32, 64, 100]. For EnDD and EnDD + AUX, we used the same temperature, temperature annealing, and optimizer that was used in the original paper. For AMT, we tried different alphas [1e1, 1e3, 1e5] and kept the rest as the original paper.

Staged tree models enhance Bayesian networks by incorporating context-specific dependencies through a stage-based structure. In this study, we present a new framework for estimating staged trees using hierarchical clustering on the probability simplex, utilizing simplex basesd divergences. We conduct a thorough evaluation of several distance and divergence metrics including Total Variation, Hellinger, Fisher, and Kaniadakis; alongside various linkage methods such as Ward.D2, average, complete, and McQuitty. We conducted the simulation experiments that reveals Total Variation, especially when combined with Ward.D2 linkage, consistently produces staged trees with better model fit, structure recovery, and computational efficiency. We assess performance by utilizing relative Bayesian Information Criterion (BIC), and Hamming distance. Our findings indicate that although Backward Hill Climbing (BHC) delivers competitive outcomes, it incurs a significantly higher computational cost. On the other, Total Variation divergence with Ward.D2 linkage, achieves similar performance while providing significantly better computational efficiency, making it a more viable option for large-scale or time sensitive tasks.

This paper presents an innovative approach to classification tasks called Credal Deep Ensembles (CreDEs), ensembles of novel Credal-Set Neural Networks (CreNets), aiming to improve EU quantification in the framework of credal inference.

When such components are expected to be embedded in safety-critical systems (e.g.,

Neural Information Processing Systems http://nips.cc/

Here, θ() is the clique coveringnumberofthegraph. Online learning models a repeated interaction between a learner and an environment.

ForDM, due to high memory requirements, we were able to go up to aBatchEnsemble with an ensemble size of 8, while being able to use only batch size of 32. In addition, for this baseline we used a bigger memory GPU, unable tofitthetraining toourstandard 11GBGPU usedfortherestofour experiments. In the procedure of creating a Mixup [8] auxiliary dataset, we used a Beta distribution withα = 0.2. In Mixup augmentation, and valueλ [0,1] is sampled from a Beta distribution. We use batch size of 64.

Neural architecture search (NAS) is inherently subject to the gap of architectures during searching and validating. To bridge this gap, we develop Differentiable ArchiTecture Approximation (DATA) with an Ensemble Gumbel-Softmax (EGS) estimator to automatically approximate architectures during searching and validating in a differentiable manner. Technically, the EGS estimator consists of a group of Gumbel-Softmax estimators, which is capable of converting probability vectors to binary codes and passing gradients from binary codes to probability vectors. Benefiting from such modeling, in searching, architecture parameters and network weights in the NAS model can be jointly optimized with the standard back-propagation, yielding an end-to-end learning mechanism for searching deep models in a large enough search space. Conclusively, during validating, a high-performance architecture that approaches to the learned one during searching is readily built. Extensive experiments on a variety of popular datasets strongly evidence that our method is capable of discovering high-performance architectures for image classification, language modeling and semantic segmentation, while guaranteeing the requisite efficiency during searching.