Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity (KDS), which enforces stationarity by evaluating expectations of the diffusion's generator in a reproducing kernel Hilbert space. Leveraging the connection between KDS and Stein discrepancies, we introduce the Stein-type KDS (SKDS) as an alternative formulation. We prove that a vanishing SKDS guarantees alignment of the learned diffusion's stationary distribution with the target. Furthermore, under broad parametrizations, SKDS is convex with an empirical version that is $ε$-quasiconvex with high probability. Empirically, learning with SKDS attains comparable accuracy to KDS while substantially reducing computational cost and yields improvements over the majority of competitive baselines.

Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model coefficients, uncertainty quantification for the learned univariate functions requires computationally intensive bootstrapping, making it hard to know which features truly matter. We provide an alternative using recent advances in statistical inference for gradient boosting, deriving methods for statistical inference as well as end-to-end theoretical guarantees. Using a moving average instead of a sum of trees (Boulevard regularization) allows the boosting process to converge to a feature-wise kernel ridge regression. This produces asymptotically normal predictions that achieve the minimax-optimal mean squared error for fitting Lipschitz GAMs with $p$ features at rate $O(pn^{-2/3})$, successfully avoiding the curse of dimensionality. We then construct prediction intervals for the response and confidence intervals for each learned univariate function with a runtime independent of the number of datapoints, enabling further explainability within EBMs.

Recent Transformer- and MLP-based models have demonstrated strong performance in long-term time series forecasting, yet Transformers remain limited by their quadratic complexity and permutation-equivariant attention, while MLPs exhibit spectral bias. We propose HaKAN, a versatile model based on Kolmogorov-Arnold Networks (KANs), leveraging Hahn polynomial-based learnable activation functions and providing a lightweight and interpretable alternative for multivariate time series forecasting. Our model integrates channel independence, patching, a stack of Hahn-KAN blocks with residual connections, and a bottleneck structure comprised of two fully connected layers. The Hahn-KAN block consists of inter- and intra-patch KAN layers to effectively capture both global and local temporal patterns. Extensive experiments on various forecasting benchmarks demonstrate that our model consistently outperforms recent state-of-the-art methods, with ablation studies validating the effectiveness of its core components.

We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we estimate using kernel methods. The proposed test is adaptive over hyperparameters such as the kernel bandwidth and the regularization parameter. We provide theoretical guarantees for statistical test power across our family of $f$-divergence estimates. While our test covers a variety of $f$-divergences, we bring particular focus to the Hockey-Stick divergence, motivated by its applications to differential privacy auditing and machine unlearning evaluation. For two-sample testing, experiments demonstrate that different $f$-divergences are sensitive to different localized differences, illustrating the importance of leveraging diverse statistics. For machine unlearning, we propose a relative test that distinguishes true unlearning failures from safe distributional variations.

Distributed learning enables scalable model training over decentralized data, but remains hindered by Byzantine faults and high communication costs. While both challenges have been studied extensively in isolation, their interplay has received limited attention. Prior work has shown that naively combining communication compression with Byzantine-robust aggregation can severely weaken resilience to faulty nodes. The current state-of-the-art, Byz-DASHA-PAGE, leverages a momentum-based variance reduction scheme to counteract the negative effect of compression noise on Byzantine robustness. In this work, we introduce RoSDHB, a new algorithm that integrates classical Polyak momentum with a coordinated compression strategy. Theoretically, RoSDHB matches the convergence guarantees of Byz-DASHA-PAGE under the standard $(G,B)$-gradient dissimilarity model, while relying on milder assumptions and requiring less memory and communication per client. Empirically, RoSDHB demonstrates stronger robustness while achieving substantial communication savings compared to Byz-DASHA-PAGE.

Urban embodied AI agents, ranging from delivery robots to quadrupeds, are increasingly populating our cities, navigating chaotic streets to provide last-mile connectivity. Training such agents requires diverse, high-fidelity urban environments to scale, yet existing human-crafted or procedurally generated simulation scenes either lack scalability or fail to capture real-world complexity. We introduce UrbanVerse, a data-driven real-to-sim system that converts crowd-sourced city-tour videos into physics-aware, interactive simulation scenes. UrbanVerse consists of: (i) UrbanVerse-100K, a repository of 100k+ annotated urban 3D assets with semantic and physical attributes, and (ii) UrbanVerse-Gen, an automatic pipeline that extracts scene layouts from video and instantiates metric-scale 3D simulations using retrieved assets. Running in IsaacSim, UrbanVerse offers 160 high-quality constructed scenes from 24 countries, along with a curated benchmark of 10 artist-designed test scenes. Experiments show that UrbanVerse scenes preserve real-world semantics and layouts, achieving human-evaluated realism comparable to manually crafted scenes. In urban navigation, policies trained in UrbanVerse exhibit scaling power laws and strong generalization, improving success by +6.3% in simulation and +30.1% in zero-shot sim-to-real transfer comparing to prior methods, accomplishing a 300 m real-world mission with only two interventions.

Machine learning solvers for partial differential equations (PDEs) have attracted growing interest. However, most existing approaches, such as neural network solvers, rely on stochastic training, which is inefficient and typically requires a great many training epochs. Gaussian process (GP)/kernel-based solvers, while mathematical principled, suffer from scalability issues when handling large numbers of collocation points often needed for challenging or higher-dimensional PDEs. To overcome these limitations, we propose TGPS, a tensor-GP-based solver that models factor functions along each input dimension using one-dimensional GPs and combines them via tensor decomposition to approximate the full solution. This design reduces the task to learning a collection of one-dimensional GPs, substantially lowering computational complexity, and enabling scalability to massive collocation sets. For efficient nonlinear PDE solving, we use a partial freezing strategy and Newton's method to linerize the nonlinear terms. We then develop an alternating least squares (ALS) approach that admits closed-form updates, thereby substantially enhancing the training efficiency. We establish theoretical guarantees on the expressivity of our model, together with convergence proof and error analysis under standard regularity assumptions. Experiments on several benchmark PDEs demonstrate that our method achieves superior accuracy and efficiency compared to existing approaches.

We introduce a novel framework for Federated Class Incremental Learning, called Federated Gaussian Task Embedding and Alignment (FedGTEA). FedGTEA is designed to capture task-specific knowledge and model uncertainty in a scalable and communication-efficient manner. At the client side, the Cardinality-Agnostic Task Encoder (CATE) produces Gaussian-distributed task embed-dings that encode task knowledge, address statistical heterogeneity, and quantify data uncertainty. Importantly, CATE maintains a fixed parameter size regardless of the number of tasks, which ensures scalability across long task sequences. On the server side, FedGTEA utilizes the 2-Wasserstein distance to measure inter-task gaps between Gaussian embeddings. We formulate the Wasserstein loss to enforce inter-task separation. This probabilistic formulation not only enhances representation learning but also preserves task-level privacy by avoiding the direct transmission of latent embed-dings, aligning with the privacy constraints in federated learning. Extensive empirical evaluations on popular datasets demonstrate that FedGTEA achieves superior classification performance and significantly mitigates forgetting, consistently outperforming strong existing baselines.

Power transforms are popular parametric techniques for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms suffer from severe numerical instabilities, which can lead to incorrect results or even crashes. In this paper, we provide a comprehensive analysis of the sources of these instabilities and propose effective remedies. We further extend power transforms to the federated learning setting, addressing both numerical and distributional challenges that arise in this context. Experiments on real-world datasets demonstrate that our methods are both effective and robust, substantially improving stability compared to existing approaches.

Deep learning models, especially large Transformers, carry substantial "memory" in their intermediate layers -- an \emph{internal world} that encodes a wealth of relational and contextual knowledge. This work harnesses that internal world for wildfire occurrence prediction by introducing a modular architecture built upon Gemma 3, a state-of-the-art multimodal model. Rather than relying on Gemma 3's original embedding and positional encoding stacks, we develop a custom feed-forward module that transforms tabular wildfire features into the hidden dimension required by Gemma 3's mid-layer Transformer blocks. We freeze these Gemma 3 sub-layers -- thus preserving their pretrained representation power -- while training only the smaller input and output networks. This approach minimizes the number of trainable parameters and reduces the risk of overfitting on limited wildfire data, yet retains the benefits of Gemma 3's broad knowledge. Evaluations on a Moroccan wildfire dataset demonstrate improved predictive accuracy and robustness compared to standard feed-forward and convolutional baselines. Ablation studies confirm that the frozen Transformer layers consistently contribute to better representations, underscoring the feasibility of reusing large-model mid-layers as a learned internal world. Our findings suggest that strategic modular reuse of pretrained Transformers can enable more data-efficient and interpretable solutions for critical environmental applications such as wildfire risk management.