There, demand is highly intermittent and bursty: long runs of zeros, with islands of high counts.

Deep neural networks (DNNs) and probabilistic graphical models (PGMs) are the two main tools for statistical modeling.

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distributions. We propose a distribution over kernels formed by modelling a spectral mixture density with a L evy process. The resulting distribution has support for all stationary covariances--including the popular RBF, periodic, and Mat ern kernels-- combined with inductive biases which enable automatic and data efficient learning, long-range extrapolation, and state of the art predictive performance. The proposed model also presents an approach to spectral regularization, as the L evy process introduces a sparsity-inducing prior over mixture components, allowing automatic selection over model order and pruning of extraneous components. We exploit the algebraic structure of the proposed process for O (n) training and O (1) predictions. We perform extrapolations having reasonable uncertainty estimates on several benchmarks, show that the proposed model can recover flexible ground truth covariances and that it is robust to errors in initialization.

We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded hierarchically in the network structure. Thus, the depth of the network is determined inherently. The proposed method casts the problem of neural network structure learning as a problem of Bayesian network structure learning. Then, instead of directly learning the discriminative structure, it learns a generative graph, constructs its stochastic inverse, and then constructs a discriminative graph. We prove that conditional-dependency relations among the latent variables in the generative graph are preserved in the class-conditional discriminative graph. We demonstrate on image classification benchmarks that the deepest layers (convolutional and dense) of common networks can be replaced by significantly smaller learned structures, while maintaining classification accuracy---state-of-the-art on tested benchmarks. Our structure learning algorithm requires a small computational cost and runs efficiently on a standard desktop CPU.

Global optimization of expensive, potentially gradient-free functions has long been a critical component of many complex problems in science and engineering.

We propose MedBayes-Lite, a lightweight Bayesian enhancement for transformer-based clinical language models designed to produce reliable, uncertainty-aware predictions. Although transformers show strong potential for clinical decision support, they remain prone to overconfidence, especially in ambiguous medical cases where calibrated uncertainty is critical. MedBayes-Lite embeds uncertainty quantification directly into existing transformer pipelines without any retraining or architectural rewiring, adding no new trainable layers and keeping parameter overhead under 3 percent. The framework integrates three components: (i) Bayesian Embedding Calibration using Monte Carlo dropout for epistemic uncertainty, (ii) Uncertainty-Weighted Attention that marginalizes over token reliability, and (iii) Confidence-Guided Decision Shaping inspired by clinical risk minimization. Across biomedical QA and clinical prediction benchmarks (MedQA, PubMedQA, MIMIC-III), MedBayes-Lite consistently improves calibration and trustworthiness, reducing overconfidence by 32 to 48 percent. In simulated clinical settings, it can prevent up to 41 percent of diagnostic errors by flagging uncertain predictions for human review. These results demonstrate its effectiveness in enabling reliable uncertainty propagation and improving interpretability in medical AI systems.

In this paper, we present gfnx, a fast and scalable package for training and evaluating Generative Flow Networks (GFlowNets) written in JAX. gfnx provides an extensive set of environments and metrics for benchmarking, accompanied with single-file implementations of core objectives for training GFlowNets. We include synthetic hypergrids, multiple sequence generation environments with various editing regimes and particular reward designs for molecular generation, phylogenetic tree construction, Bayesian structure learning, and sampling from the Ising model energy. Across different tasks, gfnx achieves significant wall-clock speedups compared to Pytorch-based benchmarks (such as torchgfn library) and author implementations. For example, gfnx achieves up to 55 times speedup on CPU-based sequence generation environments, and up to 80 times speedup with the GPU-based Bayesian network structure learning setup. Our package provides a diverse set of benchmarks and aims to standardize empirical evaluation and accelerate research and applications of GFlowNets. The library is available on GitHub (https://github.com/d-tiapkin/gfnx) and on pypi (https://pypi.org/project/gfnx/). Documentation is available on https://gfnx.readthedocs.io.

Efficient and lightweight adaptation of pre-trained Vision-Language Models (VLMs) to downstream tasks through collaborative interactions between local clients and a central server is a rapidly emerging research topic in federated learning. Existing adaptation algorithms are typically trained iteratively, which incur significant communication costs and increase the susceptibility to potential attacks. Motivated by the one-shot federated training techniques that reduce client-server exchanges to a single round, developing a lightweight one-shot federated VLM adaptation method to alleviate these issues is particularly attractive. However, current one-shot approaches face certain challenges in adapting VLMs within federated settings: (1) insufficient exploitation of the rich multimodal information inherent in VLMs; (2) lack of specialized adaptation strategies to systematically handle the severe data heterogeneity; and (3) requiring additional training resource of clients or server. To bridge these gaps, we propose a novel Training-free One-shot Federated Adaptation framework for VLMs, named TOFA. To fully leverage the generalizable multimodal features in pre-trained VLMs, TOFA employs both visual and textual pipelines to extract task-relevant representations. In the visual pipeline, a hierarchical Bayesian model learns personalized, class-specific prototype distributions. For the textual pipeline, TOFA evaluates and globally aligns the generated local text prompts for robustness. An adaptive weight calibration mechanism is also introduced to combine predictions from both modalities, balancing personalization and robustness to handle data heterogeneity. Our method is training-free, not relying on additional training resources on either the client or server side. Extensive experiments across 9 datasets in various federated settings demonstrate the effectiveness of the proposed TOFA method.

Robots today often miss a key ingredient of truly intelligent behavior: the ability to reflect on their own cognitive processes and decisions. In humans, this self-monitoring or metacognition is crucial for learning, decision making and problem solving. For instance, they can evaluate how confident they are in performing a task, thus regulating their own behavior and allocating proper resources. Taking inspiration from neuroscience, we propose a robot metacognition architecture centered on confidence (a second-order judgment on decisions) and we demonstrate it on the use case of autonomous tool invention. We propose the use of confidence as a metacognitive measure within the robot decision making scheme. Confidence-informed robots can evaluate the reliability of their decisions, improving their robustness during real-world physical deployment. This form of robotic metacognition emphasizes embodied action monitoring as a means to achieve better informed decisions. We also highlight potential applications and research directions for robot metacognition.

Imagine a world where clinical trials need far fewer patients to achieve the same statistical power, thanks to the knowledge encoded in large language models (LLMs). We present a novel framework for hierarchical Bayesian modeling of adverse events in multi-center clinical trials, leveraging LLM-informed prior distributions. Unlike data augmentation approaches that generate synthetic data points, our methodology directly obtains parametric priors from the model. Our approach systematically elicits informative priors for hyperparameters in hierarchical Bayesian models using a pre-trained LLM, enabling the incorporation of external clinical expertise directly into Bayesian safety modeling. Through comprehensive temperature sensitivity analysis and rigorous cross-validation on real-world clinical trial data, we demonstrate that LLM-derived priors consistently improve predictive performance compared to traditional meta-analytical approaches. This methodology paves the way for more efficient and expert-informed clinical trial design, enabling substantial reductions in the number of patients required to achieve robust safety assessment and with the potential to transform drug safety monitoring and regulatory decision making.