Artificial intelligence (AI) systems increasingly influence safety-critical aspects of society, from medical diagnosis to autonomous mobility, making uncertainty awareness a central requirement for trustworthy AI. We present a photonic Bayesian machine that leverages the inherent randomness of chaotic light sources to enable uncertainty reasoning within the framework of Bayesian Neural Networks. The analog processor features a 1.28 Tbit/s digital interface compatible with PyTorch, enabling probabilistic convolutions processing within 37.5 ps per convolution. We use the system for simultaneous classification and out-of-domain detection of blood cell microscope images and demonstrate reasoning between aleatoric and epistemic uncertainties. The photonic Bayesian machine removes the bottleneck of pseudo random number generation in digital systems, minimizes the cost of sampling for probabilistic models, and thus enables high-speed trustworthy AI systems.

We study the densest subgraph problem (DSG) and the densest subgraph local decomposition problem (DSG-LD) in undirected graphs. We also consider su-permodular generalizations of these problems. For large scale graphs simple iterative algorithms perform much better in practice than theoretically fast algorithms based on network-flow or LP solvers. Boob et al. [ 1 ] recently gave a fast iterative algorithm called G

Unfortunately, in its original form, MCTS can degenerate to one-step search in domains with stochasticity. Progressive widening is one way to ameliorate this issue, but we argue that it possesses undesirable properties for some settings.

Neural ODEs are a widely used, powerful machine learning technique in particular for physics. However, not every solution is physical in that it is an Euler-Lagrange equation. We present Helmholtz metrics to quantify this resemblance for a given ODE and demonstrate their capabilities on several fundamental systems with noise. We combine them with a second order neural ODE to form a Lagrangian neural ODE, which allows to learn Euler-Lagrange equations in a direct fashion and with zero additional inference cost. We demonstrate that, using only positional data, they can distinguish Lagrangian and non-Lagrangian systems and improve the neural ODE solutions.

Bob uses Alice's public key to send her an email, which lands on Alice's

The introduction of machine learning methods has led to significant advances in automation, optimization, and discoveries in various fields of science and technology. However, their widespread application faces a fundamental limitation: the transfer of models between data domains generally lacks a rigorous mathematical justification. The key problem is the lack of formal criteria to guarantee that a model trained on one type of data will retain its properties on another.This paper proposes a solution to this problem by formalizing the concept of analogy between data sets and models using first-order logic and Hoare logic.We formulate and rigorously prove a theorem that sets out the necessary and sufficient conditions for analogy in the task of knowledge transfer between machine learning models. Practical verification of the analogy theorem on model data obtained using the Monte Carlo method, as well as on MNIST and USPS data, allows us to achieving F1 scores of 0.84 and 0.88 for convolutional neural networks and random forests, respectively.The proposed approach not only allows us to justify the correctness of transfer between domains but also provides tools for comparing the applicability of models to different types of data.The main contribution of the work is a rigorous formalization of analogy at the level of program logic, providing verifiable guarantees of the correctness of knowledge transfer, which opens new opportunities for both theoretical research and the practical use of machine learning models in previously inaccessible areas.

Purpose: The FedSurg challenge was designed to benchmark the state of the art in federated learning for surgical video classification. Its goal was to assess how well current methods generalize to unseen clinical centers and adapt through local fine-tuning while enabling collaborative model development without sharing patient data. Methods: Participants developed strategies to classify inflammation stages in appendicitis using a preliminary version of the multi-center Appendix300 video dataset. The challenge evaluated two tasks: generalization to an unseen center and center-specific adaptation after fine-tuning. Submitted approaches included foundation models with linear probing, metric learning with triplet loss, and various FL aggregation schemes (FedAvg, FedMedian, FedSAM). Performance was assessed using F1-score and Expected Cost, with ranking robustness evaluated via bootstrapping and statistical testing. Results: In the generalization task, performance across centers was limited. In the adaptation task, all teams improved after fine-tuning, though ranking stability was low. The ViViT-based submission achieved the strongest overall performance. The challenge highlighted limitations in generalization, sensitivity to class imbalance, and difficulties in hyperparameter tuning in decentralized training, while spatiotemporal modeling and context-aware preprocessing emerged as promising strategies. Conclusion: The FedSurg Challenge establishes the first benchmark for evaluating FL strategies in surgical video classification. Findings highlight the trade-off between local personalization and global robustness, and underscore the importance of architecture choice, preprocessing, and loss design. This benchmarking offers a reference point for future development of imbalance-aware, adaptive, and robust FL methods in clinical surgical AI.