We propose a method to explore the flavor structure of leptons using diffusion models, which are known as one of generative artificial intelligence (generative AI). We consider a simple extension of the Standard Model with the type I seesaw mechanism and train a neural network to generate the neutrino mass matrix. By utilizing transfer learning, the diffusion model generates 104 solutions that are consistent with the neutrino mass squared differences and the leptonic mixing angles. The distributions of the CP phases and the sums of neutrino masses, which are not included in the conditional labels but are calculated from the solutions, exhibit non-trivial tendencies. In addition, the effective mass in neutrinoless double beta decay is concentrated near the boundaries of the existing confidence intervals, allowing us to verify the obtained solutions through future experiments. An inverse approach using the diffusion model is expected to facilitate the experimental verification of flavor models from a perspective distinct from conventional analytical methods.

The rapid digitalisation of contemporary society has profoundly impacted various facets of our lives, including healthcare, communication, business, and education. The ability to engage with new technologies and solve problems has become crucial, making CT skills, such as pattern recognition, decomposition, and algorithm design, essential competencies. In response, Switzerland is conducting research and initiatives to integrate CT into its educational system. This study aims to develop a comprehensive framework for large-scale assessment of CT skills, particularly focusing on AT, the ability to design algorithms. To achieve this, we first developed a competence model capturing the situated and developmental nature of CT, guiding the design of activities tailored to cognitive abilities, age, and context. This framework clarifies how activity characteristics influence CT development and how to assess these competencies. Additionally, we developed an activity for large-scale assessment of AT skills, offered in two variants: one based on non-digital artefacts (unplugged) and manual expert assessment, and the other based on digital artefacts (virtual) and automatic assessment. To provide a more comprehensive evaluation of students' competencies, we developed an IAS based on BNs with noisy gates, which offers real-time probabilistic assessment for each skill rather than a single overall score. The results indicate that the proposed instrument can measure AT competencies across different age groups and educational contexts in Switzerland, demonstrating its applicability for large-scale use. AT competencies exhibit a progressive development, with no overall gender differences, though variations are observed at the school level, significantly influenced by the artefact-based environment and its context, underscoring the importance of creating accessible and adaptable assessment tools.

Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the time dependencies in the noising process of these models lead to error accumulation and propagation during the backward process. This issue, particularly pronounced in mask diffusion, is a known limitation in sequence modeling and, as we demonstrate, also impacts discrete diffusion models for graphs. To address this problem, we propose a novel framework called Iterative Denoising, which simplifies discrete diffusion and circumvents the issue by assuming conditional independence across time. Additionally, we enhance our model by incorporating a Critic, which during generation selectively retains or corrupts elements in an instance based on their likelihood under the data distribution. Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.

Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box models, however, these representations are rarely known. We discuss how to characterize and manipulate such representations using triangular transport maps, which approximate any complex probability distribution as a transformation of a simple, well-understood distribution. The particular structure of triangular transport guarantees many desirable mathematical and computational properties that translate well into solving practical problems. Triangular maps are actively used for density estimation, (conditional) generative modelling, Bayesian inference, data assimilation, optimal experimental design, and related tasks. While there is ample literature on the development and theory of triangular transport methods, this manuscript provides a detailed introduction for scientists interested in employing measure transport without assuming a formal mathematical background. We build intuition for the key foundations of triangular transport, discuss many aspects of its practical implementation, and outline the frontiers of this field.

Robots rely on motion planning to navigate safely and efficiently while performing various tasks. In this paper, we investigate motion planning through Bayesian inference, where motion plans are inferred based on planning objectives and constraints. However, existing Bayesian motion planning methods often struggle to explore low-probability regions of the planning space, where high-quality plans may reside. To address this limitation, we propose the use of heavy-tailed distributions -- specifically, Student's-$t$ distributions -- to enhance probabilistic inferential search for motion plans. We develop a novel sequential single-pass smoothing approach that integrates Student's-$t$ distribution with Monte Carlo sampling. A special case of this approach is ensemble Kalman smoothing, which depends on short-tailed Gaussian distributions. We validate the proposed approach through simulations in autonomous vehicle motion planning, demonstrating its superior performance in planning, sampling efficiency, and constraint satisfaction compared to ensemble Kalman smoothing. While focused on motion planning, this work points to the broader potential of heavy-tailed distributions in enhancing probabilistic decision-making in robotics.

Many Monte Carlo (MC) and importance sampling (IS) methods use mixture models (MMs) for their simplicity and ability to capture multimodal distributions. Recently, subtractive mixture models (SMMs), i.e. MMs with negative coefficients, have shown greater expressiveness and success in generative modeling. However, their negative parameters complicate sampling, requiring costly auto-regressive techniques or accept-reject algorithms that do not scale in high dimensions. In this work, we use the difference representation of SMMs to construct an unbiased IS estimator ($\Delta\text{Ex}$) that removes the need to sample from the SMM, enabling high-dimensional expectation estimation with SMMs. In our experiments, we show that $\Delta\text{Ex}$ can achieve comparable estimation quality to auto-regressive sampling while being considerably faster in MC estimation. Moreover, we conduct initial experiments with $\Delta\text{Ex}$ using hand-crafted proposals, gaining first insights into how to construct safe proposals for $\Delta\text{Ex}$.

We introduce squared families, which are families of probability densities obtained by squaring a linear transformation of a statistic. Squared families are singular, however their singularity can easily be handled so that they form regular models. After handling the singularity, squared families possess many convenient properties. Their Fisher information is a conformal transformation of the Hessian metric induced from a Bregman generator. The Bregman generator is the normalising constant, and yields a statistical divergence on the family. The normalising constant admits a helpful parameter-integral factorisation, meaning that only one parameter-independent integral needs to be computed for all normalising constants in the family, unlike in exponential families. Finally, the squared family kernel is the only integral that needs to be computed for the Fisher information, statistical divergence and normalising constant. We then describe how squared families are special in the broader class of $g$-families, which are obtained by applying a sufficiently regular function $g$ to a linear transformation of a statistic. After removing special singularities, positively homogeneous families and exponential families are the only $g$-families for which the Fisher information is a conformal transformation of the Hessian metric, where the generator depends on the parameter only through the normalising constant. Even-order monomial families also admit parameter-integral factorisations, unlike exponential families. We study parameter estimation and density estimation in squared families, in the well-specified and misspecified settings. We use a universal approximation property to show that squared families can learn sufficiently well-behaved target densities at a rate of $\mathcal{O}(N^{-1/2})+C n^{-1/4}$, where $N$ is the number of datapoints, $n$ is the number of parameters, and $C$ is some constant.

We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is essential to quantum mechanical uncertainty, even if the quantum state is known, measurements may still produce an uncertain outcome. In our framework, measurements therefore play the role of acts with an uncertain outcome and our simple decision-theoretic postulates ensure that Born's rule is encapsulated in the utility functions associated with such acts. This approach allows us to uncouple (precise) probability theory from quantum mechanics, in the sense that it leaves room for a more general, so-called imprecise probabilities approach. We discuss the mathematical implications of our findings, which allow us to give a decision-theoretic foundation to recent seminal work by Benavoli, Facchini and Zaffalon, and we compare our approach to earlier and different approaches by Deutsch and Wallace.

Continual learning (CL) refers to the ability to continuously learn and accumulate new knowledge while retaining useful information from past experiences. Although numerous CL methods have been proposed in recent years, it is not straightforward to deploy them directly to real-world decision-making problems due to their computational cost and lack of uncertainty quantification. To address these issues, we propose CL-BRUNO, a probabilistic, Neural Process-based CL model that performs scalable and tractable Bayesian update and prediction. Our proposed approach uses deep-generative models to create a unified probabilistic framework capable of handling different types of CL problems such as task- and class-incremental learning, allowing users to integrate information across different CL scenarios using a single model. Our approach is able to prevent catastrophic forgetting through distributional and functional regularisation without the need of retaining any previously seen samples, making it appealing to applications where data privacy or storage capacity is of concern. Experiments show that CL-BRUNO outperforms existing methods on both natural image and biomedical data sets, confirming its effectiveness in real-world applications.

This paper describes the comprehensive safety framework th at underpinned the development, release process, and regulatory approval of BMW's first SAE Level 3 Au tomated Driving System. The framework combines established qualitative and quantitative me thods from the fields of Systems Engineering, Engineering Risk Analysis, Bayesian Data Analysis, Design of Experiments, and Statistical Learning in a novel manner. The approach systematically minimizes the r isks associated with hardware and software faults, performance limitations, and insufficient specifica tions to an acceptable level that achieves a Positive Risk Balance. At the core of the framework is the system atic identification and quantification of uncertainties associated with hazard scenarios and the red undantly designed system based on designed experiments, field data, and expert knowledge. The residual risk of the system is then estimated through Stochastic Simulation and evaluated by Sensitivity Analys is. By integrating these advanced analytical techniques into the V-Model, the framework fulfills, unifies, and complements existing automotive safety standards. It therefore provides a comprehensive, rigorou s, and transparent safety assurance process for the development and deployment of Automated Driving System s.