High-dimensional problems have long been considered the Achilles' heel of Bayesian optimization algorithms. Spurred by the curse of dimensionality, a large collection of algorithms aim to make it more performant in this setting, commonly by imposing various simplifying assumptions on the objective. In this paper, we identify the degeneracies that make vanilla Bayesian optimization poorly suited to high-dimensional tasks, and further show how existing algorithms address these degeneracies through the lens of lowering the model complexity. Moreover, we propose an enhancement to the prior assumptions that are typical to vanilla Bayesian optimization algorithms, which reduces the complexity to manageable levels without imposing structural restrictions on the objective. Our modification - a simple scaling of the Gaussian process lengthscale prior with the dimensionality - reveals that standard Bayesian optimization works drastically better than previously thought in high dimensions, clearly outperforming existing state-of-the-art algorithms on multiple commonly considered real-world high-dimensional tasks.

This paper presents the Learning the Universe Implicit Likelihood Inference (LtU-ILI) pipeline, a codebase for rapid, user-friendly, and cutting-edge machine learning (ML) inference in astrophysics and cosmology. The pipeline includes software for implementing various neural architectures, training schema, priors, and density estimators in a manner easily adaptable to any research workflow. It includes comprehensive validation metrics to assess posterior estimate coverage, enhancing the reliability of inferred results. Additionally, the pipeline is easily parallelizable, designed for efficient exploration of modeling hyperparameters. To demonstrate its capabilities, we present real applications across a range of astrophysics and cosmology problems, such as: estimating galaxy cluster masses from X-ray photometry; inferring cosmology from matter power spectra and halo point clouds; characterising progenitors in gravitational wave signals; capturing physical dust parameters from galaxy colors and luminosities; and establishing properties of semi-analytic models of galaxy formation. We also include exhaustive benchmarking and comparisons of all implemented methods as well as discussions about the challenges and pitfalls of ML inference in astronomical sciences. All code and examples are made publicly available at https://github.com/maho3/ltu-ili.

In the pursuit of novel catalyst development to address pressing environmental concerns and energy demand, conventional design and optimization methods often fall short due to the complexity and vastness of the catalyst parameter space. The advent of Machine Learning (ML) has ushered in a new era in the field of catalyst optimization, offering potential solutions to the shortcomings of traditional techniques. However, existing methods fail to effectively harness the wealth of information contained within the burgeoning body of scientific literature on catalyst synthesis. To address this gap, this study proposes an innovative Artificial Intelligence (AI) workflow that integrates Large Language Models (LLMs), Bayesian optimization, and an active learning loop to expedite and enhance catalyst optimization. Our methodology combines advanced language understanding with robust optimization strategies, effectively translating knowledge extracted from diverse literature into actionable parameters for practical experimentation and optimization. In this article, we demonstrate the application of this AI workflow in the optimization of catalyst synthesis for ammonia production. The results underscore the workflow's ability to streamline the catalyst development process, offering a swift, resource-efficient, and highprecision alternative to conventional methods. Keywords: Catalysts; Large Language Models; Active Learning; Bayesian Optimization; Ammonia Synthesis 1. Introduction The development of novel catalysts to address increasing energy demand and consumption has become an urgent task in the realm of renewable energy This surge is driven not only by escalating demands from applications in process optimization, yield improvement, and energy saving but also by a heightened awareness and concern for environmental issues, particularly the increase in carbon dioxide emissions. Several optimization strategies are conventionally employed to identify the optimal set of condition parameters, thereby enhancing the performance of the catalyst. The'One Factor At a Time' (OFAT) method is frequently employed as an alternative technique for chemical process optimization and comprehension While these conventional optimization methods and their advancements have undeniably made significant contributions to the field, certain gaps persist that limit their full potential in optimizing catalyst synthesis. The predominant reliance on the empirical knowledge and intuition of seasoned chemists, while invaluable, is not systematically scalable and transferable. Techniques like OFAT and DoE, though statistically rigorous, are often unable to keep pace with the sheer complexity and vastness of the catalyst parameter space, leaving much of it unexplored and underutilized.

Kalman Filter (KF) is an optimal linear state prediction algorithm, with applications in fields as diverse as engineering, economics, robotics, and space exploration. Here, we develop an extension of the KF, called a Pathspace Kalman Filter (PKF) which allows us to a) dynamically track the uncertainties associated with the underlying data and prior knowledge, and b) take as input an entire trajectory and an underlying mechanistic model, and using a Bayesian methodology quantify the different sources of uncertainty. An application of this algorithm is to automatically detect temporal windows where the internal mechanistic model deviates from the data in a time-dependent manner. First, we provide theorems characterizing the convergence of the PKF algorithm. Then, we numerically demonstrate that the PKF outperforms conventional KF methods on a synthetic dataset lowering the mean-squared-error by several orders of magnitude. Finally, we apply this method to biological time-course dataset involving over 1.8 million gene expression measurements.

The growing use of machine learning (ML) has raised concerns that an ML model may reveal private information about an individual who has contributed to the training dataset. To prevent leakage of sensitive data, we consider using differentially-private (DP), synthetic training data instead of real training data to train an ML model. A key desirable property of synthetic data is its ability to preserve the low-order marginals of the original distribution. Our main contribution comprises novel upper and lower bounds on the excess empirical risk of linear models trained on such synthetic data, for continuous and Lipschitz loss functions. We perform extensive experimentation alongside our theoretical results.

Graph neural networks (GNNs) have gained popularity for various graph-related tasks. However, similar to deep neural networks, GNNs are also vulnerable to adversarial attacks. Empirical studies have shown that adversarially robust generalization has a pivotal role in establishing effective defense algorithms against adversarial attacks. In this paper, we contribute by providing adversarially robust generalization bounds for two kinds of popular GNNs, graph convolutional network (GCN) and message passing graph neural network, using the PAC-Bayesian framework. Our result reveals that spectral norm of the diffusion matrix on the graph and spectral norm of the weights as well as the perturbation factor govern the robust generalization bounds of both models. Our bounds are nontrivial generalizations of the results developed in (Liao et al., 2020) from the standard setting to adversarial setting while avoiding exponential dependence of the maximum node degree. As corollaries, we derive better PAC-Bayesian robust generalization bounds for GCN in the standard setting, which improve the bounds in (Liao et al., 2020) by avoiding exponential dependence on the maximum node degree.

Spanning over two decades, the study of qubits in semiconductors for quantum computing has yielded significant breakthroughs. However, the development of large-scale semiconductor quantum circuits is still limited by challenges in efficiently tuning and operating these circuits. Identifying optimal operating conditions for these qubits is complex, involving the exploration of vast parameter spaces. This presents a real 'needle in the haystack' problem, which, until now, has resisted complete automation due to device variability and fabrication imperfections. In this study, we present the first fully autonomous tuning of a semiconductor qubit, from a grounded device to Rabi oscillations, a clear indication of successful qubit operation. We demonstrate this automation, achieved without human intervention, in a Ge/Si core/shell nanowire device. Our approach integrates deep learning, Bayesian optimization, and computer vision techniques. We expect this automation algorithm to apply to a wide range of semiconductor qubit devices, allowing for statistical studies of qubit quality metrics. As a demonstration of the potential of full automation, we characterise how the Rabi frequency and g-factor depend on barrier gate voltages for one of the qubits found by the algorithm. Twenty years after the initial demonstrations of spin qubit operation, this significant advancement is poised to finally catalyze the operation of large, previously unexplored quantum circuits.

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

Diffusion Models (DMs) have disrupted the image Super-Resolution (SR) field and further closed the gap between image quality and human perceptual preferences. They are easy to train and can produce very high-quality samples that exceed the realism of those produced by previous generative methods. Despite their promising results, they also come with new challenges that need further research: high computational demands, comparability, lack of explainability, color shifts, and more. Unfortunately, entry into this field is overwhelming because of the abundance of publications. To address this, we provide a unified recount of the theoretical foundations underlying DMs applied to image SR and offer a detailed analysis that underscores the unique characteristics and methodologies within this domain, distinct from broader existing reviews in the field. This survey articulates a cohesive understanding of DM principles and explores current research avenues, including alternative input domains, conditioning techniques, guidance mechanisms, corruption spaces, and zero-shot learning approaches. By offering a detailed examination of the evolution and current trends in image SR through the lens of DMs, this survey sheds light on the existing challenges and charts potential future directions, aiming to inspire further innovation in this rapidly advancing area.

Maximum likelihood estimation (MLE) of latent variable models is often recast as an optimization problem over the extended space of parameters and probability distributions. For example, the Expectation Maximization (EM) algorithm can be interpreted as coordinate descent applied to a suitable free energy functional over this space. Recently, this perspective has been combined with insights from optimal transport and Wasserstein gradient flows to develop particle-based algorithms applicable to wider classes of models than standard EM. Drawing inspiration from prior works which interpret `momentum-enriched' optimisation algorithms as discretizations of ordinary differential equations, we propose an analogous dynamical systems-inspired approach to minimizing the free energy functional over the extended space of parameters and probability distributions. The result is a dynamic system that blends elements of Nesterov's Accelerated Gradient method, the underdamped Langevin diffusion, and particle methods. Under suitable assumptions, we establish quantitative convergence of the proposed system to the unique minimiser of the functional in continuous time. We then propose a numerical discretization of this system which enables its application to parameter estimation in latent variable models. Through numerical experiments, we demonstrate that the resulting algorithm converges faster than existing methods and compares favourably with other (approximate) MLE algorithms.