Non-equilibrium Markov Chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. By driving a base probability distribution out of equilibrium, observables are computed without the need to thermalize. If the base distribution is characterized by mild autocorrelations, this approach provides a way to mitigate critical slowing down. Out-of-equilibrium evolutions share the same framework of flow-based approaches and they can be naturally combined into a novel architecture called Stochastic Normalizing Flows (SNFs). In this work we present the first implementation of SNFs for $\mathrm{SU}(3)$ lattice gauge theory in 4 dimensions, defined by introducing gauge-equivariant layers between out-of-equilibrium Monte Carlo updates. The core of our analysis is focused on the promising scaling properties of this architecture with the degrees of freedom of the system, which are directly inherited from NE-MCMC. Finally, we discuss how systematic improvements of this approach can realistically lead to a general and yet efficient sampling strategy at fine lattice spacings for observables affected by long autocorrelation times.

This thesis is part of a CIFRE agreement between the company Othello and the LIASD laboratory. The objective is to develop an artificial intelligence system that can detect real-time dangers in a video stream. To achieve this, a novel approach combining temporal and spatial analysis has been proposed. Several avenues have been explored to improve anomaly detection by integrating object detection, human pose detection, and motion analysis. For result interpretability, techniques commonly used for image analysis, such as activation and saliency maps, have been extended to videos, and an original method has been proposed. The proposed architecture performs binary or multiclass classification depending on whether an alert or the cause needs to be identified. Numerous neural networkmodels have been tested, and three of them have been selected. You Only Looks Once (YOLO) has been used for spatial analysis, a Convolutional Recurrent Neuronal Network (CRNN) composed of VGG19 and a Gated Recurrent Unit (GRU) for temporal analysis, and a multi-layer perceptron for classification. These models handle different types of data and can be combined in parallel or in series. Although the parallel mode is faster, the serial mode is generally more reliable. For training these models, supervised learning was chosen, and two proprietary datasets were created. The first dataset focuses on objects that may play a potential role in anomalies, while the second consists of videos containing anomalies or non-anomalies. This approach allows for the processing of both continuous video streams and finite videos, providing greater flexibility in detection.

We study the kernel instrumental variable algorithm of \citet{singh2019kernel}, a nonparametric two-stage least squares (2SLS) procedure which has demonstrated strong empirical performance. We provide a convergence analysis that covers both the identified and unidentified settings: when the structural function cannot be identified, we show that the kernel NPIV estimator converges to the IV solution with minimum norm. Crucially, our convergence is with respect to the strong $L_2$-norm, rather than a pseudo-norm. Additionally, we characterize the smoothness of the target function without relying on the instrument, instead leveraging a new description of the projected subspace size (this being closely related to the link condition in inverse learning literature). With the subspace size description and under standard kernel learning assumptions, we derive, for the first time, the minimax optimal learning rate for kernel NPIV in the strong $L_2$-norm. Our result demonstrates that the strength of the instrument is essential to achieve efficient learning. We also improve the original kernel NPIV algorithm by adopting a general spectral regularization in stage 1 regression. The modified regularization can overcome the saturation effect of Tikhonov regularization.

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of nonlinear latent hierarchical causal models, relaxing previous assumptions in literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for nonlinear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. We demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks.

Semi-supervised learning (SSL) is a machine learning methodology that leverages unlabeled data in conjunction with a limited amount of labeled data. Although SSL has been applied in various applications and its effectiveness has been empirically demonstrated, it is still not fully understood when and why SSL performs well. Some existing theoretical studies have attempted to address this issue by modeling classification problems using the so-called Gaussian Mixture Model (GMM). These studies provide notable and insightful interpretations. However, their analyses are focused on specific purposes, and a thorough investigation of the properties of GMM in the context of SSL has been lacking. In this paper, we conduct such a detailed analysis of the properties of the high-dimensional GMM for binary classification in the SSL setting. To this end, we employ the approximate message passing and state evolution methods, which are widely used in high-dimensional settings and originate from statistical mechanics. We deal with two estimation approaches: the Bayesian one and the l2-regularized maximum likelihood estimation (RMLE). We conduct a comprehensive comparison between these two approaches, examining aspects such as the global phase diagram, estimation error for the parameters, and prediction error for the labels. A specific comparison is made between the Bayes-optimal (BO) estimator and RMLE, as the BO setting provides optimal estimation performance and is ideal as a benchmark. Our analysis shows that with appropriate regularizations, RMLE can achieve near-optimal performance in terms of both the estimation error and prediction error, especially when there is a large amount of unlabeled data. These results demonstrate that the l2 regularization term plays an effective role in estimation and prediction in SSL approaches.

The field of computational pathology has been transformed with recent advances in foundation models that encode histopathology region-of-interests (ROIs) into versatile and transferable feature representations via self-supervised learning (SSL). However, translating these advancements to address complex clinical challenges at the patient and slide level remains constrained by limited clinical data in disease-specific cohorts, especially for rare clinical conditions. We propose TITAN, a multimodal whole slide foundation model pretrained using 335,645 WSIs via visual self-supervised learning and vision-language alignment with corresponding pathology reports and 423,122 synthetic captions generated from a multimodal generative AI copilot for pathology. Without any finetuning or requiring clinical labels, TITAN can extract general-purpose slide representations and generate pathology reports that generalize to resource-limited clinical scenarios such as rare disease retrieval and cancer prognosis. We evaluate TITAN on diverse clinical tasks and find that TITAN outperforms both ROI and slide foundation models across machine learning settings such as linear probing, few-shot and zero-shot classification, rare cancer retrieval and cross-modal retrieval, and pathology report generation.

Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations offer distinct advantages over sampling based methods in their computational cost and continuous representation. State-of-the-art Gaussian mixture approaches are adaptive in that individual Gaussian mixands are selectively split into mixtures to yield better approximations of the true propagated distribution. Despite the importance of the splitting process to accuracy and computational efficiency, relatively little work has been devoted to mixand selection and splitting direction optimization. The first part of this work presents splitting methods that preserve the mean and covariance of the original distribution. Then, we present and compare a number of novel heuristics for selecting the splitting direction. The choice of splitting direction is informed by the initial uncertainty distribution, properties of the nonlinear function through which the original distribution is propagated, and a whitening based natural scaling method to avoid dependence of the splitting direction on the scaling of coordinates. We compare these novel heuristics to existing techniques in three distinct examples involving Cartesian to polar coordinate transformation, Keplerian orbital element propagation, and uncertainty propagation in the circular restricted three-body problem.

Developing environmentally sustainable refrigerants is critical for mitigating the impact of anthropogenic greenhouse gases on global warming. This study presents a predictive modeling framework to estimate the 100-year global warming potential (GWP 100) of single-component refrigerants using a fully connected neural network implemented on the Multi-Sigma platform. Molecular descriptors from RDKit, Mordred, and alvaDesc were utilized to capture various chemical features. The RDKit-based model achieved the best performance, with a Root Mean Square Error (RMSE) of 481.9 and an R2 score of 0.918, demonstrating superior predictive accuracy and generalizability. Dimensionality reduction through Principal Component Analysis (PCA) and quantile transformation were applied to address the high-dimensional and skewed nature of the dataset,enhancing model stability and performance. Factor analysis identified vital molecular features, including molecular weight, lipophilicity, and functional groups, such as nitriles and allylic oxides, as significant contributors to GWP values. These insights provide actionable guidance for designing environmentally sustainable refrigerants. Integrating RDKit descriptors with Multi-Sigma's framework, which includes PCA, quantile transformation, and neural networks, provides a scalable solution for the rapid virtual screening of low-GWP refrigerants. This approach can potentially accelerate the identification of eco-friendly alternatives, directly contributing to climate mitigation by enabling the design of next-generation refrigerants aligned with global sustainability objectives.

This paper studies reinforcement learning (RL) in infinite-horizon dynamic decision processes with almost-sure safety constraints. Such safety-constrained decision processes are central to applications in autonomous systems, finance, and resource management, where policies must satisfy strict, state-dependent constraints. We consider a doubly-regularized RL framework that combines reward and parameter regularization to address these constraints within continuous state-action spaces. Specifically, we formulate the problem as a convex regularized objective with parametrized policies in the mean-field regime. Our approach leverages recent developments in mean-field theory and Wasserstein gradient flows to model policies as elements of an infinite-dimensional statistical manifold, with policy updates evolving via gradient flows on the space of parameter distributions. Our main contributions include establishing solvability conditions for safety-constrained problems, defining smooth and bounded approximations that facilitate gradient flows, and demonstrating exponential convergence towards global solutions under sufficient regularization. We provide general conditions on regularization functions, encompassing standard entropy regularization as a special case. The results also enable a particle method implementation for practical RL applications. The theoretical insights and convergence guarantees presented here offer a robust framework for safe RL in complex, high-dimensional decision-making problems.

With the rise of online education platforms, there is a growing abundance of educational content across various domain. It can be difficult to navigate the numerous available resources to find the most suitable training, especially in domains that include many interconnected areas, such as ICT. In this study, we propose a domain-specific chatbot application that requires limited resources, utilizing versions of the Phi language model to help learners with educational content. In the proposed method, Phi-2 and Phi-3 models were fine-tuned using QLoRA. The data required for fine-tuning was obtained from the Huawei Talent Platform, where courses are available at different levels of expertise in the field of computer science. RAG system was used to support the model, which was fine-tuned by 500 Q&A pairs. Additionally, a total of 420 Q&A pairs of content were extracted from different formats such as JSON, PPT, and DOC to create a vector database to be used in the RAG system. By using the fine-tuned model and RAG approach together, chatbots with different competencies were obtained. The questions and answers asked to the generated chatbots were saved separately and evaluated using ROUGE, BERTScore, METEOR, and BLEU metrics. The precision value of the Phi-2 model supported by RAG was 0.84 and the F1 score was 0.82. In addition to a total of 13 different evaluation metrics in 4 different categories, the answers of each model were compared with the created content and the most appropriate method was selected for real-life applications.