Photorealistic 3D reconstruction of street scenes is a critical technique for developing real-world simulators for autonomous driving. Despite the efficacy of Neural Radiance Fields (NeRF) for driving scenes, 3D Gaussian Splatting (3DGS) emerges as a promising direction due to its faster speed and more explicit representation. However, most existing street 3DGS methods require tracked 3D vehicle bounding boxes to decompose the static and dynamic elements for effective reconstruction, limiting their applications for in-the-wild scenarios. To facilitate efficient 3D scene reconstruction without costly annotations, we propose a self-supervised street Gaussian ($\textit{S}^3$Gaussian) method to decompose dynamic and static elements from 4D consistency. We represent each scene with 3D Gaussians to preserve the explicitness and further accompany them with a spatial-temporal field network to compactly model the 4D dynamics. We conduct extensive experiments on the challenging Waymo-Open dataset to evaluate the effectiveness of our method. Our $\textit{S}^3$Gaussian demonstrates the ability to decompose static and dynamic scenes and achieves the best performance without using 3D annotations. Code is available at: https://github.com/nnanhuang/S3Gaussian/.

Capsule networks (CapsNets) were introduced to address convolutional neural networks limitations, learning object-centric representations that are more robust, pose-aware, and interpretable. They organize neurons into groups called capsules, where each capsule encodes the instantiation parameters of an object or one of its parts. Moreover, a routing algorithm connects capsules in different layers, thereby capturing hierarchical part-whole relationships in the data. This thesis investigates the intriguing aspects of CapsNets and focuses on three key questions to unlock their full potential. First, we explore the effectiveness of the routing algorithm, particularly in small-sized networks. We propose a novel method that anneals the number of routing iterations during training, enhancing performance in architectures with fewer parameters. Secondly, we investigate methods to extract more effective first-layer capsules, also known as primary capsules. By exploiting pruned backbones, we aim to improve computational efficiency by reducing the number of capsules while achieving high generalization. This approach reduces CapsNets memory requirements and computational effort. Third, we explore part-relationship learning in CapsNets. Through extensive research, we demonstrate that capsules with low entropy can extract more concise and discriminative part-whole relationships compared to traditional capsule networks, even with reasonable network sizes. Lastly, we showcase how CapsNets can be utilized in real-world applications, including autonomous localization of unmanned aerial vehicles, quaternion-based rotations prediction in synthetic datasets, and lung nodule segmentation in biomedical imaging. The findings presented in this thesis contribute to a deeper understanding of CapsNets and highlight their potential to address complex computer vision challenges.

Adapting to the changing climate requires accurate local climate information, a computationally challenging problem. Recent studies have used Generative Adversarial Networks (GANs), a type of deep learning, to learn complex distributions and downscale climate variables efficiently. Capturing variability while downscaling is crucial for estimating uncertainty and characterising extreme events - critical information for climate adaptation. Since downscaling is an undetermined problem, many fine-scale states are physically consistent with the coarse-resolution state. To quantify this ill-posed problem, downscaling techniques should be stochastic, able to sample realisations from a high-resolution distribution conditioned on low-resolution input. Previous stochastic downscaling attempts have found substantial underdispersion, with models failing to represent the full distribution. We propose approaches to improve the stochastic calibration of GANs in three ways: a) injecting noise inside the network, b) adjusting the training process to explicitly account for the stochasticity, and c) using a probabilistic loss metric. We tested our models first on a synthetic dataset with known distributional properties, and then on a realistic downscaling scenario, predicting high-resolution wind components from low-resolution climate covariates. Injecting noise, on its own, substantially improved the quality of conditional and full distributions in tests with synthetic data, but performed less well for wind field downscaling, where models remained underdispersed. For wind downscaling, we found that adjusting the training method and including the probabilistic loss improved calibration. The best model, with all three changes, showed much improved skill at capturing the full variability of the high-resolution distribution and thus at characterising extremes.

The Robust Satisficing (RS) model is an emerging approach to robust optimization, offering streamlined procedures and robust generalization across various applications. However, the statistical theory of RS remains unexplored in the literature. This paper fills in the gap by comprehensively analyzing the theoretical properties of the RS model. Notably, the RS structure offers a more straightforward path to deriving statistical guarantees compared to the seminal Distributionally Robust Optimization (DRO), resulting in a richer set of results. In particular, we establish two-sided confidence intervals for the optimal loss without the need to solve a minimax optimization problem explicitly. We further provide finite-sample generalization error bounds for the RS optimizer. Importantly, our results extend to scenarios involving distribution shifts, where discrepancies exist between the sampling and target distributions. Our numerical experiments show that the RS model consistently outperforms the baseline empirical risk minimization in small-sample regimes and under distribution shifts. Furthermore, compared to the DRO model, the RS model exhibits lower sensitivity to hyperparameter tuning, highlighting its practicability for robustness considerations.

We explore online learning in episodic loop-free Markov decision processes on non-stationary environments (changing losses and probability transitions). Our focus is on the Concave Utility Reinforcement Learning problem (CURL), an extension of classical RL for handling convex performance criteria in state-action distributions induced by agent policies. While various machine learning problems can be written as CURL, its non-linearity invalidates traditional Bellman equations. Despite recent solutions to classical CURL, none address non-stationary MDPs. This paper introduces MetaCURL, the first CURL algorithm for non-stationary MDPs. It employs a meta-algorithm running multiple black-box algorithms instances over different intervals, aggregating outputs via a sleeping expert framework. The key hurdle is partial information due to MDP uncertainty. Under partial information on the probability transitions (uncertainty and non-stationarity coming only from external noise, independent of agent state-action pairs), we achieve optimal dynamic regret without prior knowledge of MDP changes. Unlike approaches for RL, MetaCURL handles full adversarial losses, not just stochastic ones. We believe our approach for managing non-stationarity with experts can be of interest to the RL community.

The use of machine learning methods for predicting the properties of crystalline materials encounters significant challenges, primarily related to input encoding, output versatility, and interpretability. Here, we introduce CrystalBERT, an adaptable transformer-based framework with novel structure that integrates space group, elemental, and unit cell information. The method's adaptability lies not only in its ability to seamlessly combine diverse features but also in its capability to accurately predict a wide range of physically important properties, including topological properties, superconducting transition temperatures, dielectric constants, and more. CrystalBERT also provides insightful physical interpretations regarding the features that most significantly influence the target properties. Our findings indicate that space group and elemental information are more important for predicting topological and superconducting properties, in contrast to some properties that primarily depend on the unit cell information. This underscores the intricate nature of topological and superconducting properties. By incorporating all these features, we achieve a high accuracy of 91% in topological classification, surpassing prior studies and identifying previously misclassified topological materials, further demonstrating the effectiveness of our model.

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a trade-off has to be navigated. To address this issue, this paper proposes a method to generate an approximation of a neural network which is certifiably more robust. Crucially, the method is fully convex and posed as a semi-definite programme. An application to robustifying model predictive control is used to demonstrate the results. The aim of this work is to introduce a method to navigate the neural network robustness/accuracy trade-off.

The incorporation of Artificial Intelligence (AI) models into various optimization systems is on the rise. Yet, addressing complex urban and environmental management problems normally requires in-depth domain science and informatics expertise. This expertise is essential for deriving data and simulation-driven for informed decision support. In this context, we investigate the potential of leveraging the pre-trained Large Language Models (LLMs). By adopting ChatGPT API as the reasoning core, we outline an integrated workflow that encompasses natural language processing, methontology-based prompt tuning, and transformers. This workflow automates the creation of scenario-based ontology using existing research articles and technical manuals of urban datasets and simulations. The outcomes of our methodology are knowledge graphs in widely adopted ontology languages (e.g., OWL, RDF, SPARQL). These facilitate the development of urban decision support systems by enhancing the data and metadata modeling, the integration of complex datasets, the coupling of multi-domain simulation models, and the formulation of decision-making metrics and workflow. The feasibility of our methodology is evaluated through a comparative analysis that juxtaposes our AI-generated ontology with the well-known Pizza Ontology employed in tutorials for popular ontology software (e.g., prot\'eg\'e). We close with a real-world case study of optimizing the complex urban system of multi-modal freight transportation by generating anthologies of various domain data and simulations to support informed decision-making.

The 2024 Index is our most comprehensive to date and arrives at an important moment when AI's influence on society has never been more pronounced. This year, we have broadened our scope to more extensively cover essential trends such as technical advancements in AI, public perceptions of the technology, and the geopolitical dynamics surrounding its development. Featuring more original data than ever before, this edition introduces new estimates on AI training costs, detailed analyses of the responsible AI landscape, and an entirely new chapter dedicated to AI's impact on science and medicine. The AI Index report tracks, collates, distills, and visualizes data related to artificial intelligence (AI). Our mission is to provide unbiased, rigorously vetted, broadly sourced data in order for policymakers, researchers, executives, journalists, and the general public to develop a more thorough and nuanced understanding of the complex field of AI. The AI Index is recognized globally as one of the most credible and authoritative sources for data and insights on artificial intelligence. Previous editions have been cited in major newspapers, including the The New York Times, Bloomberg, and The Guardian, have amassed hundreds of academic citations, and been referenced by high-level policymakers in the United States, the United Kingdom, and the European Union, among other places. This year's edition surpasses all previous ones in size, scale, and scope, reflecting the growing significance that AI is coming to hold in all of our lives.

For example, the backpropagation in neural network training appears in optimal control as adjoint sensitivity equation (Esteve-Yagüe and Geshkovski, 2023; Faulwasser et al., 2021; Esteve et al., 2021). Moreover, the training of Neural Networks (NNs) with constant width in each layer can be formulated as an Optimal Control Problem (OCP) (Li et al., 2018; Esteve et al., 2021). In this context, the layer-to-layer propagation of the data is considered a dynamical system on a finite horizon corresponding to the depth of the network. The solution to the OCP determines the weights and biases of the neural network, i.e., weights and biases are the control inputs to drive the data to a desired point in the terminal layer determined by the label and loss function. In particular, the system and control perspective is helpful for Residual Neural Networks (ResNets) (He et al., 2016), which can be regarded as Euler forward discretizations of neural ODEs (Chen et al., 2018). Chang et al., 2018 analyze the reversibility and stability of the ResNet dynamics based on their continuous time counterparts. Esteve et al., 2021 and Faulwasser et al., 2021 have suggested to include a regularization term based on the states of the hidden layers in the training OCP. Faulwasser et al., 2021 analyze the dissipativity and the related turnpike property from an optimal control point of view when utilizing a quadratic (l