Neural processes are a family of models which use neural networks to directly parametrise a map from data sets to predictions. Directly parametrising this map enables the use of expressive neural networks in small-data problems where neural networks would traditionally overfit. Neural processes can produce well-calibrated uncertainties, effectively deal with missing data, and are simple to train. These properties make this family of models appealing for a breadth of applications areas, such as healthcare or environmental sciences. This thesis advances neural processes in three ways. First, we propose convolutional neural processes (ConvNPs). ConvNPs improve data efficiency of neural processes by building in a symmetry called translation equivariance. ConvNPs rely on convolutional neural networks rather than multi-layer perceptrons. Second, we propose Gaussian neural processes (GNPs). GNPs directly parametrise dependencies in the predictions of a neural process. Current approaches to modelling dependencies in the predictions depend on a latent variable, which consequently requires approximate inference, undermining the simplicity of the approach. Third, we propose autoregressive conditional neural processes (AR CNPs). AR CNPs train a neural process without any modifications to the model or training procedure and, at test time, roll out the model in an autoregressive fashion. AR CNPs equip the neural process framework with a new knob where modelling complexity and computational expense at training time can be traded for computational expense at test time. In addition to methodological advancements, this thesis also proposes a software abstraction that enables a compositional approach to implementing neural processes. This approach allows the user to rapidly explore the space of neural process models by putting together elementary building blocks in different ways.

Conventional Bayesian optimal experimental design seeks to maximize the expected information gain (EIG) on model parameters. However, the end goal of the experiment often is not to learn the model parameters, but to predict downstream quantities of interest (QoIs) that depend on the learned parameters. And designs that offer high EIG for parameters may not translate to high EIG for QoIs. Goal-oriented optimal experimental design (GO-OED) thus directly targets to maximize the EIG of QoIs. We introduce LF-GO-OED (likelihood-free goal-oriented optimal experimental design), a computational method for conducting GO-OED with nonlinear observation and prediction models. LF-GO-OED is specifically designed to accommodate implicit models, where the likelihood is intractable. In particular, it builds a density ratio estimator from samples generated from approximate Bayesian computation (ABC), thereby sidestepping the need for likelihood evaluations or density estimations. The overall method is validated on benchmark problems with existing methods, and demonstrated on scientific applications of epidemiology and neural science.

In partially observable multi-agent systems, agents typically only have access to local observations. This severely hinders their ability to make precise decisions, particularly during decentralized execution. To alleviate this problem and inspired by image outpainting, we propose State Inference with Diffusion Models (SIDIFF), which uses diffusion models to reconstruct the original global state based solely on local observations. SIDIFF consists of a state generator and a state extractor, which allow agents to choose suitable actions by considering both the reconstructed global state and local observations. In addition, SIDIFF can be effortlessly incorporated into current multi-agent reinforcement learning algorithms to improve their performance. Finally, we evaluated SIDIFF on different experimental platforms, including Multi-Agent Battle City (MABC), a novel and flexible multi-agent reinforcement learning environment we developed. SIDIFF achieved desirable results and outperformed other popular algorithms.

In the emerging hybrid traffic flow environment, which includes both human-driven vehicles (HDVs) and autonomous vehicles (AVs), ensuring safe and robust decision-making and control is crucial for the effective operation of autonomous vehicle platooning. Current systems for cooperative adaptive cruise control and lane changing are inadequate in responding to real-world emergency situations, limiting the potential of autonomous vehicle platooning technology. To address the aforementioned challenges, we propose a Twin-World Safety-Enhanced Data-Model-Knowledge Hybrid-Driven autonomous vehicle platooning Cooperative Control Framework. Within this framework, a deep reinforcement learning formation decision model integrating traffic priors is designed, and a twin-world deduction model based on safety priority judgment is proposed. Subsequently, an optimal control-based multi-scenario decision-control right adaptive switching mechanism is designed to achieve adaptive switching between data-driven and model-driven methods. Through simulation experiments and hardware-in-loop tests, our algorithm has demonstrated excellent performance in terms of safety, robustness, and flexibility. A detailed account of the validation results for the model can be found in \url{https://perfectxu88.github.io/towardssafeandrobust.github.io/}.

Recent advancements in multimodal Variational AutoEncoders (VAEs) have highlighted their potential for modeling complex data from multiple modalities. However, many existing approaches use relatively straightforward aggregating schemes that may not fully capture the complex dynamics present between different modalities. This work introduces a novel multimodal VAE that incorporates a Markov Random Field (MRF) into both the prior and posterior distributions. This integration aims to capture complex intermodal interactions more effectively. Unlike previous models, our approach is specifically designed to model and leverage the intricacies of these relationships, enabling a more faithful representation of multimodal data. Our experiments demonstrate that our model performs competitively on the standard PolyMNIST dataset and shows superior performance in managing complex intermodal dependencies in a specially designed synthetic dataset, intended to test intricate relationships.

Humans observe only part of their environment at any moment but can still make complex, long-term decisions thanks to our long-term memory. To test how an AI can learn and utilize its long-term memory, we have developed a partially observable Markov decision processes (POMDP) environment, where the agent has to answer questions while navigating a maze. The environment is completely knowledge graph (KG) based, where the hidden states are dynamic KGs. A KG is both human- and machine-readable, making it easy to see what the agents remember and forget. We train and compare agents with different memory systems, to shed light on how human brains work when it comes to managing its own memory. By repurposing the given learning objective as learning a memory management policy, we were able to capture the most likely hidden state, which is not only interpretable but also reusable.

This paper explores the application of Stochastic Differential Equations (SDE) to interpret the text generation process of Large Language Models (LLMs) such as GPT-4. Text generation in LLMs is modeled as a stochastic process where each step depends on previously generated content and model parameters, sampling the next word from a vocabulary distribution. We represent this generation process using SDE to capture both deterministic trends and stochastic perturbations. The drift term describes the deterministic trends in the generation process, while the diffusion term captures the stochastic variations. We fit these functions using neural networks and validate the model on real-world text corpora. Through numerical simulations and comprehensive analyses, including drift and diffusion analysis, stochastic process property evaluation, and phase space exploration, we provide deep insights into the dynamics of text generation. This approach not only enhances the understanding of the inner workings of LLMs but also offers a novel mathematical perspective on language generation, which is crucial for diagnosing, optimizing, and controlling the quality of generated text.

The remarkable ability of single-celled organisms to sense and react to the dynamic changes in their environment is a testament to the adaptive capabilities of their internal biochemical circuitry. One of the goals of synthetic biology is to develop biochemical analogues of such systems to autonomously monitor and control biochemical processes. Such systems may have impactful applications in fields such as molecular diagnostics, smart therapeutics, and in vivo nanomedicine. So far, the attempts to create such systems have been focused on functionally replicating the behavior of traditional feedforward networks in abstract and DNA-based synthetic chemistries. However, the inherent incompatibility between digital and chemical modes of computation introduces several nonidealities into these implementations, making it challenging to realize them in practice. In this work, we present NeuralCRNs, a novel supervised learning framework constructed as a collection of deterministic chemical reaction networks (CRNs). Unlike prior works, the NeuralCRNs framework is founded on dynamical system-based learning implementations and, thus, results in chemically compatible computations. First, we show the construction and training of a supervised learning classifier for linear classification. We then extend this framework to support nonlinear classification. We then demonstrate the validity of our constructions by training and evaluating them first on several binary and multi-class classification datasets with complex class separation boundaries. Finally, we detail several considerations regarding the NeuralCRNs framework and elaborate on the pros and cons of our methodology compared to the existing works.

Unmanned Aerial Vehicles (UAVs), due to their low cost and high flexibility, have been widely used in various scenarios to enhance network performance. However, the optimization of UAV trajectories in unknown areas or areas without sufficient prior information, still faces challenges related to poor planning performance and low distributed execution. These challenges arise when UAVs rely solely on their own observation information and the information from other UAVs within their communicable range, without access to global information. To address these challenges, this paper proposes the Qedgix framework, which combines graph neural networks (GNNs) and the QMIX algorithm to achieve distributed optimization of the Age of Information (AoI) for users in unknown scenarios. The framework utilizes GNNs to extract information from UAVs, users within the observable range, and other UAVs within the communicable range, thereby enabling effective UAV trajectory planning. Due to the discretization and temporal features of AoI indicators, the Qedgix framework employs QMIX to optimize distributed partially observable Markov decision processes (Dec-POMDP) based on centralized training and distributed execution (CTDE) with respect to mean AoI values of users. By modeling the UAV network optimization problem in terms of AoI and applying the Kolmogorov-Arnold representation theorem, the Qedgix framework achieves efficient neural network training through parameter sharing based on permutation invariance. Simulation results demonstrate that the proposed algorithm significantly improves convergence speed while reducing the mean AoI values of users. The code is available at https://github.com/UNIC-Lab/Qedgix.

This study focuses on EEG-based BMI for detecting voluntary keystrokes, aiming to develop a reliable brain-computer interface (BCI) to simulate and anticipate keystrokes, especially for individuals with motor impairments. The methodology includes extensive segmentation, event alignment, ERP plot analysis, and signal analysis. Different deep learning models are trained to classify EEG data into three categories -- `resting state' (0), `d' key press (1), and `l' key press (2). Real-time keypress simulation based on neural activity is enabled through integration with a tkinter-based graphical user interface. Feature engineering utilized ERP windows, and the SVC model achieved 90.42% accuracy in event classification. Additionally, deep learning models -- MLP (89% accuracy), Catboost (87.39% accuracy), KNN (72.59%), Gaussian Naive Bayes (79.21%), Logistic Regression (90.81% accuracy), and a novel Bi-Directional LSTM-GRU hybrid model (89% accuracy) -- were developed for BCI keyboard simulation. Finally, a GUI was created to predict and simulate keystrokes using the trained MLP model.