Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process tomography, in which the goal is to retrieve the underlying quantum process based on a given set of measurement data. In this paper, we introduce a modified version of stochastic gradient descent on a Riemannian manifold that integrates recent advancements in numerical methods for Riemannian optimization. This approach inherently supports the physically driven constraints of a quantum process, takes advantage of state-of-the-art large-scale stochastic objective optimization, and has superior performance to traditional approaches such as maximum likelihood estimation and projected least squares. The data-driven approach enables accurate, order-of-magnitude faster results, and works with incomplete data. We demonstrate our approach on simulations of quantum processes and in hardware by characterizing an engineered process on quantum computers.

Synthetic microbiomes offer new possibilities for modulating microbiota, to address the barriers in multidtug resistance (MDR) research. We present a Bayesian optimization approach to enable efficient searching over the space of synthetic microbiome variants to identify candidates predictive of reduced MDR. Microbiome datasets were encoded into a low-dimensional latent space using autoencoders. Sampling from this space allowed generation of synthetic microbiome signatures. Bayesian optimization was then implemented to select variants for biological screening to maximize identification of designs with restricted MDR pathogens based on minimal samples. Four acquisition functions were evaluated: expected improvement, upper confidence bound, Thompson sampling, and probability of improvement. Based on each strategy, synthetic samples were prioritized according to their MDR detection. Expected improvement, upper confidence bound, and probability of improvement consistently produced synthetic microbiome candidates with significantly fewer searches than Thompson sampling. By combining deep latent space mapping and Bayesian learning for efficient guided screening, this study demonstrated the feasibility of creating bespoke synthetic microbiomes with customized MDR profiles.

Explanatory inference is the creation and evaluation of hypotheses that provide explanations, and is sometimes known as abduction or abductive inference. Generative AI is a new set of artificial intelligence models based on novel algorithms for generating text, images, and sounds. This paper proposes a set of benchmarks for assessing the ability of AI programs to perform explanatory inference, and uses them to determine the extent to which ChatGPT, a leading generative AI model, is capable of making explanatory inferences. Tests on the benchmarks reveal that ChatGPT performs creative and evaluative inferences in many domains, although it is limited to verbal and visual modalities. Claims that ChatGPT and similar models are incapable of explanation, understanding, causal reasoning, meaning, and creativity are rebutted.

While language models (LMs) offer significant capability in zero-shot reasoning tasks across a wide range of domains, they do not perform satisfactorily in problems which requires multi-step reasoning. Previous approaches to mitigate this involves breaking a larger, multi-step task into sub-tasks and asking the language model to generate proposals ("thoughts") for each sub-task and using exhaustive planning approaches such as DFS to compose a solution. In this work, we leverage this idea to introduce two new contributions: first, we formalize a planning-based approach to perform multi-step problem solving with LMs via Partially Observable Markov Decision Processes (POMDPs), with the LM's own reflections about the value of a state used as a search heuristic; second, leveraging the online POMDP solver POMCP, we demonstrate a superior success rate of 89.4% on the Game of 24 task as compared to existing approaches while also offering better anytime performance characteristics than fixed tree-search which is used previously. Taken together, these contributions allow modern LMs to decompose and solve larger-scale reasoning tasks more effectively.

Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may result in overconfident predictions and it prevents the use of deep learning models for sequential decision making. This thesis develops scalable methods to equip neural networks with model uncertainty. In particular, we leverage the linearised Laplace approximation to equip pre-trained neural networks with the uncertainty estimates provided by their tangent linear models. This turns the problem of Bayesian inference in neural networks into one of Bayesian inference in conjugate Gaussian-linear models. Alas, the cost of this remains cubic in either the number of network parameters or in the number of observations times output dimensions. By assumption, neither are tractable. We address this intractability by using stochastic gradient descent (SGD) -- the workhorse algorithm of deep learning -- to perform posterior sampling in linear models and their convex duals: Gaussian processes. With this, we turn back to linearised neural networks, finding the linearised Laplace approximation to present a number of incompatibilities with modern deep learning practices -- namely, stochastic optimisation, early stopping and normalisation layers -- when used for hyperparameter learning. We resolve these and construct a sample-based EM algorithm for scalable hyperparameter learning with linearised neural networks. We apply the above methods to perform linearised neural network inference with ResNet-50 (25M parameters) trained on Imagenet (1.2M observations and 1000 output dimensions). Additionally, we apply our methods to estimate uncertainty for 3d tomographic reconstructions obtained with the deep image prior network.

In the classical Reinforcement Learning from Human Feedback (RLHF) framework, Proximal Policy Optimization (PPO) is employed to learn from sparse, sentence-level rewards -- a challenging scenario in traditional deep reinforcement learning. Despite the great successes of PPO in the alignment of state-of-the-art closed-source large language models (LLMs), its open-source implementation is still largely sub-optimal, as widely reported by numerous research studies. To address these issues, we introduce a framework that models RLHF problems as a Markov decision process (MDP), enabling the capture of fine-grained token-wise information. Furthermore, we provide theoretical insights that demonstrate the superiority of our MDP framework over the previous sentence-level bandit formulation. Under this framework, we introduce an algorithm, dubbed as Reinforced Token Optimization (\texttt{RTO}), which learns the token-wise reward function from preference data and performs policy optimization based on this learned token-wise reward signal. Theoretically, \texttt{RTO} is proven to have the capability of finding the near-optimal policy sample-efficiently. For its practical implementation, \texttt{RTO} innovatively integrates Direct Preference Optimization (DPO) and PPO. DPO, originally derived from sparse sentence rewards, surprisingly provides us with a token-wise characterization of response quality, which is seamlessly incorporated into our subsequent PPO training stage. Extensive real-world alignment experiments verify the effectiveness of the proposed approach.

We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. All past work on high-dimensional matrix graphical models assumes that independent and identically distributed (i.i.d.) observations of the matrix-variate are available. Here we allow dependent observations. We consider a sparse-group lasso-based frequency-domain formulation of the problem with a Kronecker-decomposable power spectral density (PSD), and solve it via an alternating direction method of multipliers (ADMM) approach. The problem is bi-convex which is solved via flip-flop optimization. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This result also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data.

We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the means and covariances lie in a ball of bounded radius. We give an algorithm that draws $d^{\mathrm{poly}(k/\varepsilon)}$ samples from the target mixture, runs in sample-polynomial time, and constructs a sampler whose output distribution is $\varepsilon$-far from the unknown mixture in total variation. Prior works for this problem either (i) required exponential runtime in the dimension $d$, (ii) placed strong assumptions on the instance (e.g., spherical covariances or clusterability), or (iii) had doubly exponential dependence on the number of components $k$. Our approach departs from commonly used techniques for this problem like the method of moments. Instead, we leverage a recently developed reduction, based on diffusion models, from distribution learning to a supervised learning task called score matching. We give an algorithm for the latter by proving a structural result showing that the score function of a Gaussian mixture can be approximated by a piecewise-polynomial function, and there is an efficient algorithm for finding it. To our knowledge, this is the first example of diffusion models achieving a state-of-the-art theoretical guarantee for an unsupervised learning task.

In recent years, the widespread application of multi-robot systems in areas such as power inspection, autonomous vehicle fleets has made multi-robot technology a research hotspot in the field of robotics. This paper investigates multi-robot cooperative exploration in unknown environments, proposing a training framework and decision strategy based on multi-agent reinforcement learning. Specifically we propose a Asymmetric Topological Representation based mapping framework (ATR-Mapping), combining the advantages of methods based on raw grid maps and methods based on topology, the structural information from the raw grid maps is extracted and combined with a topological graph constructed based on geometric distance information for decision-making. Leveraging this topological graph representation, we employs a decision network based on topological graph matching to assign corresponding boundary points to each robot as long-term target points for decision-making. We conducts testing and application of the proposed algorithms in real world scenarios using the Gazebo and Gibson simulation environments. It validates that the proposed method, when compared to existing methods, achieves a certain degree of performance improvement.

We consider the problem of an autonomous agent equipped with multiple sensors, each with different sensing precision and energy costs. The agent's goal is to explore the environment and gather information subject to its resource constraints in unknown, partially observable environments. The challenge lies in reasoning about the effects of sensing and movement while respecting the agent's resource and dynamic constraints. We formulate the problem as a trajectory optimization problem and solve it using a projection-based trajectory optimization approach where the objective is to reduce the variance of the Gaussian process world belief. Our approach outperforms previous approaches in long horizon trajectories by achieving an overall variance reduction of up to 85% and reducing the root-mean square error in the environment belief by 50%. This approach was developed in support of rover path planning for the NASA VIPER Mission.