Two pressing topics in the theory of deep learning are the interpretation of feature learning mechanisms and the determination of implicit bias of networks in the rich regime. Current theories of rich feature learning, often appear in the form of high-dimensional non-linear equations, which require computationally intensive numerical solutions. Given the many details that go into defining a deep learning problem, this complexity is a significant and often unavoidable challenge. Here, we propose a powerful heuristic route for predicting the data and width scales at which various patterns of feature learning emerge. This form of scale analysis is considerably simpler than exact theories and reproduces the scaling exponents of various known results. In addition, we make novel predictions on complex toy architectures, such as three-layer non-linear networks and attention heads, thus extending the scope of first-principle theories of deep learning.

Preliminary mission design of low-thrust spacecraft trajectories in the Circular Restricted Three-Body Problem is a global search characterized by a complex objective landscape and numerous local minima. Formulating the problem as sampling from an unnormalized distribution supported on neighborhoods of locally optimal solutions, provides the opportunity to deploy Markov chain Monte Carlo methods and generative machine learning. In this work, we extend our previous self-supervised diffusion model fine-tuning framework to employ gradient-informed Markov chain Monte Carlo. We compare two algorithms - the Metropolis-Adjusted Langevin Algorithm and Hamiltonian Monte Carlo - both initialized from a distribution learned by a diffusion model. Derivatives of an objective function that balances fuel consumption, time of flight and constraint violations are computed analytically using state transition matrices. We show that incorporating the gradient drift term accelerates mixing and improves convergence of the Markov chain for a multi-revolution transfer in the Saturn-Titan system. Among the evaluated methods, MALA provides the best trade-off between performance and computational cost. Starting from samples generated by a baseline diffusion model trained on a related transfer, MALA explicitly targets Pareto-optimal solutions. Compared to a random walk Metropolis algorithm, it increases the feasibility rate from 17.34% to 63.01% and produces a denser, more diverse coverage of the Pareto front. By fine-tuning a diffusion model on the generated samples and associated reward values with reward-weighted likelihood maximization, we learn the global solution structure of the problem and eliminate the need for a tedious separate data generation phase.

Recent advances in Multimodal Large Language Models (MLLMs) have enabled their use as intelligent agents for smartphone operation. However, existing methods depend on the Android Debug Bridge (ADB) for data transmission and action execution, limiting their applicability to Android devices. In this work, we introduce the novel Embodied Smartphone Operation (ESO) task and present See-Control, a framework that enables smartphone operation via direct physical interaction with a low-DoF robotic arm, offering a platform-agnostic solution. See-Control comprises three key components: (1) an ESO benchmark with 155 tasks and corresponding evaluation metrics; (2) an MLLM-based embodied agent that generates robotic control commands without requiring ADB or system back-end access; and (3) a richly annotated dataset of operation episodes, offering valuable resources for future research. By bridging the gap between digital agents and the physical world, See-Control provides a concrete step toward enabling home robots to perform smartphone-dependent tasks in realistic environments.

Understanding how humans respond to uncertainty is critical for designing safe and effective physical human-robot interaction (pHRI), as physically working with robots introduces multiple sources of uncertainty, including trust, comfort, and perceived safety. Conventional pHRI control frameworks typically build on optimal control theory, which assumes that human actions minimize a cost function; however, human behavior under uncertainty often departs from such optimal patterns. To address this gap, additional understanding of human behavior under uncertainty is needed. This pilot study implemented a physically coupled target-reaching task in which the robot delivered assistance or disturbances with systematically varied probabilities (10\% to 90\%). Analysis of participants' force inputs and decision-making strategies revealed two distinct behavioral clusters: a "trade-off" group that modulated their physical responses according to disturbance likelihood, and an "always-compensate" group characterized by strong risk aversion irrespective of probability. These findings provide empirical evidence that human decision-making in pHRI is highly individualized and that the perception of probability can differ to its true value. Accordingly, the study highlights the need for more interpretable behavioral models, such as cumulative prospect theory (CPT), to more accurately capture these behaviors and inform the design of future adaptive robot controllers.

The deployment of Unmanned Aerial Vehicle (UAV) swarms as dynamic communication relays is critical for next-generation tactical networks. However, operating in contested environments requires solving a complex trade-off, including maximizing system throughput while ensuring collision avoidance and resilience against adversarial jamming. Existing heuristic-based approaches often struggle to find effective solutions due to the dynamic and multi-objective nature of this problem. This paper formulates this challenge as a cooperative Multi-Agent Reinforcement Learning (MARL) problem, solved using the Centralized Training with Decentralized Execution (CTDE) framework. Our approach employs a centralized critic that uses global state information to guide decentralized actors which operate using only local observations. Simulation results show that our proposed framework significantly outperforms heuristic baselines, increasing the total system throughput by approximately 50% while simultaneously achieving a near-zero collision rate. A key finding is that the agents develop an emergent anti-jamming strategy without explicit programming. They learn to intelligently position themselves to balance the trade-off between mitigating interference from jammers and maintaining effective communication links with ground users.

Humans interpret safety not as a binary signal but as a continuous, context- and spatially-dependent notion of risk. While risk is subjective, humans form rational mental models that guide action selection in dynamic environments. This work proposes a framework for extracting implicit human risk models by introducing a novel, semantically-conditioned and spatially-varying parametrization of risk, supervised directly from safe human demonstration videos and VLM common sense. Notably, we define risk through a Bayesian formulation. The prior is furnished by a pretrained vision-language model. In order to encourage the risk estimate to be more human aligned, a likelihood function modulates the prior to produce a relative metric of risk. Specifically, the likelihood is a learned ViT that maps pretrained features, to pixel-aligned risk values. Our pipeline ingests RGB images and a query object string, producing pixel-dense risk images. These images that can then be used as value-predictors in robot planning tasks or be projected into 3D for use in conventional trajectory optimization to produce human-like motion. This learned mapping enables generalization to novel objects and contexts, and has the potential to scale to much larger training datasets. In particular, the Bayesian framework that is introduced enables fast adaptation of our model to additional observations or common sense rules. We demonstrate that our proposed framework produces contextual risk that aligns with human preferences. Additionally, we illustrate several downstream applications of the model; as a value learner for visuomotor planners or in conjunction with a classical trajectory optimization algorithm. Our results suggest that our framework is a significant step toward enabling autonomous systems to internalize human-like risk. Code and results can be found at https://riskbayesian.github.io/bayesian_risk/.

Learning about the causal structure of the world is a fundamental problem for human cognition. Causal models and especially causal learning have proved to be difficult for large pretrained models using standard techniques of deep learning. In contrast, cognitive scientists have applied advances in our formal understanding of causation in computer science, particularly within the Causal Bayes Net formalism, to understand human causal learning. In the very different tradition of reinforcement learning, researchers have described an intrinsic reward signal called "empowerment" which maximizes mutual information between actions and their outcomes. "Empowerment" may be an important bridge between classical Bayesian causal learning and reinforcement learning and may help to characterize causal learning in humans and enable it in machines. If an agent learns an accurate causal world model, they will necessarily increase their empowerment, and increasing empowerment will lead to a more accurate causal world model. Empowerment may also explain distinctive features of childrens causal learning, as well as providing a more tractable computational account of how that learning is possible. In an empirical study, we systematically test how children and adults use cues to empowerment to infer causal relations, and design effective causal interventions.

The growing prevalence of artificial intelligence (AI) in various applications underscores the need for agents that can successfully navigate and adapt to an ever-changing, open-ended world. A key challenge is ensuring these AI agents are robust, excelling not only in familiar settings observed during training but also effectively generalising to previously unseen and varied scenarios. In this thesis, we harness methodologies from open-endedness and multi-agent learning to train and evaluate robust AI agents capable of generalising to novel environments, out-of-distribution inputs, and interactions with other co-player agents. We begin by introducing MiniHack, a sandbox framework for creating diverse environments through procedural content generation. Based on the game of NetHack, MiniHack enables the construction of new tasks for reinforcement learning (RL) agents with a focus on generalisation. We then present Maestro, a novel approach for generating adversarial curricula that progressively enhance the robustness and generality of RL agents in two-player zero-sum games. We further probe robustness in multi-agent domains, utilising quality-diversity methods to systematically identify vulnerabilities in state-of-the-art, pre-trained RL policies within the complex video game football domain, characterised by intertwined cooperative and competitive dynamics. Finally, we extend our exploration of robustness to the domain of LLMs. Here, our focus is on diagnosing and enhancing the robustness of LLMs against adversarial prompts, employing evolutionary search to generate a diverse range of effective inputs that aim to elicit undesirable outputs from an LLM. This work collectively paves the way for future advancements in AI robustness, enabling the development of agents that not only adapt to an ever-evolving world but also thrive in the face of unforeseen challenges and interactions.

Abstract: Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior over the continuous-time dynamics and latent state trajectory in state-space form and updating it through a targeted marginal Metropolis-Hastings sampler equipped with a numerical ODE integrator. The resulting posterior samples are used to formulate a scenario-based optimal control problem that accounts for both model and measurement uncertainty and is solved using standard nonlinear programming methods. The approach is validated in a numerical case study on glucose regulation using a Type 1 diabetes model. Keywords: Probabilistic and Bayesian methods for system identification, Nonlinear system identification, Time series modeling, Statistical inference, Learning methods for optimal control, Model predictive control, Data-driven control theory 1. INTRODUCTION Accurate dynamical models are fundamental for the predictive and optimal control of nonlinear systems. Although first-principles models may describe the general structure of many systems, important parameters or effects often remain unknown, limiting their direct use for control.

Verifiers can improve language model capabilities by scoring and ranking responses from generated candidates. Currently, high-quality verifiers are either unscalable (e.g., humans) or limited in utility (e.g., tools like Lean). While LM judges and reward models have become broadly useful as general-purpose verifiers, a significant performance gap remains between them and oracle verifiers (verifiers with perfect accuracy). To help close this gap, we introduce Weaver, a framework for designing a strong verifier by combining multiple weak, imperfect verifiers. We find weighted ensembles of verifiers, which typically require learning from labeled data, significantly outperform unweighted combinations due to differences in verifier accuracies. To reduce dependency on labeled data, Weaver leverages weak supervision to estimate each verifier's accuracy and combines outputs into a unified score that better reflects true response quality. However, directly applying weak supervision algorithms poses challenges, including inconsistent verifier output formats and handling low-quality verifiers. Weaver addresses these using dataset statistics to normalize outputs and filter specific verifiers. We study Weaver's effectiveness in test-time repeated sampling, where a model generates multiple candidate responses and selects one. Our evaluations show Weaver significantly improves over Pass@1-performance when selecting the first candidate-across reasoning and math tasks, achieving o3-mini-level accuracy with Llama 3.3 70B Instruct as generator, and an ensemble of 70B or smaller judge and reward models as verifiers (87.7% average). This gain mirrors the jump between GPT-4o and o3-mini (69.0% vs. 86.7%), which required extensive finetuning and post-training. To reduce computational costs of verifier ensembles, we train a 400M cross-encoder using Weaver's combined output scores.