Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph halfspaces defined through closure under induced paths. Our main result is a $2$-satisfiability based decomposition theorem, which allows one to represent monophonic halfspaces as a disjoint union of certain vertex subsets. Using this decomposition, we achieve efficient and (nearly) optimal algorithms for various learning problems, such as teaching, active, and online learning. Most notably, we obtain a polynomial-time algorithm for empirical risk minimization. Independently of the decomposition theorem, we obtain an efficient, stable, and proper sample compression scheme. This makes monophonic halfspaces efficiently learnable with proper learners and linear error rate $1/\varepsilon$ in the realizable PAC setting. Our results answer open questions from the literature, and show a stark contrast with geodesic halfspaces, for which most of the said learning problems are NP-hard.

Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. While traditionally studied within Euclidean spaces, contemporary applications increasingly involve complex, non-Euclidean data structures that reside in abstract metric spaces, known as random objects, such as images, shapes, networks, and distributions. This paper introduces a novel framework for causal inference with continuous treatments applied to non-Euclidean data. To address the challenges posed by the lack of linear structures, we leverage Hilbert space embeddings of the metric spaces to facilitate Fréchet mean estimation and causal effect mapping. Motivated by a study on the impact of exposure to fine particulate matter on age-at-death distributions across U.S. counties, we propose a nonparametric, doubly-debiased causal inference approach for outcomes as random objects with continuous treatments. Our framework can accommodate moderately high-dimensional vector-valued confounders and derive efficient influence functions for estimation to ensure both robustness and interpretability. We establish rigorous asymptotic properties of the cross-fitted estimators and employ conformal inference techniques for counterfactual outcome prediction. Validated through numerical experiments and applied to real-world environmental data, our framework extends causal inference methodologies to complex data structures, broadening its applicability across scientific disciplines.

Most of the widely used estimators of the average treatment effect (ATE) in causal inference rely on the assumptions of unconfoundedness and overlap. Unconfoundedness requires that the observed covariates account for all correlations between the outcome and treatment. Overlap requires the existence of randomness in treatment decisions for all individuals. Nevertheless, many types of studies frequently violate unconfoundedness or overlap, for instance, observational studies with deterministic treatment decisions - popularly known as Regression Discontinuity designs - violate overlap. In this paper, we initiate the study of general conditions that enable the identification of the average treatment effect, extending beyond unconfoundedness and overlap. In particular, following the paradigm of statistical learning theory, we provide an interpretable condition that is sufficient and necessary for the identification of ATE. Moreover, this condition also characterizes the identification of the average treatment effect on the treated (ATT) and can be used to characterize other treatment effects as well. To illustrate the utility of our condition, we present several well-studied scenarios where our condition is satisfied and, hence, we prove that ATE can be identified in regimes that prior works could not capture. For example, under mild assumptions on the data distributions, this holds for the models proposed by Tan (2006) and Rosenbaum (2002), and the Regression Discontinuity design model introduced by Thistlethwaite and Campbell (1960). For each of these scenarios, we also show that, under natural additional assumptions, ATE can be estimated from finite samples. We believe these findings open new avenues for bridging learning-theoretic insights and causal inference methodologies, particularly in observational studies with complex treatment mechanisms.

Alignment of large language models (LLMs) with human values has recently garnered significant attention, with prominent examples including the canonical yet costly Reinforcement Learning from Human Feedback (RLHF) and the simple Direct Preference Optimization (DPO). In this work, we demonstrate that both RLHF and DPO can be interpreted from the perspective of mutual information (MI) maximization, uncovering a profound connection to contrastive learning. Within this framework, both RLHF and DPO can be viewed as methods that perform contrastive learning based on the positive and negative samples derived from the base model, leveraging the Donsker-Varadhan (DV) lower bound on MI (equivalently, the MINE estimator). This paradigm further explains why RLHF may not intrinsically incentivize reasoning capacities in LLMs beyond what is already present in the base model. Building on this perspective, we replace the DV/MINE bound with the Jensen-Shannon MI estimator and propose Mutual Information Optimization (MIO). Comprehensive theoretical analysis and extensive empirical evaluations demonstrate that MIO mitigates the late-stage decline in chosen-likelihood observed in DPO, achieving competitive or superior performance across various challenging reasoning and mathematical benchmarks. We will release the model and code upon acceptance.

This paper investigates a hybrid learning framework for reinforcement learning (RL) in which the agent can leverage both an offline dataset and online interactions to learn the optimal policy. We present a unified algorithm and analysis and show that augmenting confidence-based online RL algorithms with the offline dataset outperforms any pure online or offline algorithm alone and achieves state-of-the-art results under two learning metrics, i.e., sub-optimality gap and online learning regret. Specifically, we show that our algorithm achieves a sub-optimality gap $\tilde{O}(\sqrt{1/(N_0/\mathtt{C}(π^*|ρ)+N_1}) )$, where $\mathtt{C}(π^*|ρ)$ is a new concentrability coefficient, $N_0$ and $N_1$ are the numbers of offline and online samples, respectively. For regret minimization, we show that it achieves a constant $\tilde{O}( \sqrt{N_1/(N_0/\mathtt{C}(π^{-}|ρ)+N_1)} )$ speed-up compared to pure online learning, where $\mathtt{C}(π^-|ρ)$ is the concentrability coefficient over all sub-optimal policies. Our results also reveal an interesting separation on the desired coverage properties of the offline dataset for sub-optimality gap minimization and regret minimization. We further validate our theoretical findings in several experiments in special RL models such as linear contextual bandits and Markov decision processes (MDPs).

Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and communications. In this work, we introduce Multi-Environment Generalized Long AMP, a novel AMP framework that applies to transfer learning problems with multiple data sources and distribution shifts. We rigorously establish state evolution for multi-environment GLAMP. We demonstrate the utility of this framework by precisely characterizing the risk of three Lasso-based transfer learning estimators for the first time: the Stacked Lasso, the Model Averaging Estimator, and the Second Step Estimator. We also demonstrate the remarkable finite sample accuracy of our theory via extensive simulations.

A key challenge in this domain is the balance between exploration and exploitation, which often results in slow learning and suboptimal performance [10], [11]. These limitations highlight the need for more effective learning strategies that can improve both the speed and performance of skill acquisition, especially for high-dimensional humanoid control tasks. During human development, external assistance plays a crucial role in learning motion skills [12]. Infants, for example, often rely on parental support during their first steps, with walkers or direct physical assistance to help them gain the confidence and balance needed for independent locomotion [13], [14]. Similarly, in the case of highly complexmovementslikebackflips,experiencedcoachesprovide physical guidance, supporting the learner's back and applying upward forces to prevent falls and promote proper technique [15]. Studies indicate that such external aids not only expedite the learning process but also help prevent learners from adopting ineffective or unsafe strategies [16].

Scientific information expresses human understanding of nature. This knowledge is largely disseminated in different forms of text, including scientific papers, news articles, and discourse among people on social media. While important for accelerating our pursuit of knowledge, not all scientific text is faithful to the underlying science. As the volume of this text has burgeoned online in recent years, it has become a problem of societal importance to be able to identify the faithfulness of a given piece of scientific text automatically. This thesis is concerned with the cultivation of datasets, methods, and tools for machine understanding of scientific language, in order to analyze and understand science communication at scale. To arrive at this, I present several contributions in three areas of natural language processing and machine learning: automatic fact checking, learning with limited data, and scientific text processing. These contributions include new methods and resources for identifying check-worthy claims, adversarial claim generation, multi-source domain adaptation, learning from crowd-sourced labels, cite-worthiness detection, zero-shot scientific fact checking, detecting exaggerated scientific claims, and modeling degrees of information change in science communication. Critically, I demonstrate how the research outputs of this thesis are useful for effectively learning from limited amounts of scientific text in order to identify misinformative scientific statements and generate new insights into the science communication process

This study examines the impact of an Artificial Intelligence tutor teammate (AI) on student curiosity-driven engagement and learning effectiveness during Interactive Molecular Dynamics (IMD) tasks on the Visual Molecular Dynamics platform. It explores the role of the AI's curiosity-triggering and response behaviors in stimulating and sustaining student curiosity, affecting the frequency and complexity of student-initiated questions. The study further assesses how AI interventions shape student engagement, foster discovery curiosity, and enhance team performance within the IMD learning environment. Using a Wizard-of-Oz paradigm, a human experimenter dynamically adjusts the AI tutor teammate's behavior through a large language model. By employing a mixed-methods exploratory design, a total of 11 high school students participated in four IMD tasks that involved molecular visualization and calculations, which increased in complexity over a 60-minute period. Team performance was evaluated through real-time observation and recordings, whereas team communication was measured by question complexity and AI's curiosity-triggering and response behaviors. Cross Recurrence Quantification Analysis (CRQA) metrics reflected structural alignment in coordination and were linked to communication behaviors. High-performing teams exhibited superior task completion, deeper understanding, and increased engagement. Advanced questions were associated with AI curiosity-triggering, indicating heightened engagement and cognitive complexity. CRQA metrics highlighted dynamic synchronization in student-AI interactions, emphasizing structured yet adaptive engagement to promote curiosity. These proof-of-concept findings suggest that the AI's dual role as a teammate and educator indicates its capacity to provide adaptive feedback, sustaining engagement and epistemic curiosity.

This paper reconceptualises peer review as structured public commentary. Traditional academic validation is hindered by anonymity, latency, and gatekeeping. We propose a transparent, identity-linked, and reproducible system of scholarly evaluation anchored in open commentary. Leveraging blockchain for immutable audit trails and AI for iterative synthesis, we design a framework that incentivises intellectual contribution, captures epistemic evolution, and enables traceable reputational dynamics. This model empowers fields from computational science to the humanities, reframing academic knowledge as a living process rather than a static credential.