Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys methodological and theoretical developments at the intersection of operator learning and inverse problems. It begins by summarizing the probabilistic and deterministic approaches to inverse problems, and pays special attention to emerging measure-centric formulations that treat observed data or unknown parameters as probability distributions. The discussion then turns to operator learning by covering essential components such as data generation, loss functions, and widely used architectures for representing function-to-function maps. The core of the chapter centers on the end-to-end inverse operator learning paradigm, which aims to directly map observed data to the solution of the inverse problem without requiring explicit knowledge of the forward map. It highlights the unique challenge that noise plays in this data-driven inversion setting, presents structure-aware architectures for both point predictions and posterior estimates, and surveys relevant theory for linear and nonlinear inverse problems. The chapter also discusses the estimation of priors and regularizers, where operator learning is used more selectively within classical inversion algorithms.

This thesis develops methods for causal inference and causal representation learning (CRL) in high-dimensional, time-varying data. The first contribution introduces the Causal Dynamic Variational Autoencoder (CDVAE), a model for estimating Individual Treatment Effects (ITEs) by capturing unobserved heterogeneity in treatment response driven by latent risk factors that affect only outcomes. CDVAE comes with theoretical guarantees on valid latent adjustment and generalization bounds for ITE error. Experiments on synthetic and real datasets show that CDVAE outperforms baselines, and that state-of-the-art models greatly improve when augmented with its latent substitutes, approaching oracle performance without access to true adjustment variables. The second contribution proposes an efficient framework for long-term counterfactual regression based on RNNs enhanced with Contrastive Predictive Coding (CPC) and InfoMax. It captures long-range dependencies under time-varying confounding while avoiding the computational cost of transformers, achieving state-of-the-art results and introducing CPC into causal inference. The third contribution advances CRL by addressing how latent causes manifest in observed variables. We introduce a model-agnostic interpretability layer based on the geometry of the decoder Jacobian. A sparse self-expression prior induces modular, possibly overlapping groups of observed features aligned with shared latent influences. We provide recovery guarantees in both disjoint and overlapping settings and show that meaningful latent-to-observed structure can be recovered without anchor features or single-parent assumptions. Scalable Jacobian-based regularization techniques are also developed.

Earth observation (EO) models are frequently trained under implicit sampling policies that optimize global accuracy but provide no explicit guarantees on who (which regions, classes, or mission-critical strata) is being served throughout training. This paper introduces a contract-governed training paradigm for EO in which training samples are grouped into service contracts -- semantically meaningful units such as (dataset, region, rare-crop indicator) -- and each contract is assigned a target service share. We instantiate this paradigm as an Observed Service Agreement Graph (OSAG), a lightweight governance layer that (i) monitors contract-level exposure (coverage) during optimization, (ii) drives empirical coverage toward target shares via contract-normalized sampling weights, and (iii) exposes explicit accuracy-governance trade-offs through two knobs: a sampling mixture coefficient alpha and a contract-regularization weight lambda_C. We provide a compact theory in a toy setting: OSAG sampling concentrates empirical coverage to targets; coverage deviations upper-bound service-risk deviations; and contract design (coarse vs. fine) modulates governance cost. Experiments on AVIRIS hyperspectral scenes (Indian Pines plus Salinas) and multispectral Sentinel-2 EuroSAT demonstrate that OSAG can substantially reduce priority coverage error while maintaining global accuracy and improving high-priority accuracy. A EuroSAT coarse-vs-fine contract ablation further evidences how semantically refined contracts can reduce the accuracy cost per unit of governance improvement.

The main focus of Hierarchical Reinforcement Learning (HRL) is studying how large Markov Decision Processes (MDPs) can be more efficiently solved when addressed in a modular way, by combining partial solutions computed for smaller subtasks. Despite their very intuitive role for learning, most notions of MDP abstractions proposed in the HRL literature have limited expressive power or do not possess formal efficiency guarantees. This work addresses these fundamental issues by defining Realizable Abstractions, a new relation between generic low-level MDPs and their associated high-level decision processes. The notion we propose avoids non-Markovianity issues and has desirable near-optimality guarantees. Indeed, we show that any abstract policy for Realizable Abstractions can be translated into near-optimal policies for the low-level MDP, through a suitable composition of options. As demonstrated in the paper, these options can be expressed as solutions of specific constrained MDPs. Based on these findings, we propose RARL, a new HRL algorithm that returns compositional and near-optimal low-level policies, taking advantage of the Realizable Abstraction given in the input. We show that RARL is Probably Approximately Correct, it converges in a polynomial number of samples, and it is robust to inaccuracies in the abstraction.

This paper presents a novel approach to automated stripboard circuit layout design using Answer Set Programming (ASP). The work formulates the layout problem as both a synthesis and multi-objective optimization task that simultaneously generates viable layouts while minimizing board area and component strip crossing. By leveraging ASP's declarative nature, this work expresses complex geometric and electrical constraints in a natural and concise manner. The two-phase solving methodology first ensures feasibility before optimizing layout quality. Experimental results demonstrate that this approach generates compact, manufacturable layouts for a range of circuit complexities. This work represents a significant advancement in automated stripboard layout, offering a practical tool for electronics prototyping and education while showcasing the power of declarative programming for solving complex design automation problems.

Multimodal Artificial Intelligence (AI) systems, particularly Vision-Language Models (VLMs), have become integral to critical applications ranging from autonomous decision-making to automated document processing. As these systems scale, they rely heavily on preprocessing pipelines to handle diverse inputs efficiently. However, this dependency on standard preprocessing operations, specifically image downscaling, creates a significant yet often overlooked security vulnerability. While intended for computational optimization, scaling algorithms can be exploited to conceal malicious visual prompts that are invisible to human observers but become active semantic instructions once processed by the model. Current adversarial strategies remain largely static, failing to account for the dynamic nature of modern agentic workflows. To address this gap, we propose Chameleon, a novel, adaptive adversarial framework designed to expose and exploit scaling vulnerabilities in production VLMs. Unlike traditional static attacks, Chameleon employs an iterative, agent-based optimization mechanism that dynamically refines image perturbations based on the target model's real-time feedback. This allows the framework to craft highly robust adversarial examples that survive standard downscaling operations to hijack downstream execution. We evaluate Chameleon against Gemini 2.5 Flash model. Our experiments demonstrate that Chameleon achieves an Attack Success Rate (ASR) of 84.5% across varying scaling factors, significantly outperforming static baseline attacks which average only 32.1%. Furthermore, we show that these attacks effectively compromise agentic pipelines, reducing decision-making accuracy by over 45% in multi-step tasks. Finally, we discuss the implications of these vulnerabilities and propose multi-scale consistency checks as a necessary defense mechanism.

Human-annotated datasets with explicit difficulty ratings are essential in intelligent educational systems. Although embedding vector spaces are widely used to represent semantic closeness and are promising for analyzing text difficulty, the abundance of embedding methods creates a challenge in selecting the most suitable method. This study proposes the Educational Cone Model, which is a geometric framework based on the assumption that easier texts are less diverse (focusing on fundamental concepts), whereas harder texts are more diverse. This assumption leads to a cone-shaped distribution in the embedding space regardless of the embedding method used. The model frames the evaluation of embeddings as an optimization problem with the aim of detecting structured difficulty-based patterns. By designing specific loss functions, efficient closed-form solutions are derived that avoid costly computation. Empirical tests on real-world datasets validated the model's effectiveness and speed in identifying the embedding spaces that are best aligned with difficulty-annotated educational texts.

Variational Quantum Algorithms (VQAs) are becoming the primary computational primitive for next-generation quantum computers, particularly those embedded as resource-constrained accelerators in the emerging Quantum Internet of Things (QIoT). However, under such device-constrained execution conditions, the scalability of learning is severely limited by barren plateaus, where gradients collapse to zero and training stalls. This poses a practical challenge to delivering VQA-enabled intelligence on QIoT endpoints, which often have few qubits, constrained shot budgets, and strict latency requirements. In this paper, we present a novel approach for escaping barren plateaus by including negative learning rates into the optimization process in QIoT devices. Our method introduces controlled instability into model training by switching between positive and negative learning phases, allowing recovery of significant gradients and exploring flatter areas in the loss landscape. We theoretically evaluate the effect of negative learning on gradient variance and propose conditions under which it helps escape from barren zones. The experimental findings on typical VQA benchmarks show consistent improvements in both convergence and simulation results over traditional optimizers. By escaping barren plateaus, our approach leads to a novel pathway for robust optimization in quantum-classical hybrid models.

High quality data is needed to unlock the full potential of AI for end users. However finding new sources of such data is getting harder: most publicly-available human generated data will soon have been used. Additionally, publicly available data often is not representative of users of a particular system -- for example, a research speech dataset of contractors interacting with an AI assistant will likely be more homogeneous, well articulated and self-censored than real world commands that end users will issue. Therefore unlocking high-quality data grounded in real user interactions is of vital interest. However, the direct use of user data comes with significant privacy risks. Differential Privacy (DP) is a well established framework for reasoning about and limiting information leakage, and is a gold standard for protecting user privacy. The focus of this work, \emph{Differentially Private Synthetic data}, refers to synthetic data that preserves the overall trends of source data,, while providing strong privacy guarantees to individuals that contributed to the source dataset. DP synthetic data can unlock the value of datasets that have previously been inaccessible due to privacy concerns and can replace the use of sensitive datasets that previously have only had rudimentary protections like ad-hoc rule-based anonymization. In this paper we explore the full suite of techniques surrounding DP synthetic data, the types of privacy protections they offer and the state-of-the-art for various modalities (image, tabular, text and decentralized). We outline all the components needed in a system that generates DP synthetic data, from sensitive data handling and preparation, to tracking the use and empirical privacy testing. We hope that work will result in increased adoption of DP synthetic data, spur additional research and increase trust in DP synthetic data approaches.

We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output of a black box. The algorithms considered can be cast under the umbrella of a generalised gradient descent recursion, where the gradient is that of a smooth approximation of the objective function. The framework we develop includes as special cases model-based and mollification methods, two classical approaches to zero-th order optimisation. The convergence results are obtained under very weak assumptions on the regularity of the objective function and involve a trade-off between the degree of smoothing and size of the steps taken in the parameter updates. As expected, additional assumptions are required in the stochastic case. We illustrate the relevance of these algorithms and our convergence results through a challenging classification example from machine learning.