Discrete time linear dynamical systems, including Markov chains, have found many applications including in security settings such as in cybersecurity operations center (CSOC) management and in managing health risks. However, in these two scenarios, there is uncertainty about the time horizon for which the system runs. This creates uncertainty about the cost (or reward) incurred based on the state distribution when the system stops. Given past data samples of how long a system ran, we theoretically analyze the cost incurred at the stop of the system as a distributional robust cost estimation task in a Wasserstein ambiguity set. Towards this, we show an equivalence between a discrete time Markov Chain on a probability simplex and a global asymptotic stable (GAS) discrete time linear dynamical system, allowing us to base our study on a GAS system only. Then, we provide various polynomial time algorithms and hardness results for different cases in our theoretical study, including a novel proof of a fundamental result about Wassertein distance based polytope. We experiment with real world data in CSOC domain and prior data in health domain to reveal the benefits of our model and approach.

Abstract-- Autonomous Surface V ehicles (ASVs) play a crucial role in maritime operations, yet their navigation in shallow-water environments remains challenging due to dynamic disturbances and depth constraints. In this paper, we propose a reinforcement learning (RL) framework for ASV navigation under depth constraints, where the vehicle must reach a target while avoiding unsafe areas with only a single depth measurement per timestep from a downward-facing Single Beam Echosounder (SBES). T o enhance environmental awareness, we integrate Gaussian Process (GP) regression into the RL framework, enabling the agent to progressively estimate a bathymetric depth map from sparse sonar readings. This approach improves decision-making by providing a richer representation of the environment. Furthermore, we demonstrate effective sim-to-real transfer, ensuring that trained policies generalize well to real-world aquatic conditions. Experimental results validate our method's capability to improve ASV navigation performance while maintaining safety in challenging shallow-water environments. I. INTRODUCTION Autonomous Surface V ehicles (ASVs) are unmanned vessels increasingly employed for a variety of maritime operations, including environmental monitoring, search-and-rescue, and surveillance.

We introduce the Schrodinger Neural Network (SNN), a principled architecture for conditional density estimation and uncertainty quantification inspired by quantum mechanics. The SNN maps each input to a normalized wave function on the output domain and computes predictive probabilities via the Born rule. The SNN departs from standard parametric likelihood heads by learning complex coefficients of a spectral expansion (e . g ., Chebyshev polynomials) whose squared modulus yields the conditional density $p(y|x)=\left| ψ_x(y)\right| {}^2$ with analytic normalization. This representation confers three practical advantages: positivity and exact normalization by construction, native multimodality through interference among basis modes without explicit mixture bookkeeping, and yields closed-form (or efficiently computable) functionals$-$such as moments and several calibration diagnostics$-$as quadratic forms in coefficient space. We develop the statistical and computational foundations of the SNN, including (i) training by exact maximum-likelihood with unit-sphere coefficient parameterization, (ii) physics-inspired quadratic regularizers (kinetic and potential energies) motivated by uncertainty relations between localization and spectral complexity, (iii) scalable low-rank and separable extensions for multivariate outputs, (iv) operator-based extensions that represent observables, constraints, and weak labels as self-adjoint matrices acting on the amplitude space, and (v) a comprehensive framework for evaluating multimodal predictions. The SNN provides a coherent, tractable framework to elevate probabilistic prediction from point estimates to physically inspired amplitude-based distributions.

This thesis works to address a pivotal challenge in medical image analysis: the reliance on extensive labeled datasets, which are often limited due to the need for expert annotation and constrained by privacy and legal issues. By focusing on the development of self-supervised learning techniques and domain adaptation methods, this research aims to circumvent these limitations, presenting a novel approach to enhance the utility and efficacy of deep learning in medical imaging. Central to this thesis is the development of the Medformer, an innovative neural network architecture designed for multitask learning and deep domain adaptation. This model is adept at pre-training on diverse medical image datasets, handling varying sizes and modalities, and is equipped with a dynamic input-output adaptation mechanism. This enables efficient processing and integration of a wide range of medical image types, from 2D X-rays to complex 3D MRIs, thus mitigating the dependency on large labeled datasets. Further, the thesis explores the current state of self-supervised learning in medical imaging. It introduces novel pretext tasks that are capable of extracting meaningful information from unlabeled data, significantly advancing the model's interpretative abilities. This approach is validated through rigorous experimentation, including the use of the MedMNIST dataset, demonstrating the model's proficiency in learning generalized features applicable to various downstream tasks. In summary, this thesis contributes to the advancement of medical image analysis by offering a scalable, adaptable framework that reduces reliance on labeled data. It paves the way for more accurate, efficient diagnostic tools in healthcare, signifying a major step forward in the application of deep learning in medical imaging.

Time series segmentation is a fundamental task in analyzing temporal data across various domains, from human activity recognition to energy monitoring. While numerous state-of-the-art methods have been developed to tackle this problem, the evaluation of their performance remains critically limited. Existing measures predominantly focus on change point accuracy or rely on point-based measures such as Adjusted Rand Index (ARI), which fail to capture the quality of the detected segments, ignore the nature of errors, and offer limited interpretability. In this paper, we address these shortcomings by introducing two novel evaluation measures: WARI (Weighted Adjusted Rand Index), that accounts for the position of segmentation errors, and SMS (State Matching Score), a fine-grained measure that identifies and scores four fundamental types of segmentation errors while allowing error-specific weighting. We empirically validate WARI and SMS on synthetic and real-world benchmarks, showing that they not only provide a more accurate assessment of segmentation quality but also uncover insights, such as error provenance and type, that are inaccessible with traditional measures.

Machine learning has achieved remarkable successes, yet its deployment in safety-critical domains remains hindered by an inherent inability to manage uncertainty, resulting in overconfident and unreliable predictions when models encounter out-of-distribution data, adversarial perturbations, or naturally fluctuating environments. This thesis, titled Epistemic Deep Learning: Enabling Machine Learning Models to 'Know When They Do Not Know', addresses these critical challenges by advancing the paradigm of Epistemic Artificial Intelligence, which explicitly models and quantifies epistemic uncertainty: the uncertainty arising from limited, biased, or incomplete training data, as opposed to the irreducible randomness of aleatoric uncertainty, thereby empowering models to acknowledge their limitations and refrain from overconfident decisions when uncertainty is high. Central to this work is the development of the Random-Set Neural Network (RS-NN), a novel methodology that leverages random set theory to predict belief functions over sets of classes, capturing the extent of epistemic uncertainty through the width of associated credal sets, applications of RS-NN, including its adaptation to Large Language Models (LLMs) and its deployment in weather classification for autonomous racing. In addition, the thesis proposes a unified evaluation framework for uncertainty-aware classifiers. Extensive experiments validate that integrating epistemic awareness into deep learning not only mitigates the risks associated with overconfident predictions but also lays the foundation for a paradigm shift in artificial intelligence, where the ability to 'know when it does not know' becomes a hallmark of robust and dependable systems. The title encapsulates the core philosophy of this work, emphasizing that true intelligence involves recognizing and managing the limits of one's own knowledge.

Multi-modal large language models (MLLMs) are making rapid progress toward general-purpose embodied agents. However, existing MLLMs do not reliably capture fine-grained links between low-level visual features and high-level textual semantics, leading to weak grounding and inaccurate perception. To overcome this challenge, we propose ESCA, a framework that contextualizes embodied agents by grounding their perception in spatial-temporal scene graphs. At its core is SGCLIP, a novel, open-domain, promptable foundation model for generating scene graphs that is based on CLIP. SGCLIP is trained on 87K+ open-domain videos using a neurosymbolic pipeline that aligns automatically generated captions with scene graphs produced by the model itself, eliminating the need for human-labeled annotations. We demonstrate that SGCLIP excels in both prompt-based inference and task-specific fine-tuning, achieving state-of-the-art results on scene graph generation and action localization benchmarks. ESCA with SGCLIP improves perception for embodied agents based on both open-source and commercial MLLMs, achieving state of-the-art performance across two embodied environments. Notably, ESCA significantly reduces agent perception errors and enables open-source models to surpass proprietary baselines. We release the source code for SGCLIP model training at https://github.com/video-fm/LASER and for the embodied agent at https://github.com/video-fm/ESCA.

Ensuring responsible use of artificial intelligence (AI) has become imperative as autonomous systems increasingly influence critical societal domains. However, the concept of trustworthy AI remains broad and multi-faceted. This thesis advances knowledge in the safety, fairness, transparency, and accountability of AI systems. In safety, we extend classical deterministic shielding techniques to become resilient against delayed observations, enabling practical deployment in real-world conditions. We also implement both deterministic and probabilistic safety shields into simulated autonomous vehicles to prevent collisions with road users, validating the use of these techniques in realistic driving simulators. We introduce fairness shields, a novel post-processing approach to enforce group fairness in sequential decision-making settings over finite and periodic time horizons. By optimizing intervention costs while strictly ensuring fairness constraints, this method efficiently balances fairness with minimal interference. For transparency and accountability, we propose a formal framework for assessing intentional behaviour in probabilistic decision-making agents, introducing quantitative metrics of agency and intention quotient. We use these metrics to propose a retrospective analysis of intention, useful for determining responsibility when autonomous systems cause unintended harm. Finally, we unify these contributions through the ``reactive decision-making'' framework, providing a general formalization that consolidates previous approaches. Collectively, the advancements presented contribute practically to the realization of safer, fairer, and more accountable AI systems, laying the foundations for future research in trustworthy AI.

Buildings account for a significant share of global energy consumption and emissions, making it critical to operate them efficiently. As electricity grids become more volatile with renewable penetration, buildings must provide flexibility to support grid stability. Building automation plays a key role in enhancing efficiency and flexibility via centralized operations, but it must prioritize occupant-centric strategies to balance energy and comfort targets. However, incorporating occupant information into large-scale, centralized building operations remains challenging due to data limitations. We investigate the potential of using whole-building smart meter data to infer both occupancy and system operations. Integrating these insights into data-driven building energy analysis allows more occupant-centric energy-saving and flexibility at scale. Specifically, we propose OccuEMBED, a unified framework for occupancy inference and system-level load analysis. It combines two key components: a probabilistic occupancy profile generator, and a controllable and interpretable load disaggregator supported by Kolmogorov-Arnold Networks (KAN). This design embeds knowledge of occupancy patterns and load-occupancy-weather relationships into deep learning models. We conducted comprehensive evaluations to demonstrate its effectiveness across synthetic and real-world datasets compared to various occupancy inference baselines. OccuEMBED always achieved average F1 scores above 0.8 in discrete occupancy inference and RMSE within 0.1-0.2 for continuous occupancy ratios. We further demonstrate how OccuEMBED integrates with building load monitoring platforms to display occupancy profiles, analyze system-level operations, and inform occupant-responsive strategies. Our model lays a robust foundation in scaling occupant-centric building management systems to meet the challenges of an evolving energy system.

Cognitive studies and artificial intelligence have developed distinct models for various inferential mechanisms (categorization, induction, abduction, causal inference, contrast, merge, ...). Yet, both natural and artificial views on cognition lack apparently a unifying framework. This paper formulates a speculative answer attempting to respond to this gap. To postulate on higher-level activation processes from a material perspective, we consider inferential mechanisms informed by symbolic AI modelling techniques, through the simplistic lenses of electronic circuits based on logic gates. We observe that a logic gate view entails a different treatment of implication and negation compared to standard logic and logic programming. Then, by combinatorial exploration, we identify four main forms of dependencies that can be realized by these inferential circuits. Looking at how these forms are generally used in the context of logic programs, we identify eight common inferential patterns, exposing traditionally distinct inferential mechanisms in an unifying framework. Finally, following a probabilistic interpretation of logic programs, we unveil inner functional dependencies. The paper concludes elaborating in what sense, even if our arguments are mostly informed by symbolic means and digital systems infrastructures, our observations may pinpoint to more generally applicable structures.