Protecting cyberspace requires not only advanced tools but also a shift in how we reason about threats, trust, and autonomy. Traditional cybersecurity methods rely on manual responses and brittle heuristics. To build proactive and intelligent defense systems, we need integrated theoretical frameworks and software tools. Game theory provides a rigorous foundation for modeling adversarial behavior, designing strategic defenses, and enabling trust in autonomous systems. Meanwhile, software tools process cyber data, visualize attack surfaces, verify compliance, and suggest mitigations. Yet a disconnect remains between theory and practical implementation. The rise of Large Language Models (LLMs) and agentic AI offers a new path to bridge this gap. LLM-powered agents can operationalize abstract strategies into real-world decisions. Conversely, game theory can inform the reasoning and coordination of these agents across complex workflows. LLMs also challenge classical game-theoretic assumptions, such as perfect rationality or static payoffs, prompting new models aligned with cognitive and computational realities. This co-evolution promises richer theoretical foundations and novel solution concepts. Agentic AI also reshapes software design: systems must now be modular, adaptive, and trust-aware from the outset. This chapter explores the intersection of game theory, agentic AI, and cybersecurity. We review key game-theoretic frameworks (e.g., static, dynamic, Bayesian, and signaling games) and solution concepts. We then examine how LLM agents can enhance cyber defense and introduce LLM-driven games that embed reasoning into AI agents. Finally, we explore multi-agent workflows and coordination games, outlining how this convergence fosters secure, intelligent, and adaptive cyber systems.

In the study of complex dynamical systems, understanding and accurately modeling the underlying physical processes is crucial for predicting system behavior and designing effective interventions. Yet real-world systems exhibit pronounced input (or system) variability and are observed through noisy, limited data conditions that confound traditional discovery methods that assume fixed-coefficient deterministic models. In this work, we theorize that accounting for system variability together with measurement noise is the key to consistently discover the governing equations underlying dynamical systems. As such, we introduce a stochastic inverse physics-discovery (SIP) framework that treats the unknown coefficients as random variables and infers their posterior distribution by minimizing the Kullback-Leibler divergence between the push-forward of the posterior samples and the empirical data distribution. Benchmarks on four canonical problems -- the Lotka-Volterra predator-prey system (multi- and single-trajectory), the historical Hudson Bay lynx-hare data, the chaotic Lorenz attractor, and fluid infiltration in porous media using low- and high-viscosity liquids -- show that SIP consistently identifies the correct equations and lowers coefficient root-mean-square error by an average of 82\% relative to the Sparse Identification of Nonlinear Dynamics (SINDy) approach and its Bayesian variant. The resulting posterior distributions yield 95\% credible intervals that closely track the observed trajectories, providing interpretable models with quantified uncertainty. SIP thus provides a robust, data-efficient approach for consistent physics discovery in noisy, variable, and data-limited settings.

There is no much doubt that biotic interactions shape community assembly and ultimately the spatial co-variations between species. There is a hope that the signal of these biotic interactions can be observed and retrieved by investigating the spatial associations between species while accounting for the direct effects of the environment. By definition, biotic interactions can be both symmetric and asymmetric. Yet, most models that attempt to retrieve species associations from co-occurrence or co-abundance data internally assume symmetric relationships between species. Here, we propose and validate a machine-learning framework able to retrieve bidirectional associations by analyzing species community and environmental data. Our framework (1) models pairwise species associations as directed influences from a source to a target species, parameterized with two species-specific latent embeddings: the effect of the source species on the community, and the response of the target species to the community; and (2) jointly fits these associations within a multi-species conditional generative model with different modes of interactions between environmental drivers and biotic associations. Using both simulated and empirical data, we demonstrate the ability of our framework to recover known asymmetric and symmetric associations and highlight the properties of the learned association networks. By comparing our approach to other existing models such as joint species distribution models and probabilistic graphical models, we show its superior capacity at retrieving symmetric and asymmetric interactions. The framework is intuitive, modular and broadly applicable across various taxonomic groups.

Stochastic simulators exhibit intrinsic stochasticity due to unobservable, uncontrollable, or unmodeled input variables, resulting in random outputs even at fixed input conditions. Such simulators are common across various scientific disciplines; however, emulating their entire conditional probability distribution is challenging, as it is a task traditional deterministic surrogate modeling techniques are not designed for. Additionally, accurately characterizing the response distribution can require prohibitively large datasets, especially for computationally expensive high-fidelity (HF) simulators. When lower-fidelity (LF) stochastic simulators are available, they can enhance limited HF information within a multifidelity surrogate modeling (MFSM) framework. While MFSM techniques are well-established for deterministic settings, constructing multifidelity emulators to predict the full conditional response distribution of stochastic simulators remains a challenge. In this paper, we propose multifidelity generalized lambda models (MF-GLaMs) to efficiently emulate the conditional response distribution of HF stochastic simulators by exploiting data from LF stochastic simulators. Our approach builds upon the generalized lambda model (GLaM), which represents the conditional distribution at each input by a flexible, four-parameter generalized lambda distribution. MF-GLaMs are non-intrusive, requiring no access to the internal stochasticity of the simulators nor multiple replications of the same input values. We demonstrate the efficacy of MF-GLaM through synthetic examples of increasing complexity and a realistic earthquake application. Results show that MF-GLaMs can achieve improved accuracy at the same cost as single-fidelity GLaMs, or comparable performance at significantly reduced cost.

This study introduces an integrated framework for predictive causal inference designed to overcome limitations inherent in conventional single model approaches. Specifically, we combine a Hidden Markov Model (HMM) for spatial health state estimation with a Multi Task and Multi Graph Convolutional Network (MTGCN) for capturing temporal outcome trajectories. The framework asymmetrically treats temporal and spatial information regarding them as endogenous variables in the outcome regression, and exogenous variables in the propensity score model, thereby expanding the standard doubly robust treatment effect estimation to jointly enhance bias correction and predictive accuracy. To demonstrate its utility, we focus on clinical domains such as cancer, dementia, and Parkinson disease, where treatment effects are challenging to observe directly. Simulation studies are conducted to emulate latent disease dynamics and evaluate the model performance under varying conditions. Overall, the proposed framework advances predictive causal inference by structurally adapting to spatiotemporal complexities common in biomedical data.

Data privacy is a central concern in many applications involving ranking from incomplete and noisy pairwise comparisons, such as recommendation systems, educational assessments, and opinion surveys on sensitive topics. In this work, we propose differentially private algorithms for ranking based on pairwise comparisons. Specifically, we develop and analyze ranking methods under two privacy notions: edge differential privacy, which protects the confidentiality of individual comparison outcomes, and individual differential privacy, which safeguards potentially many comparisons contributed by a single individual. Our algorithms--including a perturbed maximum likelihood estimator and a noisy count-based method--are shown to achieve minimax optimal rates of convergence under the respective privacy constraints. We further demonstrate the practical effectiveness of our methods through experiments on both simulated and real-world data.

Continual learning is an online paradigm where a learner continually accumulates knowledge from different tasks encountered over sequential time steps. Importantly, the learner is required to extend and update its knowledge without forgetting about the learning experience acquired from the past, and while avoiding the need to retrain from scratch. Given its sequential nature and its resemblance to the way humans think, continual learning offers an opportunity to address several challenges which currently stand in the way of widening the range of applicability of deep models to further real-world problems. The continual need to update the learner with data arriving sequentially strikes inherent congruence between continual learning and Bayesian inference which provides a principal platform to keep updating the prior beliefs of a model given new data, without completely forgetting the knowledge acquired from the old data. This survey inspects different settings of Bayesian continual learning, namely task-incremental learning and class-incremental learning. We begin by discussing definitions of continual learning along with its Bayesian setting, as well as the links with related fields, such as domain adaptation, transfer learning and meta-learning. Afterwards, we introduce a taxonomy offering a comprehensive categorization of algorithms belonging to the Bayesian continual learning paradigm. Meanwhile, we analyze the state-of-the-art while zooming in on some of the most prominent Bayesian continual learning algorithms to date. Furthermore, we shed some light on links between continual learning and developmental psychology, and correspondingly introduce analogies between both fields. We follow that with a discussion of current challenges, and finally conclude with potential areas for future research on Bayesian continual learning.

We show that deep neural networks, including transformers and RNNs, pretrained as usual on next-token prediction, intrinsically discover and represent beliefs over 'quantum' and 'post-quantum' low-dimensional generative models of their training data -- as if performing iterative Bayesian updates over the latent state of this world model during inference as they observe more context. Notably, neural nets easily find these representation whereas there is no finite classical circuit that would do the job. The corresponding geometric relationships among neural activations induced by different input sequences are found to be largely independent of neural-network architecture. Each point in this geometry corresponds to a history-induced probability density over all possible futures, and the relative displacement of these points reflects the difference in mechanism and magnitude for how these distinct pasts affect the future.

We argue that in-context learning (ICL) predictably arises from standard self-supervised next-token pretraining, rather than being an exotic emergent property. This work establishes the foundational principles of this emergence by focusing on in-distribution ICL, demonstrating how models necessarily adapt to context when trained on token sequences, especially from non-ergodic sources. Our information-theoretic framework precisely predicts these in-distribution ICL dynamics (i.e., context-dependent loss reduction). We verify this with experiments using synthetic datasets of differing types of correlational structure, reproducing characteristic phenomena like phase transitions in training loss for induction head formation and power-law scaling of in-context loss. We further show that a model's in-context performance on any task is mathematically coupled to the ensemble of tasks seen in pretraining, offering a fundamental explanation, grounded in architecture- and modality-independent principles, for such inference-time learning.

As Large Language Models (LLMs) and other AI systems evolve, robustly estimating their capabilities from inherently stochastic outputs while systematically quantifying uncertainty in these estimates becomes increasingly important. Further, advanced AI evaluations often have a nested hierarchical structure, exhibit high levels of complexity, and come with high costs in testing the most advanced AI systems. To address these challenges, we introduce HiBayES, a generalizable Hierarchical Bayesian modeling framework for AI Evaluation Statistics. HiBayES supports robust inferences in classical question-answer benchmarks and advanced agentic evaluations, particularly in low-data scenarios (e.g., < 20 data points per evaluation). Built on Generalized Linear Models (GLMs), Bayesian data analysis, and formal model comparison, HiBayES provides principled uncertainty quantification and robust parameter estimation. This paper offers a comprehensive introduction to HiBayES, including illustrative examples, comparisons to conventional statistical methods, and practical guidance for implementing multilevel Bayesian GLMs. Additionally, we provide a HiBayES software package [4] (Beta version) for out-of-the-box implementation.