Causal discovery from observational data is challenging, especially with large datasets and complex relationships. Traditional methods often struggle with scalability and capturing global structural information. To overcome these limitations, we introduce a novel graph neural network (GNN)-based probabilistic framework that learns a probability distribution over the entire space of causal graphs, unlike methods that output a single deterministic graph. Our framework leverages a GNN that encodes both node and edge attributes into a unified graph representation, enabling the model to learn complex causal structures directly from data. The GNN model is trained on a diverse set of synthetic datasets augmented with statistical and information-theoretic measures, such as mutual information and conditional entropy, capturing both local and global data properties. We frame causal discovery as a supervised learning problem, directly predicting the entire graph structure. Our approach demonstrates superior performance, outperforming both traditional and recent non-GNN-based methods, as well as a GNN-based approach, in terms of accuracy and scalability on synthetic and real-world datasets without further training. This probabilistic framework significantly improves causal structure learning, with broad implications for decision-making and scientific discovery across various fields.

Due to the remarkable capabilities and growing impact of large language models (LLMs), they have been deeply integrated into many aspects of society. Thus, ensuring their alignment with human values and intentions has emerged as a critical challenge. This survey provides a comprehensive overview of practical alignment techniques, training protocols, and empirical findings in LLM alignment. We analyze the development of alignment methods across diverse paradigms, characterizing the fundamental trade-offs between core alignment objectives. Our analysis shows that while supervised fine-tuning enables basic instruction-following, preference-based methods offer more flexibility for aligning with nuanced human intent. We discuss state-of-the-art techniques, including Direct Preference Optimization (DPO), Constitutional AI, brain-inspired methods, and alignment uncertainty quantification (AUQ), highlighting their approaches to balancing quality and efficiency. We review existing evaluation frameworks and benchmarking datasets, emphasizing limitations such as reward misspecification, distributional robustness, and scalable oversight. We summarize strategies adopted by leading AI labs to illustrate the current state of practice. We conclude by outlining open problems in oversight, value pluralism, robustness, and continuous alignment. This survey aims to inform both researchers and practitioners navigating the evolving landscape of LLM alignment.

Classical game-theoretic models typically assume rational agents, complete information, and common knowledge of payoffs - assumptions that are often violated in real-world MAS characterized by uncertainty, misaligned perceptions, and nested beliefs. To overcome these limitations, researchers have proposed extensions that incorporate models of cognitive constraints, subjective beliefs, and heterogeneous reasoning. Among these, hypergame theory extends the classical paradigm by explicitly modeling agents' subjective perceptions of the strategic scenario, known as perceptual games, in which agents may hold divergent beliefs about the structure, payoffs, or available actions. We present a systematic review of agent-compatible applications of hypergame theory, examining how its descriptive capabilities have been adapted to dynamic and interactive MAS contexts. We analyze 44 selected studies from cybersecurity, robotics, social simulation, communications, and general game-theoretic modeling. Building on a formal introduction to hypergame theory and its two major extensions - hierarchical hypergames and HNF - we develop agent-compatibility criteria and an agent-based classification framework to assess integration patterns and practical applicability. Our analysis reveals prevailing tendencies, including the prevalence of hierarchical and graph-based models in deceptive reasoning and the simplification of extensive theoretical frameworks in practical applications. We identify structural gaps, including the limited adoption of HNF-based models, the lack of formal hypergame languages, and unexplored opportunities for modeling human-agent and agent-agent misalignment. By synthesizing trends, challenges, and open research directions, this review provides a new roadmap for applying hypergame theory to enhance the realism and effectiveness of strategic modeling in dynamic multi-agent environments.

Probabilistic circuits (PCs) are powerful probabilistic models that enable exact and tractable inference, making them highly suitable for probabilistic reasoning and inference tasks. While dominant in neural networks, representation learning with PCs remains underexplored, with prior approaches relying on external neural embeddings or activation-based encodings. To address this gap, we introduce autoencoding probabilistic circuits (APCs), a novel framework leveraging the tractability of PCs to model probabilistic embeddings explicitly. APCs extend PCs by jointly modeling data and embeddings, obtaining embedding representations through tractable probabilistic inference. The PC encoder allows the framework to natively handle arbitrary missing data and is seamlessly integrated with a neural decoder in a hybrid, end-to-end trainable architecture enabled by differentiable sampling. Our empirical evaluation demonstrates that APCs outperform existing PC-based autoencoding methods in reconstruction quality, generate embeddings competitive with, and exhibit superior robustness in handling missing data compared to neural autoencoders. These results highlight APCs as a powerful and flexible representation learning method that exploits the probabilistic inference capabilities of PCs, showing promising directions for robust inference, out-of-distribution detection, and knowledge distillation.

Photonic device development (PDD) has achieved remarkable success in designing and implementing new devices for controlling light across various wavelengths, scales, and applications, including telecommunications, imaging, sensing, and quantum information processing. PDD is an iterative, five-step process that consists of: i) deriving device behavior from design parameters, ii) simulating device performance, iii) finding the optimal candidate designs from simulations, iv) fabricating the optimal device, and v) measuring device performance. Classically, all these steps involve Bayesian optimization, material science, control theory, and direct physics-driven numerical methods. However, many of these techniques are computationally intractable, monetarily costly, or difficult to implement at scale. In addition, PDD suffers from large optimization landscapes, uncertainties in structural or optical characterization, and difficulties in implementing robust fabrication processes. However, the advent of machine learning over the past decade has provided novel, data-driven strategies for tackling these challenges, including surrogate estimators for speeding up computations, generative modeling for noisy measurement modeling and data augmentation, reinforcement learning for fabrication, and active learning for experimental physical discovery. In this review, we present a comprehensive perspective on these methods to enable machine-learning-assisted PDD (ML-PDD) for efficient design optimization with powerful generative models, fast simulation and characterization modeling under noisy measurements, and reinforcement learning for fabrication. This review will provide researchers from diverse backgrounds with valuable insights into this emerging topic, fostering interdisciplinary efforts to accelerate the development of complex photonic devices and systems.

We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank parameterisation of previous methods and show that Flow-SSNs can estimate arbitrarily high-rank pixel-wise covariances without assuming the rank or storing the distributional parameters. Flow-SSNs are also more efficient to sample from than standard diffusion-based segmentation models, thanks to most of the model capacity being allocated to learning the base distribution of the flow, constituting an expressive prior. We apply Flow-SSNs to challenging medical imaging benchmarks and achieve state-of-the-art results. Code available: https://github.com/biomedia-mira/flow-ssn.

The discovery of causal relationships is a foundational problem in artificial intelligence, statistics, epidemiology, economics, and beyond. While elegant theories exist for accurate causal discovery given infinite data, real-world applications are inherently resource-constrained. Effective methods for inferring causal relationships from observational data must perform well under finite data and time constraints, where "performing well" implies achieving high, though not perfect accuracy. In his seminal paper A Theory of the Learnable (Valiant, 1984), Valiant highlighted the importance of resource constraints in supervised machine learning, introducing the concept of Probably Approximately Correct (PAC) learning as an alternative to exact learning. Inspired by Valiant's work, we propose the Probably Approximately Correct Causal (PACC) Discovery framework, which extends PAC learning principles to the causal field. This framework emphasizes both computational and sample efficiency for established causal methods such as propensity score techniques and instrumental variable approaches. Furthermore, we show that it can provide theoretical guarantees for other widely used methods, such as the Self-Controlled Case Series (SCCS) method, which had previously lacked such guarantees.

Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.

As demand for high-purity lithium surges with the growth of the electric vehicle (EV) industry, cost-effective extraction from lower-grade North American sources like the Smackover Formation is critical. These resources, unlike high-purity South American brines, require innovative purification techniques to be economically viable. Continuous crystallization is a promising method for producing battery-grade lithium carbonate, but its optimization is challenged by a complex parameter space and limited data. This study introduces a Human-in-the-Loop (HITL) assisted active learning framework to optimize the continuous crystallization of lithium carbonate. By integrating human expertise with data-driven insights, our approach accelerates the optimization of lithium extraction from challenging sources. Our results demonstrate the framework's ability to rapidly adapt to new data, significantly improving the process's tolerance to critical impurities like magnesium from the industry standard of a few hundred ppm to as high as 6000 ppm. This breakthrough makes the exploitation of low-grade, impurity-rich lithium resources feasible, potentially reducing the need for extensive pre-refinement processes. By leveraging artificial intelligence, we have refined operational parameters and demonstrated that lower-grade materials can be used without sacrificing product quality. This advancement is a significant step towards economically harnessing North America's vast lithium reserves, such as those in the Smackover Formation, and enhancing the sustainability of the global lithium supply chain.

Differentiated thyroid cancer DTC recurrence is a major public health concern, requiring classification and predictive models that are not only accurate but also interpretable and uncertainty aware. This study introduces a comprehensive framework for DTC recurrence classification using a dataset containing 383 patients and 16 clinical and pathological variables. Initially, 11 machine learning ML models were employed using the complete dataset, where the Support Vector Machines SVM model achieved the highest accuracy of 0.9481. To reduce complexity and redundancy, feature selection was carried out using the Boruta algorithm, and the same ML models were applied to the reduced dataset, where it was observed that the Logistic Regression LR model obtained the maximum accuracy of 0.9611. However, these ML models often lack uncertainty quantification, which is critical in clinical decision making. Therefore, to address this limitation, the Bayesian Neural Networks BNN with six varying prior distributions, including Normal 0,1, Normal 0,10, Laplace 0,1, Cauchy 0,1, Cauchy 0,2.5, and Horseshoe 1, were implemented on both the complete and reduced datasets. The BNN model with Normal 0,10 prior distribution exhibited maximum accuracies of 0.9740 and 0.9870 before and after feature selection, respectively.