Causal discovery from observational data typically assumes full access to data and availability of domain experts. In practice, data often arrive in batches, and expert knowledge is scarce. Language Models (LMs) offer a surrogate but come with their own issues-hallucinations, inconsistencies, and bias. We present BLANCE (Bayesian LM-Augmented Causal Estimation)-a hybrid Bayesian framework that bridges these gaps by adaptively integrating sequential batch data with LM-derived noisy, expert knowledge while accounting for both data-induced and LM-induced biases. Our proposed representation shift from Directed Acyclic Graph (DAG) to Partial Ancestral Graph (PAG) accommodates ambiguities within a coherent Bayesian framework, allowing grounding the global LM knowledge in local observational data. To guide LM interaction, we use a sequential optimization scheme that adaptively queries the most informative edges. Across varied datasets, BLANCE outperforms prior work in structural accuracy and extends to Bayesian parameter estimation, showing robustness to LM noise.

The crisis of epistemic overload in modern scientific inquiry has exposed a critical deficiency in how truth claims are assessed, validated, and integrated across time and domain. The exponential growth in peer-reviewed publications, accompanied by inconsistent replication rates, entrenched citation biases, and the sociological entanglements of scientific authorship, has rendered traditional mechanisms of epistemic filtering increasingly obsolete. Simultaneously, artificial intelligence--while having demonstrated capacity in data correlation and language generation--remains fundamentally ill-equipped to perform rigorous epistemic reasoning. This gap is not merely technical but conceptual: current AI systems lack any principled framework for evaluating the truth-promoting value of claims, discerning authoritative sources, or understanding belief as a structured probabilistic relation between agents, claims, and contexts. The present work introduces a formal architecture--Bayesian Epistemology with Weighted Authority (BEW A)--which systematically encodes the logic of belief formation, update, and decay, guided by the core axioms of Bayesian rationality, tempered by structural mechanisms for authority weighting, replication scoring, and temporal reassessment.

We propose co-creative learning as a novel paradigm where humans and AI, i.e., biological and artificial agents, mutually integrate their partial perceptual information and knowledge to construct shared external representations, a process we interpret as symbol emergence. Unlike traditional AI teaching based on unilateral knowledge transfer, this addresses the challenge of integrating information from inherently different modalities. We empirically test this framework using a human-AI interaction model based on the Metropolis-Hastings naming game (MHNG), a decentralized Bayesian inference mechanism. In an online experiment, 69 participants played a joint attention naming game (JA-NG) with one of three computer agent types (MH-based, always-accept, or always-reject) under partial observability. Results show that human-AI pairs with an MH-based agent significantly improved categorization accuracy through interaction and achieved stronger convergence toward a shared sign system. Furthermore, human acceptance behavior aligned closely with the MH-derived acceptance probability. These findings provide the first empirical evidence for co-creative learning emerging in human-AI dyads via MHNG-based interaction. This suggests a promising path toward symbiotic AI systems that learn with humans, rather than from them, by dynamically aligning perceptual experiences, opening a new venue for symbiotic AI alignment.

In this work, we introduce Contextual Analog Logic with Multimodality (CALM). CALM unites symbolic reasoning with neural generation, enabling systems to make context-sensitive decisions grounded in real-world multi-modal data. Background: Classic bivalent logic systems cannot capture the nuance of human decision-making. They also require human grounding in multi-modal environments, which can be ad-hoc, rigid, and brittle. Neural networks are good at extracting rich contextual information from multi-modal data, but lack interpretable structures for reasoning. Objectives: CALM aims to bridge the gap between logic and neural perception, creating an analog logic that can reason over multi-modal inputs. Without this integration, AI systems remain either brittle or unstructured, unable to generalize robustly to real-world tasks. In CALM, symbolic predicates evaluate to analog truth values computed by neural networks and constrained search. Methods: CALM represents each predicate using a domain tree, which iteratively refines its analog truth value when the contextual groundings of its entities are determined. The iterative refinement is predicted by neural networks capable of capturing multi-modal information and is filtered through a symbolic reasoning module to ensure constraint satisfaction. Results: In fill-in-the-blank object placement tasks, CALM achieved 92.2% accuracy, outperforming classical logic (86.3%) and LLM (59.4%) baselines. It also demonstrated spatial heatmap generation aligned with logical constraints and delicate human preferences, as shown by a human study. Conclusions: CALM demonstrates the potential to reason with logic structure while aligning with preferences in multi-modal environments. It lays the foundation for next-gen AI systems that require the precision and interpretation of logic and the multimodal information processing of neural networks.

Ferry quays experience rapid deterioration due to their exposure to harsh maritime environments and ferry impacts. Vibration-based structural health monitoring offers a valuable approach to assessing structural integrity and understanding the structural implications of these impacts. However, practical limitations often restrict sensor placement at critical locations. Consequently, virtual sensing techniques become essential for establishing a Digital Twin and estimating the structural response. This study investigates the application of the Gaussian Process Latent Force Model (GPLFM) for virtual sensing on the Magerholm ferry quay, combining in-operation experimental data collected during a ferry impact with a detailed physics-based model. The proposed Physics-Encoded Machine Learning model integrates a reduced-order structural model with a data-driven GPLFM representing the unknown impact forces via their modal contributions. Significant challenges are addressed for the development of the Digital Twin of the ferry quay, including unknown impact characteristics (location, direction, intensity), time-varying boundary conditions, and sparse sensor configurations. Results show that the GPLFM provides accurate acceleration response estimates at most locations, even under simplifying modeling assumptions such as linear time-invariant behavior during the impact phase. Lower accuracy was observed at locations in the impact zone. A numerical study was conducted to explore an optimal real-world sensor placement strategy using a Backward Sequential Sensor Placement approach. Sensitivity analyses were conducted to examine the influence of sensor types, sampling frequencies, and incorrectly assumed damping ratios. The results suggest that the GP latent forces can help accommodate modeling and measurement uncertainties, maintaining acceptable estimation accuracy across scenarios.

We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel time-dependent binary classifier trained using a contrastive estimation-based objective that trains the classifier to discriminate between realizations of the stochastic process at two nearby time instants. Significantly, the proposed method explicitly models the time-dependent probability distribution, which means that it is possible to obtain the value of the probability density within the time horizon of interest. Additionally, the input before the final activation in the time-dependent classifier is a second-order approximation to the partial derivative, with respect to time, of the logarithm of the density. We apply the proposed approach to approximate the time-dependent probability density functions for systems driven by stochastic excitations. We also use the proposed approach to synthesize new samples of a random vector from a given set of its realizations. In such applications, we generate sample paths necessary for training using stochastic interpolants. Subsequently, new samples are generated using gradient-based Markov chain Monte Carlo methods because automatic differentiation can efficiently provide the necessary gradient. Further, we demonstrate the utility of an explicit approximation to the time-dependent probability density function through applications in unsupervised outlier detection. Through several numerical experiments, we show that the proposed method accurately reconstructs complex time-dependent, multi-modal, and near-degenerate densities, scales effectively to moderately high-dimensional problems, and reliably detects rare events among real-world data.

The Susceptible-Infected-Susceptible (SIS) model is a widely used model for the spread of information and infectious diseases, particularly non-immunizing ones, on a graph. Given a highly contagious disease, a natural question is how to best vaccinate individuals to minimize the disease's extinction time. While previous works showed that the problem of optimal vaccination is closely linked to the NP-hard Spectral Radius Minimization (SRM) problem, they assumed that the graph is known, which is often not the case in practice. In this work, we consider the problem of minimizing the extinction time of an outbreak modeled by an SIS model where the graph on which the disease spreads is unknown and only the infection states of the vertices are observed. To this end, we split the problem into two: learning the graph and determining effective vaccination strategies. We propose a novel inclusion-exclusion-based learning algorithm and, unlike previous approaches, establish its sample complexity for graph recovery. We then detail an optimal algorithm for the SRM problem and prove that its running time is polynomial in the number of vertices for graphs with bounded treewidth. This is complemented by an efficient and effective polynomial-time greedy heuristic for any graph. Finally, we present experiments on synthetic and real-world data that numerically validate our learning and vaccination algorithms.

Real-time identification and quantification of greenhouse-gas emissions under transient atmospheric conditions is a critical challenge in environmental monitoring. We introduce a spatio-temporal inversion framework that embeds a deep-learning surrogate of computational fluid dynamics (CFD) within a sequential Monte Carlo algorithm to perform Bayesian inference of both emission rate and source location in dynamic flow fields. By substituting costly numerical solvers with a multilayer perceptron trained on high-fidelity CFD outputs, our surrogate captures spatial heterogeneity and temporal evolution of gas dispersion, while delivering near-real-time predictions. Validation on the Chilbolton methane release dataset demonstrates comparable accuracy to full CFD solvers and Gaussian plume models, yet achieves orders-of-magnitude faster runtimes. Further experiments under simulated obstructed-flow scenarios confirm robustness in complex environments. This work reconciles physical fidelity with computational feasibility, offering a scalable solution for industrial emissions monitoring and other time-sensitive spatio-temporal inversion tasks in environmental and scientific modeling.

Humans interpret the world around them in terms of cause and effect and communicate their understanding of the world to each other in causal terms. These causal aspects of human cognition are thought to underlie humans' ability to generalize and learn efficiently in new domains, an area where current machine learning systems are weak. Building human-like causal competency into machine learning systems may facilitate the construction of effective and interpretable AI. Indeed, the machine learning community has been importing ideas on causality formalized by the Structural Causal Model (SCM) framework, which provides a rigorous formal language for many aspects of causality and has led to significant advances. However, the SCM framework fails to capture some salient aspects of human causal cognition and has likewise not yet led to advances in machine learning in certain critical areas where humans excel. We contend that the problem of causality in the ``human niche'' -- for a social, autonomous, and goal-driven agent sensing and acting in the world in which humans live -- is quite different from the kind of causality captured by SCMs. For example, everyday objects come in similar types that have similar causal properties, and so humans readily generalize knowledge of one type of object (cups) to another related type (bowls) by drawing causal analogies between objects with similar properties, but such analogies are at best awkward to express in SCMs. We explore how such causal capabilities are adaptive in, and motivated by, the human niche. By better appreciating properties of human causal cognition and, crucially, how those properties are adaptive in the niche in which humans live, we hope that future work at the intersection of machine learning and causality will leverage more human-like inductive biases to create more capable, controllable, and interpretable systems.

In domains where transparency and trustworthiness are crucial, such as healthcare, rule-based systems are widely used and often preferred over black-box models for decision support systems due to their inherent interpretability. However, as rule-based models grow complex, discerning crucial features, understanding their interactions, and comparing feature contributions across different rule sets becomes challenging. To address this, we propose a comprehensive framework for estimating feature contributions in rule-based systems, introducing a graph-based feature visualisation strategy, a novel feature importance metric agnostic to rule-based predictors, and a distance metric for comparing rule sets based on feature contributions. By experimenting on two clinical datasets and four rule-based methods (decision trees, logic learning machines, association rules, and neural networks with rule extraction), we showcase our method's capability to uncover novel insights on the combined predictive value of clinical features, both at the dataset and class-specific levels. These insights can aid in identifying new risk factors, signature genes, and potential biomarkers, and determining the subset of patient information that should be prioritised to enhance diagnostic accuracy. Comparative analysis of the proposed feature importance score with state-of-the-art methods on 15 public benchmarks demonstrates competitive performance and superior robustness.