A central question in psycholinguistics is the timing of syntax in sentence processing. Much of the existing evidence comes from violation paradigms, which conflate two separable processes - syntactic category detection and phrase structure construction - and implicitly assume that phrase structure follows category detection. In this study, we use co-registered EEG and eye-tracking data from the ZuCo corpus to disentangle these processes and test their temporal order under naturalistic reading conditions. Analyses of gaze transitions showed that readers preferentially moved between syntactic heads, suggesting that phrase structures, rather than serial word order, organize scanpaths. Bayesian network modeling further revealed that structural depth was the strongest driver of deviations from linear reading, outweighing lexical familiarity and surprisal. Finally, fixation-related potentials demonstrated that syntactic surprisal influences neural activity before word onset (-184 to -10 ms) and during early integration (48 to 300 ms). These findings extend current models of syntactic timing by showing that phrase structure construction can precede category detection and dominate lexical influences, supporting a predictive "tree-scaffolding" account of comprehension.

Abstract--This work introduces an adaptive Bayesian algorithm for real-time trajectory prediction via intention inference, where a target's intentions and motion characteristics are unknown and subject to change. The method concurrently estimates two critical variables: the target's current intention, modeled as a Markovian latent state, and an intention parameter that describes the target's adherence to a shortest-path policy. By integrating this joint update technique, the algorithm maintains robustness against abrupt intention shifts and unknown motion dynamics. A sampling-based trajectory prediction mechanism then exploits these adaptive estimates to generate probabilistic forecasts with quantified uncertainty. Experimental results demonstrate that the proposed approach significantly outperforms non-adaptive and partially adaptive methods. The method operates in real time around 270 Hz without requiring training or detailed prior knowledge of target behavior, showcasing its applicability in various robotic systems. Real-world autonomous systems such as self-driving cars, service robots, and surveillance drones frequently face intention inference tasks [1]: they must determine what another agent or human is trying to achieve and where it is likely to go next [2], [3]. These tasks are inherently challenging for several reasons. First, the target's motion dynamics are often unknown. For example, a pedestrian may switch between walking, jogging, or stopping unpredictably. Second, the agent's intention may shift during execution, such as changing to a new goal without any observable signal, i.e., in a non-cooperative fashion.

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of real biological datasets are prohibitively laborious, and often impossible. To this end, we introduce a Bayesian meta-learning framework designed to automatically convert raw functional predictions from normative theories into tractable probabilistic models. We employ adaptive deep kernel Gaussian processes, meta-learning a kernel on synthetic data generated from a normative theory. This Theory-Informed Kernel specifies a probabilistic model representing the theory predictions -- usable for both fitting data and rigorously validating the theory. As a demonstration, we apply our framework to the early visual system, using efficient coding as our normative theory. We show improved response prediction accuracy in ex vivo recordings of mouse retinal ganglion cells stimulated by natural scenes compared to conventional data-driven baselines, while providing well-calibrated uncertainty estimates and interpretable representations. Using exact Bayesian model selection, we also show that our informed kernel can accurately infer the degree of theory-match from data, confirming faithful encapsulation of theory structure. This work provides a more general, scalable, and automated approach for integrating theoretical knowledge into data-driven scientific inquiry in neuroscience and beyond.

The very expressiveness of Bayesian networks can introduce fresh challenges due to the large number of relationships they often model. In many domains, it is thus often essential to supplement any available data with elicited expert judgements. This in turn leads to two key challenges: the cognitive burden of these judgements is often very high, and there are a very large number of judgements required to obtain a full probability model. We can mitigate both issues by introducing assumptions such as independence of causal influences (ICI) on the local structures throughout the network, restricting the parameter space of the model. However, the assumption of ICI is often unjustified and overly strong. In this paper, we introduce the surjective independence of causal influences (SICI) model which relaxes the ICI assumption and provides a more viable, practical alternative local structure model that facilitates efficient Bayesian network parameterisation.

Solving inverse problems with diffusion models has shown promise in tasks such as image restoration. A common approach is to formulate the problem in a Bayesian framework and sample from the posterior by combining the prior score with the likelihood score. Since the likelihood term is often intractable, estimators like DPS, DMPS, and $π$GDM are widely adopted. However, these methods rely on a fixed, manually tuned scale to balance prior and likelihood contributions. Such a static design is suboptimal, as the ideal balance varies across timesteps and tasks, limiting performance and generalization. To address this issue, we propose SAIP, a plug-and-play module that adaptively refines the scale at each timestep without retraining or altering the diffusion backbone. SAIP integrates seamlessly into existing samplers and consistently improves reconstruction quality across diverse image restoration tasks, including challenging scenarios.

Prior-data fitted networks (PFNs) have recently been proposed as a promising way to train tabular foundation models. PFNs are transformers that are pre-trained on synthetic data generated from a prespecified prior distribution and that enable Bayesian inference through in-context learning. In this paper, we introduce CausalFM, a comprehensive framework for training PFN-based foundation models in various causal inference settings. First, we formalize the construction of Bayesian priors for causal inference based on structural causal models (SCMs) in a principled way and derive necessary criteria for the validity of such priors. Building on this, we propose a novel family of prior distributions using causality-inspired Bayesian neural networks that enable CausalFM to perform Bayesian causal inference in various settings, including for back-door, front-door, and instrumental variable adjustment. Finally, we instantiate CausalFM and explicitly train models to perform in-context learning in these settings. We show that CausalFM achieves competitive in-context learning performance even when compared to baselines that are specifically trained for the task at hand. In sum, our framework can be used as a general recipe to train foundation models for various causal inference settings. In contrast to the current state-of-the-art in causal inference, CausalFM offers a novel paradigm with the potential to fundamentally change how practitioners perform causal inference in medicine, economics, and other disciplines.

LLM leaderboards often rely on single stochastic runs, but how many repetitions are required for reliable conclusions remains unclear. We re-evaluate eight state-of-the-art models on the AI4Math Benchmark with three independent runs per setting. Using mixed-effects logistic regression, domain-level marginal means, rank-instability analysis, and run-to-run reliability, we assessed the value of additional repetitions. Our findings shows that Single-run leaderboards are brittle: 10/12 slices (83\%) invert at least one pairwise rank relative to the three-run majority, despite a zero sign-flip rate for pairwise significance and moderate overall interclass correlation. Averaging runs yields modest SE shrinkage ($\sim$5\% from one to three) but large ranking gains; two runs remove $\sim$83\% of single-run inversions. We provide cost-aware guidance for practitioners: treat evaluation as an experiment, report uncertainty, and use $\geq 2$ repetitions under stochastic decoding. These practices improve robustness while remaining feasible for small teams and help align model comparisons with real-world reliability.

Modern causal discovery methods face critical limitations in scalability, computational efficiency, and adaptability to mixed data types, as evidenced by benchmarks on node scalability (30, $\le 50$, $\ge 70$ nodes), computational energy demands, and continuous/non-continuous data handling. While traditional algorithms like PC, GES, and ICA-LiNGAM struggle with these challenges, exhibiting prohibitive energy costs for higher-order nodes and poor scalability beyond 70 nodes, we propose \textbf{GUIDE}, a framework that integrates Large Language Model (LLM)-generated adjacency matrices with observational data through a dual-encoder architecture. GUIDE uniquely optimizes computational efficiency, reducing runtime on average by $\approx 42%$ compared to RL-BIC and KCRL methods, while achieving an average $\approx 117%$ improvement in accuracy over both NOTEARS and GraN-DAG individually. During training, GUIDE's reinforcement learning agent dynamically balances reward maximization (accuracy) and penalty avoidance (DAG constraints), enabling robust performance across mixed data types and scalability to $\ge 70$ nodes -- a setting where baseline methods fail.

Post-hoc calibration methods are widely used to improve the reliability of probabilistic predictions from machine learning models. Despite their prevalence, a comprehensive theoretical understanding of these methods remains elusive, particularly regarding their performance across different datasets and model architectures. Input features play a crucial role in shaping model predictions and, consequently, their calibration. However, the interplay between feature quality and calibration performance has not been thoroughly investigated. In this work, we present a rigorous theoretical analysis of post-hoc calibration methods, focusing on Platt scaling and isotonic regression. We derive convergence guarantees, computational complexity bounds, and finite-sample performance metrics for these methods. Furthermore, we explore the impact of feature informativeness on calibration performance through controlled synthetic experiments. Our empirical evaluation spans a diverse set of real-world datasets and model architectures, demonstrating consistent improvements in calibration metrics across various scenarios. By examining calibration performance under varying feature conditions utilizing only informative features versus complete feature spaces including noise dimensions, we provide fundamental insights into the robustness and reliability of different calibration approaches. Our findings offer practical guidelines for selecting appropriate calibration methods based on dataset characteristics and computational constraints, bridging the gap between theoretical understanding and practical implementation in uncertainty quantification. Code and experimental data are available at: https://github.com/Ajwebdevs/calibration-analysis-experiments.

Prognostic information is essential for decision-making in breast cancer management. Recently trials have predominantly focused on genomic prognostication tools, even though clinicopathological prognostication is less costly and more widely accessible. Machine learning (ML), transfer learning and ensemble integration offer opportunities to build robust prognostication frameworks. We evaluate this potential to improve survival prognostication in breast cancer by comparing de-novo ML, transfer learning from a pre-trained prognostic tool and ensemble integration. Data from the MA.27 trial was used for model training, with external validation on the TEAM trial and a SEER cohort. Transfer learning was applied by fine-tuning the pre-trained prognostic tool PREDICT v3, de-novo ML included Random Survival Forests and Extreme Gradient Boosting, and ensemble integration was realized through a weighted sum of model predictions. Transfer learning, de-novo RSF, and ensemble integration improved calibration in MA.27 over the pre-trained model (ICI reduced from 0.042 in PREDICT v3 to <=0.007) while discrimination remained comparable (AUC increased from 0.738 in PREDICT v3 to 0.744-0.799). Invalid PREDICT v3 predictions were observed in 23.8-25.8% of MA.27 individuals due to missing information. In contrast, ML models and ensemble integration could predict survival regardless of missing information. Across all models, patient age, nodal status, pathological grading and tumor size had the highest SHAP values, indicating their importance for survival prognostication. External validation in SEER, but not in TEAM, confirmed the benefits of transfer learning, RSF and ensemble integration. This study demonstrates that transfer learning, de-novo RSF, and ensemble integration can improve prognostication in situations where relevant information for PREDICT v3 is lacking or where a dataset shift is likely.