The PC algorithm is a widely used method in causal inference for learning the structure of Bayesian networks. Despite its popularity, the PC algorithm suffers from significant time complexity, particularly as the size of the dataset increases, which limits its applicability in large-scale real-world problems. In this study, we propose a novel approach that utilises the Tsetlin Machine (TM) to construct Bayesian structures more efficiently. Our method leverages the most significant literals extracted from the TM and performs conditional independence (CI) tests on these selected literals instead of the full set of variables, resulting in a considerable reduction in computational time. We implemented our approach and compared it with various state-of-the-art methods. Our evaluation includes categorical datasets from the bnlearn repository, such as Munin1, Hepar2. The findings indicate that the proposed TM-based method not only reduces computational complexity but also maintains competitive accuracy in causal discovery, making it a viable alternative to traditional PC algorithm implementations by offering improved efficiency without compromising performance.

Automated decision-making under uncertainty requires balancing exploitation and exploration. Classical methods treat these separately using heuristics, while Active Inference unifies them through Expected Free Energy (EFE) minimization. However, EFE minimization is computationally expensive, limiting scalability. We build on recent theory recasting EFE minimization as variational inference, formally unifying it with Planning-as-Inference and showing the epistemic drive as a unique entropic contribution. Our main contribution is a novel message-passing scheme for this unified objective, enabling scalable Active Inference in factored-state MDPs and overcoming high-dimensional planning intractability.

Multimodal trajectory prediction generates multiple plausible future trajectories to address vehicle motion uncertainty from intention ambiguity and execution variability. However, HD map-dependent models suffer from costly data acquisition, delayed updates, and vulnerability to corrupted inputs, causing prediction failures. Map-free approaches lack global context, with pairwise attention over-amplifying straight patterns while suppressing transitional patterns, resulting in motion-intention misalignment. This paper proposes GContextFormer, a plug-and-play encoder-decoder architecture with global context-aware hybrid attention and scaled additive aggregation achieving intention-aligned multimodal prediction without map reliance. The Motion-Aware Encoder builds scene-level intention prior via bounded scaled additive aggregation over mode-embedded trajectory tokens and refines per-mode representations under shared global context, mitigating inter-mode suppression and promoting intention alignment. The Hierarchical Interaction Decoder decomposes social reasoning into dual-pathway cross-attention: a standard pathway ensures uniform geometric coverage over agent-mode pairs while a neighbor-context-enhanced pathway emphasizes salient interactions, with gating module mediating their contributions to maintain coverage-focus balance. Experiments on eight highway-ramp scenarios from TOD-VT dataset show GContextFormer outperforms state-of-the-art baselines. Compared to existing transformer models, GContextFormer achieves greater robustness and concentrated improvements in high-curvature and transition zones via spatial distributions. Interpretability is achieved through motion mode distinctions and neighbor context modulation exposing reasoning attribution. The modular architecture supports extensibility toward cross-domain multimodal reasoning tasks. Source: https://fenghy-chen.github.io/sources/.

Understanding physical properties such as friction, stiffness, hardness, and material composition is essential for enabling robots to interact safely and effectively with their surroundings. However, existing 3D reconstruction methods focus on geometry and appearance and cannot infer these underlying physical properties. We present PhysGS, a Bayesian-inferred extension of 3D Gaussian Splatting that estimates dense, per-point physical properties from visual cues and vision--language priors. We formulate property estimation as Bayesian inference over Gaussian splats, where material and property beliefs are iteratively refined as new observations arrive. PhysGS also models aleatoric and epistemic uncertainties, enabling uncertainty-aware object and scene interpretation. Across object-scale (ABO-500), indoor, and outdoor real-world datasets, PhysGS improves accuracy of the mass estimation by up to 22.8%, reduces Shore hardness error by up to 61.2%, and lowers kinetic friction error by up to 18.1% compared to deterministic baselines. Our results demonstrate that PhysGS unifies 3D reconstruction, uncertainty modeling, and physical reasoning in a single, spatially continuous framework for dense physical property estimation. Additional results are available at https://samchopra2003.github.io/physgs.

Probabilistic Time-Series Forecasting (PTSF) is critical for uncertainty-aware decision making, but existing generative models, such as diffusion-based approaches, are computationally prohibitive due to expensive iterative sampling. Non-sampling frameworks like Multiple Choice Learning (MCL) offer an efficient alternative, but suffer from severe training instability and hypothesis collapse, which has historically hindered their performance. This problem is dramatically exacerbated when attempting to combine them with modern, efficient MLP-based backbones. To resolve this fundamental incompatibility, we propose TimePre, a novel framework that successfully unifies the efficiency of MLP-based models with the distributional flexibility of the MCL paradigm. The core of our solution is Stabilized Instance Normalization (SIN), a novel normalization layer that explicitly remedies this incompatibility. SIN stabilizes the hybrid architecture by correcting channel-wise statistical shifts, definitively resolving the catastrophic hypothesis collapse. Extensive experiments on six benchmark datasets demonstrate that TimePre achieves new state-of-the-art accuracy on key probabilistic metrics. Critically, TimePre achieves inference speeds orders of magnitude faster than sampling-based models and, unlike prior MCL work, demonstrates stable performance scaling. It thus bridges the long-standing gap between accuracy, efficiency, and stability in probabilistic forecasting.

Sparse dynamics identification is an essential tool for discovering interpretable physical models and enabling efficient control in engineering systems. However, existing methods rely on batch learning with full historical data, limiting their applicability to real-time scenarios involving sequential and partially observable data. To overcome this limitation, this paper proposes an online Sparse Kalman Identification (SKI) method by integrating the Augmented Kalman Filter (AKF) and Automatic Relevance Determination (ARD). The main contributions are: (1) a theoretically grounded Bayesian sparsification scheme that is seamlessly integrated into the AKF framework and adapted to sequentially collected data in online scenarios; (2) an update mechanism that adapts the Kalman posterior to reflect the updated selection of the basis functions that define the model structure; (3) an explicit gradient-descent formulation that enhances computational efficiency. Consequently, the SKI method achieves accurate model structure selection with millisecond-level efficiency and higher identification accuracy, as demonstrated by extensive simulations and real-world experiments (showing an 84.21\% improvement in accuracy over the baseline AKF).

Robots must learn from both what people do and what they say, but either modality alone is often incomplete: physical corrections are grounded but ambiguous in intent, while language expresses high-level goals but lacks physical grounding. We introduce QuickLAP: Quick Language-Action Preference learning, a Bayesian framework that fuses physical and language feedback to infer reward functions in real time. Our key insight is to treat language as a probabilistic observation over the user's latent preferences, clarifying which reward features matter and how physical corrections should be interpreted. QuickLAP uses Large Language Models (LLMs) to extract reward feature attention masks and preference shifts from free-form utterances, which it integrates with physical feedback in a closed-form update rule. This enables fast, real-time, and robust reward learning that handles ambiguous feedback. In a semi-autonomous driving simulator, QuickLAP reduces reward learning error by over 70% compared to physical-only and heuristic multimodal baselines. A 15-participant user study further validates our approach: participants found QuickLAP significantly more understandable and collaborative, and preferred its learned behavior over baselines. Code is available at https://github.com/MIT-CLEAR-Lab/QuickLAP.

Large language models (LLMs) solve complex problems yet fail on simpler variants, suggesting they achieve correct outputs through mechanisms fundamentally different from human reasoning. To understand this gap, we synthesize cognitive science research into a taxonomy of 28 cognitive elements spanning reasoning invariants, meta-cognitive controls, representations for organizing reasoning & knowledge, and transformation operations. We introduce a fine-grained evaluation framework and conduct the first large-scale empirical analysis of 192K traces from 18 models across text, vision, and audio, complemented by 54 human think-aloud traces, which we make publicly available. We find that models under-utilize cognitive elements correlated with success, narrowing to rigid sequential processing on ill-structured problems where diverse representations and meta-cognitive monitoring are critical. Human traces show more abstraction and conceptual processing, while models default to surface-level enumeration. Meta-analysis of 1.6K LLM reasoning papers reveals the research community concentrates on easily quantifiable elements (sequential organization: 55%, decomposition: 60%) but neglecting meta-cognitive controls (self-awareness: 16%) that correlate with success. Models possess behavioral repertoires associated with success but fail to deploy them spontaneously. Leveraging these patterns, we develop test-time reasoning guidance that automatically scaffold successful structures, improving performance by up to 66.7% on complex problems. By establishing a shared vocabulary between cognitive science and LLM research, our framework enables systematic diagnosis of reasoning failures and principled development of models that reason through robust cognitive mechanisms rather than spurious shortcuts, while providing tools to test theories of human cognition at scale.

Many sequential decision settings in healthcare feature funnel structures characterized by a series of stages, such as screenings or evaluations, where the number of patients who advance to each stage progressively decreases and decisions become increasingly costly. For example, an oncologist may first conduct a breast exam, followed by a mammogram for patients with concerning exams, followed by a biopsy for patients with concerning mammograms. A key challenge is that the ground truth outcome, such as the biopsy result, is only revealed at the end of this funnel. The selective censoring of the ground truth can introduce statistical biases in risk estimation, especially in underserved patient groups, whose outcomes are more frequently censored. We develop a Bayesian model for funnel decision structures, drawing from prior work on selective labels and censoring. We first show in synthetic settings that our model is able to recover the true parameters and predict outcomes for censored patients more accurately than baselines. We then apply our model to a dataset of emergency department visits, where in-hospital mortality is observed only for those who are admitted to either the hospital or ICU. We find that there are gender-based differences in hospital and ICU admissions. In particular, our model estimates that the mortality risk threshold to admit women to the ICU is higher for women (5.1%) than for men (4.5%).

We propose a recursive particle filter for high-dimensional problems that inherently never degenerates. The state estimate is represented by deterministic low-discrepancy particle sets. We focus on the measurement update step, where a likelihood function is used for representing the measurement and its uncertainty. This likelihood is progressively introduced into the filtering procedure by homotopy continuation over an artificial time. A generalized Cramér distance between particle sets is derived in closed form that is differentiable and invariant to particle order. A Newton flow then continually minimizes this distance over artificial time and thus smoothly moves particles from prior to posterior density. The new filter is surprisingly simple to implement and very efficient. It just requires a prior particle set and a likelihood function, never estimates densities from samples, and can be used as a plugin replacement for classic approaches.