We study the problem of likelihood maximization when the likelihood function is intractable but model simulations are readily available. We propose a sequential, gradient-based optimization method that directly models the Fisher score based on a local score matching technique which uses simulations from a localized region around each parameter iterate. By employing a linear parameterization for the surrogate score model, our technique admits a closed-form, least-squares solution. This approach yields a fast, flexible, and efficient approximation to the Fisher score, effectively smoothing the likelihood objective and mitigating the challenges posed by complex likelihood landscapes. We provide theoretical guarantees for our score estimator, including bounds on the bias introduced by the smoothing. Empirical results on a range of synthetic and real-world problems demonstrate the superior performance of our method compared to existing benchmarks.

The iterative and stochastic nature of diffusion models enables test-time scaling, whereby spending additional compute during denoising generates higher-fidelity samples. Increasing the number of denoising steps is the primary scaling axis, but this yields quickly diminishing returns. Instead, optimizing the noise trajectory--the sequence of injected noise vectors--is promising, as the specific noise realizations critically affect sample quality; but this is challenging due to a high-dimensional search space, complex noise-outcome interactions, and costly trajectory evaluations. We address this by first casting diffusion as a Markov Decision Process (MDP) with a terminal reward, showing tree-search methods such as Monte Carlo tree search (MCTS) to be meaningful but impractical. To balance performance and efficiency, we then resort to a relaxation of MDP, where we view denoising as a sequence of independent contextual bandits. This allows us to introduce an ϵ-greedy search algorithm that globally explores at extreme timesteps and locally exploits during the intermediate steps where de-mixing occurs.

Causal discovery methods are powerful tools for uncovering the structure of relationships among variables, yet they face significant challenges in scalability and interpretability, especially in high-dimensional settings. In many domains, researchers are not only interested in causal links between individual variables, but also in relationships among sets or clusters of variables. Learning causal structure at the cluster level can both reveal higher-order relationships of interest and improve scalability. In this work, we introduce an approach for causal discovery over clusters in Markov causal systems. We propose a new graphical model that encodes knowledge of relationships between user-defined clusters while fully representing independencies and dependencies over clusters, faithful to a given distribution. We then define and characterize a graphical equivalence class of these models that share cluster-level independence information. Lastly, we present a sound and complete algorithm for causal discovery to represent learnable causal relationships between clusters of variables.

There is growing interest in using machine learning (ML) to support clinical diagnosis, but most approaches rely on static, fully observed datasets and fail to reflect the sequential, resource-aware reasoning clinicians use in practice. Diagnosis remains complex and error prone, especially in high-pressure or resource-limited settings, underscoring the need for frameworks that help clinicians make timely and cost-effective decisions. We propose ACTMED(Adaptive Clinical Test selection via Model-based Experimental Design), a diagnostic framework that integrates Bayesian Experimental Design (BED) with large language models (LLMs) to better emulate real-world diagnostic reasoning. At each step, ACTMED selects the test expected to yield the greatest reduction in diagnostic uncertainty for a given patient. LLMs act as flexible simulators, generating plausible patient state distributions and supporting belief updates without requiring structured, task-specific training data. Clinicians can remain in the loop; reviewing test suggestions, interpreting intermediate outputs, and applying clinical judgment throughout. We evaluate ACTMEDon real-world datasets and show it can optimize test selection to improve diagnostic accuracy, interpretability, and resource use. This represents a step toward transparent, adaptive, and clinician-aligned diagnostic systems that generalize across settings with reduced reliance on domain-specific data.

Inverse folding models have proven to be highly effective zero-shot predictors of protein stability. Despite this success, the link between the amino acid preferences of an inverse folding model and the free-energy considerations underlying thermodynamic stability remains incompletely understood. A better understanding would be of interest not only from a theoretical perspective, but also potentially provide the basis for stronger zero-shot stability prediction. In this paper, we take steps to clarify the free-energy foundations of inverse folding models. Our derivation reveals the standard practice of likelihood ratios as a simplistic approximation and suggests several paths towards better estimates of the relative stability. We empirically assess these approaches and demonstrate that considerable gains in zero-shot performance can be achieved with fairly simple means.

While deep neural networks possess the capability to perform semantic segmentation, producing a single deterministic output limits reliability in safety-critical applications caused by uncertainty and annotation variability. To address this, stochastic segmentation models using Conditional Variational Autoencoders (CVAE), Bayesian networks, and diffusion have been explored. However, existing approaches suffer from limited latent expressiveness and interpretability. Furthermore, our experiments showed that models like Probabilistic U-Net rely excessively on high latent variance, leading to posterior collapse. This work propose a novel framework by integrating Gaussian Mixture Model (GMM) with Normalizing Flow (NF) in CVAE for stochastic segmentation. GMM structures the latent space into meaningful semantic clusters, while NF captures feature deformations with quantified uncertainty. Our method stabilizes latent distributions through constrained variance and mean ranges. Experiments on LIDC, Crack500, and Cityscapes datasets show that our approach outperformed state-of-the-art in curvilinear structure and medical image segmentation.

Open-world reinforcement learning challenges agents to develop intelligent behavior in vast exploration spaces. Recent approaches like LS-Imagine have advanced the field by extending imagination horizons through jumpy state transitions, yet remain limited by fixed exploration mechanisms and static jump thresholds that cannot adapt across changing task phases, resulting in inefficient exploration and lower completion rates. Humans demonstrate remarkable capabilities in openworld decision-making through a chain-like process of task decomposition, selective memory utilization, and adaptive uncertainty regulation. Inspired by human decision-making processes, we present Cognitive Predictive Processing (CPP), a novel framework that integrates three neurologically-inspired systems: a phaseadaptive cognitive controller that dynamically decomposes tasks into exploration, approach, and completion phases with adaptive parameters; a dual-memory integration system implementing dual-modal memory that balances immediate context with selective long-term storage; and an uncertainty-modulated prediction regulator that continuously updates environmental predictions to modulate exploration behavior. Comprehensive experiments in MineDojo demonstrate that these humaninspired decision-making strategies enhance performance over recent techniques, with success rates improving by an average of 4.6% across resource collection tasks while reducing task completion steps by an average of 7.1%. Our approach bridges cognitive neuroscience and reinforcement learning, excelling in complex scenarios that require sustained exploration and strategic adaptation while demonstrating how neural-inspired models can solve key challenges in open-world AI systems.

The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its performance in learning from the training data is only well understood in cases that essentially reduce to singular value decomposition of the data. Here, we consider the limit of a large dimension of the input space and a constant number of hidden units. In this limit, we simplify the standard RBM training objective into a form that is equivalent to the multi-index model with non-separable regularization. This opens a path to analyze training of the RBM using methods that are established for multi-index models, such as Approximate Message Passing (AMP) and its state evolution, and the analysis of Gradient Descent (GD) via the dynamical mean-field theory. We then give rigorous asymptotics of the training dynamics of RBMs on data generated by the spiked covariance model as a prototype of a structure suitable for unsupervised learning. We show in particular that RBMs reach the optimal computational weak recovery threshold, aligning with the Baik-Ben Arous-Péché (BBP) transition, in the spiked covariance model.

Vehicle trajectory prediction serves as a critical enabler for autonomous navigation and intelligent transportation systems. While existing approaches predominantly focus on pattern extraction and vehicle-environment interaction modeling, they exhibit a fundamental limitation in addressing trajectory heterogeneity originating from human driving styles. This oversight constrains prediction reliability in complex real-world scenarios. To bridge this gap, we propose the Driving-StyleAdaptive (DSA) framework, which establishes the first systematic integration of heterogeneous driving behaviors into trajectory prediction models. Specifically, our framework employs a set of basis functions tailored to each driving style to approximate the trajectory patterns. By dynamically combining and adaptively adjusting the degree of these basis functions, DSA not only enhances prediction accuracy but also provides explanations insights into the prediction process. Extensive experiments on public real-world datasets demonstrate that the DSA framework outperforms state-of-the-art methods.

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