We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function $π\propto\mathrm{e}^{-U}$ is known up to a normalizing constant, which is an important task in fields such as statistical physics, machine learning, combinatorial optimization, etc. To better address this challenging task when the state space has a large cardinality and the distribution is multi-modal, we propose $\textbf{M}$asked $\textbf{D}$iffusion $\textbf{N}$eural $\textbf{S}$ampler ($\textbf{MDNS}$), a novel framework for training discrete neural samplers by aligning two path measures through a family of learning objectives, theoretically grounded in the stochastic optimal control of the continuous-time Markov chains. We validate the efficiency and scalability of MDNS through extensive experiments on various distributions with distinct statistical properties, where MDNS learns to accurately sample from the target distributions despite the extremely high problem dimensions and outperforms other learning-based baselines by a large margin. A comprehensive study of ablations and extensions is also provided to demonstrate the efficacy and potential of the proposed framework.

We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on contemporaneous or past explanatory variables and persistent stochastic shocks, including financial modeling, hydrological forecasting, and meteorological applications requiring temporal dependency capture. Our methodology uses hierarchical Bayesian models with spike-and-slab priors to simultaneously select relevant covariates and lagged error terms. We propose an efficient two-stage MCMC algorithm separating sampling of variable inclusion indicators and model parameters to address high-dimensional computational challenges. Theoretical analysis establishes posterior selection consistency under mild conditions, even when candidate predictors grow exponentially with sample size, common in modern time series with many potential lagged variables. Through simulations and real applications (groundwater depth prediction, S&P 500 log returns modeling), we demonstrate substantial gains in variable selection accuracy and predictive performance. Compared to existing methods, our framework achieves lower MSPE, improved true model component identification, and greater robustness with autocorrelated noise, underscoring practical utility for model interpretation and forecasting in autoregressive settings.

The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift, our goal here is to learn the entire drift function directly from data without strong structural assumptions, making it especially relevant in scientific disciplines where system dynamics are partially understood or highly complex. We cast the estimation problem as minimization of the penalized negative log-likelihood functional over a reproducing kernel Hilbert space (RKHS). In the sparse observation regime, the presence of unobserved trajectory segments makes the SDE likelihood intractable. To address this, we develop an Expectation-Maximization (EM) algorithm that employs a novel Sequential Monte Carlo (SMC) method to approximate the filtering distribution and generate Monte Carlo estimates of the E-step objective. The M-step then reduces to a penalized empirical risk minimization problem in the RKHS, whose minimizer is given by a finite linear combination of kernel functions via a generalized representer theorem. To control model complexity across EM iterations, we also develop a hybrid Bayesian variant of the algorithm that uses shrinkage priors to identify significant coefficients in the kernel expansion. We establish important theoretical convergence results for both the exact and approximate EM sequences. The resulting EM-SMC-RKHS procedure enables accurate estimation of the drift function of stochastic dynamical systems in low-data regimes and is broadly applicable across domains requiring continuous-time modeling under observational constraints. We demonstrate the effectiveness of our method through a series of numerical experiments.

We characterize a notion of confidence that arises in learning or updating beliefs: the amount of trust one has in incoming information and its impact on the belief state. This learner's confidence can be used alongside (and is easily mistaken for) probability or likelihood, but it is fundamentally a different concept -- one that captures many familiar concepts in the literature, including learning rates and number of training epochs, Shafer's weight of evidence, and Kalman gain. We formally axiomatize what it means to learn with confidence, give two canonical ways of measuring confidence on a continuum, and prove that confidence can always be represented in this way. Under additional assumptions, we derive more compact representations of confidence-based learning in terms of vector fields and loss functions. These representations induce an extended language of compound "parallel" observations. We characterize Bayes Rule as the special case of an optimizing learner whose loss representation is a linear expectation.

Introduction As engineering fields mature, new technologies are emerging that are beginning to serve as the foundation of many societal improvements. For example, modern medical diagnostic equipment provides valuable information that gives medical professionals a better understanding of a patient's needs and ultimately improves quality of life [1]. Improvements to vehicle designs make transportation in cars or aircraft safer and more environmentally friendly [2]. Military equipment continues to be developed that better supports and protects personnel in the field [3]. Manufacturing practices and robotic equipment improve work safety conditions and reduce a product's price point, making amenities available to a wider range of consumers [4]. One approach to maximizing system availability is to incorporate some means of health assessment into the system itself. Doing so is often referred to as "integrated system health management" (ISHM) or "prognostics and health management" (PHM), which has been applied successfully to many complex systems [5]. By integrating health assessment into the very functioning of a system, more information can be obtained that provides a better understanding of the system as a whole, thus allowing system owners to become proactive in how they deal with system degradation. ISHM and PHM promise to focus on system conditions, thus supporting initiatives in what has become known as condition-based maintenance (CBM). This, in turn, enables maintenance events to be initiated based on specific system conditions rather than waiting until a failure occurs [6]. One of the key ingredients of ISHM/PHM is diagnostics, which corresponds to the process of determining the health state of the system based on sets of observations (or tests). Such tests are designed specifically to track system behavior and determine whether or not a failure has occurred. In many cases it is impossible to identify a single fault that explains the observations with certainty. Instead, candidate sets of faults are often indicated, and when using applicable models, probabilities or confidence values are associated with the faults to provide additional information. One historic approach to using test observations for diagnosis is to apply a decision tree - sometimes referred to as a fault tree1 [7].

Open-vocabulary Object Goal Navigation requires an embodied agent to reach objects described by free-form language, including categories never seen during training. Existing end-to-end policies overfit small simulator datasets, achieving high success on training scenes but failing to generalize and exhibiting unsafe behaviour (frequent collisions). We introduce OVSegDT, a lightweight transformer policy that tackles these issues with two synergistic components. The first component is the semantic branch, which includes an encoder for the target binary mask and an auxiliary segmentation loss function, grounding the textual goal and providing precise spatial cues. The second component consists of a proposed Entropy-Adaptive Loss Modulation that is a per-sample scheduler that continuously balances imitation and reinforcement signals according to the policy entropy, eliminating brittle manual phase switches. These additions cut the sample complexity of training by 33%, and reduce collision count in two times while keeping inference cost low (130M parameters, RGB-only input). On HM3D-OVON, our model matches the performance on unseen categories to that on seen ones and establishes state-of-the-art results (40.1% SR, 20.9% SPL on val unseen) without depth, odom-etry, or large vision-language models.

We present Dual-Feedback Actor (DFA), a reinforcement learning algorithm that fuses both individual rewards and pairwise preferences (if available) into a single update rule. DFA uses the policy's log-probabilities directly to model the preference probability, avoiding a separate reward-modeling step. Preferences can be provided by human-annotators (at state-level or trajectory-level) or be synthesized online from Q-values stored in an off-policy replay buffer. Under a Bradley-Terry model, we prove that minimizing DFA's preference loss recovers the entropy-regularized Soft Actor-Critic (SAC) policy. Our simulation results show that DFA trained on generated preferences matches or exceeds SAC on six control environments and demonstrates a more stable training process. With only a semi-synthetic preference dataset under Bradley-Terry model, our algorithm outperforms reward-modeling reinforcement learning from human feedback (RLHF) baselines in a stochastic GridWorld and approaches the performance of an oracle with true rewards.

Instruction fine-tuned large language models (LLMs) enable a simple zero-shot or few-shot prompting paradigm, also known as in-context learning, for building prediction models. This convenience, combined with continued advances in LLM capability, has the potential to drive their adoption across a broad range of domains, including high-stakes applications where group fairness -- preventing disparate impacts across demographic groups -- is essential. The majority of existing approaches to enforcing group fairness on LLM-based classifiers rely on traditional fair algorithms applied via model fine-tuning or head-tuning on final-layer embeddings, but they are no longer applicable to closed-weight LLMs under the in-context learning setting, which include some of the most capable commercial models today, such as GPT-4, Gemini, and Claude. In this paper, we propose a framework for deriving fair classifiers from closed-weight LLMs via prompting: the LLM is treated as a feature extractor, and features are elicited from its probabilistic predictions (e.g., token log probabilities) using prompts strategically designed for the specified fairness criterion to obtain sufficient statistics for fair classification; a fair algorithm is then applied to these features to train a lightweight fair classifier in a post-hoc manner. Experiments on five datasets, including three tabular ones, demonstrate strong accuracy-fairness tradeoffs for the classifiers derived by our framework from both open-weight and closed-weight LLMs; in particular, our framework is data-efficient and outperforms fair classifiers trained on LLM embeddings (i.e., head-tuning) or from scratch on raw tabular features.

Sampling efficiency is critical for deploying visuomotor learning in real-world robotic manipulation. While task symmetry has emerged as a promising inductive bias to improve efficiency, most prior work is limited to isometric symmetries -- applying the same group transformation to all task objects across all timesteps. In this work, we explore non-isometric symmetries, applying multiple independent group transformations across spatial and temporal dimensions to relax these constraints. We introduce a novel formulation of the partially observable Markov decision process (POMDP) that incorporates the non-isometric symmetry structures, and propose a simple yet effective data augmentation method, Multi-Group Equivariance Augmentation (MEA). We integrate MEA with offline reinforcement learning to enhance sampling efficiency, and introduce a voxel-based visual representation that preserves translational equivariance. Extensive simulation and real-robot experiments across two manipulation domains demonstrate the effectiveness of our approach.

Grasping is a fundamental task in robot-assisted surgery (RAS), and automating it can reduce surgeon workload while enhancing efficiency, safety, and consistency beyond teleoperated systems. Most prior approaches rely on explicit object pose tracking or handcrafted visual features, limiting their generalization to novel objects, robustness to visual disturbances, and the ability to handle deformable objects. Visuomotor learning offers a promising alternative, but deploying it in RAS presents unique challenges, such as low signal-to-noise ratio in visual observations, demands for high safety and millimeter-level precision, as well as the complex surgical environment. This paper addresses three key challenges: (i) sim-to-real transfer of visuomotor policies to ex vivo surgical scenes, (ii) visuomotor learning using only a single stereo camera pair -- the standard RAS setup, and (iii) object-agnostic grasping with a single policy that generalizes to diverse, unseen surgical objects without retraining or task-specific models. We introduce Grasp Anything for Surgery V2 (GASv2), a visuomotor learning framework for surgical grasping. GASv2 leverages a world-model-based architecture and a surgical perception pipeline for visual observations, combined with a hybrid control system for safe execution. We train the policy in simulation using domain randomization for sim-to-real transfer and deploy it on a real robot in both phantom-based and ex vivo surgical settings, using only a single pair of endoscopic cameras. Extensive experiments show our policy achieves a 65% success rate in both settings, generalizes to unseen objects and grippers, and adapts to diverse disturbances, demonstrating strong performance, generality, and robustness.