Floorplan reconstruction provides structural priors essential for reliable indoor robot navigation and high-level scene understanding. However, existing approaches either require time-consuming offline processing with a complete map, or rely on expensive sensors and substantial computational resources. To address the problems, we propose Floorplan-SLAM, which incorporates floorplan reconstruction tightly into a multi-session SLAM system by seamlessly interacting with plane extraction, pose estimation, and back-end optimization, achieving real-time, high-accuracy, and long-term floorplan reconstruction using only a stereo camera. Specifically, we present a robust plane extraction algorithm that operates in a compact plane parameter space and leverages spatially complementary features to accurately detect planar structures, even in weakly textured scenes. Furthermore, we propose a floorplan reconstruction module tightly coupled with the SLAM system, which uses continuously optimized plane landmarks and poses to formulate and solve a novel optimization problem, thereby enabling real-time incremental floorplan reconstruction. Note that by leveraging the map merging capability of multi-session SLAM, our method supports long-term floorplan reconstruction across multiple sessions without redundant data collection. Experiments on the VECtor and the self-collected datasets indicate that Floorplan-SLAM significantly outperforms state-of-the-art methods in terms of plane extraction robustness, pose estimation accuracy, and floorplan reconstruction fidelity and speed, achieving real-time performance at 25-45 FPS without GPU acceleration, which reduces the floorplan reconstruction time for a 1000 square meters scene from over 10 hours to just 9.44 minutes.

Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches. However, we identify a critical issue in these methods, which we term ''wandering in contours''. This behavior refers to sampling new different solutions that share very similar objective values for a long time, leading to computational inefficiency and suboptimal exploration of potential solutions. In this paper, we introduce a novel reheating mechanism inspired by the concept of critical temperature and specific heat in physics, aimed at overcoming this limitation. Empirically, our method demonstrates superiority over existing sampling-based and data-driven algorithms across a diverse array of CO problems.

Prediction is one of the most important inferential tasks for actuaries since it forms the basis for many key aspects of an insurer's business operations, such as premium calculation and reserves estimation. According to Shmueli (2010), there are two key goals in data science and statistics: to explain and to predict. However, these two goals often warrant different approaches. For example, as demonstrated in Shmueli (2010), a wrong model, under some conditions, can even beat the oracle model in prediction, but the same cannot be said for explanation. This paper only concerns prediction. In the existing insurance literature, prediction is often performed using either a parametric approach or a non-parametric approach (e.g., Frees et al. 2014). In the parametric approach, the actuary posits a model, applies model selection tools to choose the "best" model, trains the chosen model, and finally makes predictions; see, for example, Claeskens and Hjort (2008) and Part I of Frees (2010). While this parametric approach has been widely applied in insurance, it has several drawbacks. First, the posited model may be misspecified, leading to grossly misleading predictions (Hong and Martin 2020).

Early-stopped iterative optimization methods are widely used as alternatives to explicit regularization, and direct comparisons between early-stopping and explicit regularization have been established for many optimization geometries. However, most analyses depend heavily on the specific properties of the optimization geometry or strong convexity of the empirical objective, and it remains unclear whether early-stopping could ever be less statistically efficient than explicit regularization for some particular shape constraint, especially in the overparameterized regime. To address this question, we study the setting of high-dimensional linear regression under additive Gaussian noise when the ground truth is assumed to lie in a known convex body and the task is to minimize the in-sample mean squared error. Our main result shows that for any convex body and any design matrix, up to an absolute constant factor, the worst-case risk of unconstrained early-stopped mirror descent with an appropriate potential is at most that of the least squares estimator constrained to the convex body. We achieve this by constructing algorithmic regularizers based on the Minkowski functional of the convex body.

We use tools from random matrix theory to study the multi-spiked tensor model, i.e., a rank-$r$ deformation of a symmetric random Gaussian tensor. In particular, thanks to the nature of local optimization methods used to find the maximum likelihood estimator of this model, we propose to study the phase transition phenomenon for finding critical points of the corresponding optimization problem, i.e., those points defined by the Karush-Kuhn-Tucker (KKT) conditions. Moreover, we characterize the limiting alignments between the estimated signals corresponding to a critical point of the likelihood and the ground truth signals. With the help of these results, we propose a new estimator of the rank-$r$ tensor weights by solving a system of polynomial equations, which is asymptotically unbiased contrary the maximum likelihood estimator.

Mixture of experts (MoE) has recently emerged as an effective framework to advance the efficiency and scalability of machine learning models by softly dividing complex tasks among multiple specialized sub-models termed experts. Central to the success of MoE is an adaptive softmax gating mechanism which takes responsibility for determining the relevance of each expert to a given input and then dynamically assigning experts their respective weights. Despite its widespread use in practice, a comprehensive study on the effects of the softmax gating on the MoE has been lacking in the literature. To bridge this gap in this paper, we perform a convergence analysis of parameter estimation and expert estimation under the MoE equipped with the standard softmax gating or its variants, including a dense-to-sparse gating and a hierarchical softmax gating, respectively. Furthermore, our theories also provide useful insights into the design of sample-efficient expert structures. In particular, we demonstrate that it requires polynomially many data points to estimate experts satisfying our proposed \emph{strong identifiability} condition, namely a commonly used two-layer feed-forward network. In stark contrast, estimating linear experts, which violate the strong identifiability condition, necessitates exponentially many data points as a result of intrinsic parameter interactions expressed in the language of partial differential equations. All the theoretical results are substantiated with a rigorous guarantee.

Reactor physics is the study of neutron properties, focusing on using models to examine the interactions between neutrons and materials in nuclear reactors. Artificial intelligence (AI) has made significant contributions to reactor physics, e.g., in operational simulations, safety design, real-time monitoring, core management and maintenance. This paper presents a comprehensive review of AI approaches in reactor physics, especially considering the category of Machine Learning (ML), with the aim of describing the application scenarios, frontier topics, unsolved challenges and future research directions. From equation solving and state parameter prediction to nuclear industry applications, this paper provides a step-by-step overview of ML methods applied to steady-state, transient and combustion problems. Most literature works achieve industry-demanded models by enhancing the efficiency of deterministic methods or correcting uncertainty methods, which leads to successful applications. However, research on ML methods in reactor physics is somewhat fragmented, and the ability to generalize models needs to be strengthened. Progress is still possible, especially in addressing theoretical challenges and enhancing industrial applications such as building surrogate models and digital twins.

Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, we are referring to the classical entropies: the Boltzmann-Gibbs, von Neumann, Shannon, Kolmogorov-Sinai and topological entropies. In addition to their common name, which is historically justified (as we briefly describe in this review), other commonality of the classical entropies is the important role that they have played and are still playing in the theory and applications of their respective fields and beyond. Therefore, it is not surprising that, in the course of time, many other instances of the overarching concept of entropy have been proposed, most of them tailored to specific purposes. Following the current usage, we will refer to all of them, whether classical or new, simply as entropies. Precisely, the subject of this review is their applications in data analysis and machine learning. The reason for these particular applications is that entropies are very well suited to characterize probability mass distributions, typically generated by finite-state processes or symbolized signals. Therefore, we will focus on entropies defined as positive functionals on probability mass distributions and provide an axiomatic characterization that goes back to Shannon and Khinchin. Given the plethora of entropies in the literature, we have selected a representative group, including the classical ones. The applications summarized in this review finely illustrate the power and versatility of entropy in data analysis and machine learning.

Discovering physical laws from data is a fundamental challenge in scientific research, particularly when high-quality data are scarce or costly to obtain. Traditional methods for identifying dynamical systems often struggle with noise sensitivity, inefficiency in data usage, and the inability to quantify uncertainty effectively. To address these challenges, we propose Langevin-Assisted Active Physical Discovery (LAPD), a Bayesian framework that integrates replica-exchange stochastic gradient Langevin Monte Carlo to simultaneously enable efficient system identification and robust uncertainty quantification (UQ). By balancing gradient-driven exploration in coefficient space and generating an ensemble of candidate models during exploitation, LAPD achieves reliable, uncertainty-aware identification with noisy data. In the face of data scarcity, the probabilistic foundation of LAPD further promotes the integration of active learning (AL) via a hybrid uncertainty-space-filling acquisition function. This strategy sequentially selects informative data to reduce data collection costs while maintaining accuracy. We evaluate LAPD on diverse nonlinear systems such as the Lotka-Volterra, Lorenz, Burgers, and Convection-Diffusion equations, demonstrating its robustness with noisy and limited data as well as superior uncertainty calibration compared to existing methods. The AL extension reduces the required measurements by around 60% for the Lotka-Volterra system and by around 40% for Burgers' equation compared to random data sampling, highlighting its potential for resource-constrained experiments. Our framework establishes a scalable, uncertainty-aware methodology for data-efficient discovery of dynamical systems, with broad applicability to problems where high-fidelity data acquisition is prohibitively expensive.

Early diagnosis of Alzheimer's Disease (AD) faces multiple data-related challenges, including high variability in patient data, limited access to specialized diagnostic tests, and overreliance on single-type indicators. These challenges are exacerbated by the progressive nature of AD, where subtle pathophysiological changes often precede clinical symptoms by decades. To address these limitations, this study proposes a novel approach that takes advantage of routinely collected general laboratory test histories for the early detection and differential diagnosis of AD. By modeling lab test sequences as "sentences", we apply word embedding techniques to capture latent relationships between tests and employ deep time series models, including long-short-term memory (LSTM) and Transformer networks, to model temporal patterns in patient records. Experimental results demonstrate that our approach improves diagnostic accuracy and enables scalable and costeffective AD screening in diverse clinical settings.