In various real-world robot applications, MOS describes the problem of locating multiple objects efficiently [1], in domains such as warehouse management [2, 3], construction inspection [4], or hospitality [5, 6, 7], and retail assistance [8, 9]. Existing MOS methods can be categorized into: 1) probabilistic planning (PP) [1, 10, 11, 12], and 2) deep reinforcement learning (DRL) methods [13, 14, 15, 16, 17, 18, 19, 20]. PP methods utilize Partially Observable Markov Decision Processes (POMDPs) to estimate belief states and plan actions under uncertainty in object locations, while DRL methods optimizes action selection using a reward function [21]. However, both approaches face challenges such as inefficient exploration due to limited semantic modeling between objects and scenes [18], and poor generlization caused by the sim-to-real gap [19]. Recently, Large Foundation Models (LFMs) such as vision-language models (VLMs) and large language models (LLMs) have been applied to single object search (SOS) tasks by using either: 1) VLMs (e.g., CLIP, BLIP, etc.) to generate scene-level embeddings that capture the semantic correlations between the robot's environment and the target object to guide the robot towards regions with high target object likelihood [19, 22, 23, 24, 25]; or, 2) VLMs/LLMs to generate scene captions that describe both the spatial layout and semantic details of the robot's environment which are then used to plan the robot's actions [26, 27, 28, 29, 30, 31, 32]. However, these SOS methods have limitations: 1) they cannot be directly applied to MOS, as they lack explicit mechanisms to track and reason about multiple objects simultaneously, and 2) scene-level embeddings are often noisy and coarse [33], which cannot be effectively applied in object-dense environments. In such cases, fine-grained, object-level embeddings are needed. In this paper, we introduce Finder, the first MOS approach that leverages VLMs to locate multiple target objects in various unknown environments.

We study high-dimensional, ridge-regularized logistic regression in a setting in which the covariates may be missing or corrupted by additive noise. When both the covariates and the additive corruptions are independent and normally distributed, we provide exact characterizations of both the prediction error as well as the estimation error. Moreover, we show that these characterizations are universal: as long as the entries of the data matrix satisfy a set of independence and moment conditions, our guarantees continue to hold. Universality, in turn, enables the detailed study of several imputation-based strategies when the covariates are missing completely at random. We ground our study by comparing the performance of these strategies with the conjectured performance -- stemming from replica theory in statistical physics -- of the Bayes optimal procedure. Our analysis yields several insights including: (i) a distinction between single imputation and a simple variant of multiple imputation and (ii) that adding a simple ridge regularization term to single-imputed logistic regression can yield an estimator whose prediction error is nearly indistinguishable from the Bayes optimal prediction error. We supplement our findings with extensive numerical experiments.

The Gibbs sampler (a.k.a. Glauber dynamics and heat-bath algorithm) is a popular Markov Chain Monte Carlo algorithm which iteratively samples from the conditional distributions of a probability measure $\pi$ of interest. Under the assumption that $\pi$ is strongly log-concave, we show that the random scan Gibbs sampler contracts in relative entropy and provide a sharp characterization of the associated contraction rate. Assuming that evaluating conditionals is cheap compared to evaluating the joint density, our results imply that the number of full evaluations of $\pi$ needed for the Gibbs sampler to mix grows linearly with the condition number and is independent of the dimension. If $\pi$ is non-strongly log-concave, the convergence rate in entropy degrades from exponential to polynomial. Our techniques are versatile and extend to Metropolis-within-Gibbs schemes and the Hit-and-Run algorithm. A comparison with gradient-based schemes and the connection with the optimization literature are also discussed.

Large Language Models (LLMs) based on the pre-trained fine-tuning paradigm have become pivotal in solving natural language processing tasks, consistently achieving state-of-the-art performance. Nevertheless, the theoretical understanding of how model complexity influences fine-tuning performance remains challenging and has not been well explored yet. In this paper, we focus on autoregressive LLMs and propose to employ Hidden Markov Models (HMMs) to model them. Based on the HMM modeling, we investigate the relationship between model complexity and the generalization capability in downstream tasks. Specifically, we consider a popular tuning paradigm for downstream tasks, head tuning, where all pre-trained parameters are frozen and only individual heads are trained atop pre-trained LLMs. Our theoretical analysis reveals that the risk initially increases and then decreases with rising model complexity, showcasing a "double descent" phenomenon. In this case, the initial "descent" is degenerate, signifying that the "sweet spot" where bias and variance are balanced occurs when the model size is zero. Obtaining the presented in this study conclusion confronts several challenges, primarily revolving around effectively modeling autoregressive LLMs and downstream tasks, as well as conducting a comprehensive risk analysis for multivariate regression. Our research is substantiated by experiments conducted on data generated from HMMs, which provided empirical support and alignment with our theoretical insights.

Active inference is a mathematical framework for understanding how agents (biological or artificial) interact with their environments, enabling continual adaptation and decision-making. It combines Bayesian inference and free energy minimization to model perception, action, and learning in uncertain and dynamic contexts. Unlike reinforcement learning, active inference integrates exploration and exploitation seamlessly by minimizing expected free energy. In this paper, we present a continual learning framework for agents operating in discrete time environments, using active inference as the foundation. We derive the mathematical formulations of variational and expected free energy and apply them to the design of a self-learning research agent. This agent updates its beliefs and adapts its actions based on new data without manual intervention. Through experiments in changing environments, we demonstrate the agent's ability to relearn and refine its models efficiently, making it suitable for complex domains like finance and healthcare. The paper concludes by discussing how the proposed framework generalizes to other systems, positioning active inference as a flexible approach for adaptive AI.

Current efforts to detect nuclear detonations and correctly categorize explosion sources with ground- and space-collected discriminants presents challenges that remain unaddressed by the Event Categorization Matrix (ECM) model. Smaller events (lower yield explosions) often include only sparse observations among few modalities and can therefore lack a complete set of discriminants. The covariance structures can also vary significantly between such observations of event (source-type) categories. Both obstacles are problematic for ``classic'' ECM. Our work addresses this gap and presents a Bayesian update to the previous ECM model, termed B-ECM, which can be trained on partial observations and does not rely on a pooled covariance structure. We further augment ECM with Bayesian Decision Theory so that false negative or false positive rates of an event categorization can be reduced in an intuitive manner. To demonstrate improved categorization rates with B-ECM, we compare an array of B-ECM and classic ECM models with multiple performance metrics that leverage Monte Carlo experiments. We use both synthetic and real data. Our B-ECM models show consistent gains in overall accuracy and a lower false negative rates relative to the classic ECM model. We propose future avenues to improve B-ECM that expand its decision-making and predictive capability.

Addressing multiagent decision problems in AI, especially those involving collaborative or competitive agents acting concurrently in a partially observable and stochastic environment, remains a formidable challenge. While Interactive Dynamic Influence Diagrams~(I-DIDs) have offered a promising decision framework for such problems, they encounter limitations when the subject agent encounters unknown behaviors exhibited by other agents that are not explicitly modeled within the I-DID. This can lead to sub-optimal responses from the subject agent. In this paper, we propose a novel data-driven approach that utilizes an encoder-decoder architecture, particularly a variational autoencoder, to enhance I-DID solutions. By integrating a perplexity-based tree loss function into the optimization algorithm of the variational autoencoder, coupled with the advantages of Zig-Zag One-Hot encoding and decoding, we generate potential behaviors of other agents within the I-DID that are more likely to contain their true behaviors, even from limited interactions. This new approach enables the subject agent to respond more appropriately to unknown behaviors, thus improving its decision quality. We empirically demonstrate the effectiveness of the proposed approach in two well-established problem domains, highlighting its potential for handling multi-agent decision problems with unknown behaviors. This work is the first time of using neural networks based approaches to deal with the I-DID challenge in agent planning and learning problems.

The rapid advancements in artificial intelligence (AI) have revolutionized smart healthcare, driving innovations in wearable technologies, continuous monitoring devices, and intelligent diagnostic systems. However, security, explainability, robustness, and performance optimization challenges remain critical barriers to widespread adoption in clinical environments. This research presents an innovative algorithmic method using the Adaptive Feature Evaluator (AFE) algorithm to improve feature selection in healthcare datasets and overcome problems. AFE integrating Genetic Algorithms (GA), Explainable Artificial Intelligence (XAI), and Permutation Combination Techniques (PCT), the algorithm optimizes Clinical Decision Support Systems (CDSS), thereby enhancing predictive accuracy and interpretability. The proposed method is validated across three diverse healthcare datasets using six distinct machine learning algorithms, demonstrating its robustness and superiority over conventional feature selection techniques. The results underscore the transformative potential of AFE in smart healthcare, enabling personalized and transparent patient care. Notably, the AFE algorithm, when combined with a Multi-layer Perceptron (MLP), achieved an accuracy of up to 98.5%, highlighting its capability to improve clinical decision-making processes in real-world healthcare applications.

Predicting human intent is challenging yet essential to achieving seamless Human-Robot Collaboration (HRC). Many existing approaches fail to fully exploit the inherent relationships between objects, tasks, and the human model. Current methods for predicting human intent, such as Gaussian Mixture Models (GMMs) and Conditional Random Fields (CRFs), often lack interpretability due to their failure to account for causal relationships between variables. To address these challenges, in this paper, we developed a novel Bayesian Intention (BI) framework to predict human intent within a multi-modality information framework in HRC scenarios. This framework captures the complexity of intent prediction by modeling the correlations between human behavior conventions and scene data. Our framework leverages these inferred intent predictions to optimize the robot's response in real-time, enabling smoother and more intuitive collaboration. We demonstrate the effectiveness of our approach through a HRC task involving a UR5 robot, highlighting BI's capability for real-time human intent prediction and collision avoidance using a unique dataset we created. Our evaluations show that the multi-modality BI model predicts human intent within 2.69ms, with a 36% increase in precision, a 60% increase in F1 Score, and an 85% increase in accuracy compared to its best baseline method. The results underscore BI's potential to advance real-time human intent prediction and collision avoidance, making a significant contribution to the field of HRC.

This paper offers a roadmap for the development of scalable aligned artificial intelligence (AI) from first principle descriptions of natural intelligence. In brief, a possible path toward scalable aligned AI rests upon enabling artificial agents to learn a good model of the world that includes a good model of our preferences. For this, the main objective is creating agents that learn to represent the world and other agents' world models; a problem that falls under structure learning (a.k.a. causal representation learning). We expose the structure learning and alignment problems with this goal in mind, as well as principles to guide us forward, synthesizing various ideas across mathematics, statistics, and cognitive science. 1) We discuss the essential role of core knowledge, information geometry and model reduction in structure learning, and suggest core structural modules to learn a wide range of naturalistic worlds. 2) We outline a way toward aligned agents through structure learning and theory of mind. As an illustrative example, we mathematically sketch Asimov's Laws of Robotics, which prescribe agents to act cautiously to minimize the ill-being of other agents. We supplement this example by proposing refined approaches to alignment. These observations may guide the development of artificial intelligence in helping to scale existing -- or design new -- aligned structure learning systems.