Despite tremendous advancements in large language models (LLMs) over recent years, a notably urgent challenge for their practical deployment is the phenomenon of hallucination, where the model fabricates facts and produces non-factual statements. In response, we propose PoLLMgraph, a Polygraph for LLMs, as an effective model-based white-box detection and forecasting approach. PoLLMgraph distinctly differs from the large body of existing research that concentrates on addressing such challenges through black-box evaluations. In particular, we demonstrate that hallucination can be effectively detected by analyzing the LLM's internal state transition dynamics during generation via tractable probabilistic models. Experimental results on various open-source LLMs confirm the efficacy of PoLLMgraph, outperforming state-of-the-art methods by a considerable margin, evidenced by over 20% improvement in AUC-ROC on common benchmarking datasets like TruthfulQA. Our work paves a new way for model-based white-box analysis of LLMs, motivating the research community to further explore, understand, and refine the intricate dynamics of LLM behaviors.

The remarkable generalization performance of overparameterized models has challenged the conventional wisdom of statistical learning theory. While recent theoretical studies have shed light on this behavior in linear models or nonlinear classifiers, a comprehensive understanding of overparameterization in nonlinear regression models remains lacking. This paper explores the predictive properties of overparameterized nonlinear regression within the Bayesian framework, extending the methodology of adaptive prior based on the intrinsic spectral structure of the data. We establish posterior contraction for single-neuron models with Lipschitz continuous activation functions and for generalized linear models, demonstrating that our approach achieves consistent predictions in the overparameterized regime. Moreover, our Bayesian framework allows for uncertainty estimation of the predictions. The proposed method is validated through numerical simulations and a real data application, showcasing its ability to achieve accurate predictions and reliable uncertainty estimates. Our work advances the theoretical understanding of the blessing of overparameterization and offers a principled Bayesian approach for prediction in large nonlinear models.

The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks and Boltzmann machines are versions of the Ising model, a model extensively studied in statistical mechanics for over a century. In the first part of this chapter, we provide an overview of the principles, models, and applications of ANNs, highlighting their connections to statistical mechanics and statistical learning theory. Artificial neural networks can be seen as high-dimensional mathematical functions, and understanding the geometric properties of their loss landscapes (i.e., the high-dimensional space on which one wishes to find extrema or saddles) can provide valuable insights into their optimization behavior, generalization abilities, and overall performance. Visualizing these functions can help us design better optimization methods and improve their generalization abilities. Thus, the second part of this chapter focuses on quantifying geometric properties and visualizing loss functions associated with deep ANNs.

In robotic insertion tasks where the uncertainty exceeds the allowable tolerance, a good search strategy is essential for successful insertion and significantly influences efficiency. The commonly used blind search method is time-consuming and does not exploit the rich contact information. In this paper, we propose a novel search strategy that actively utilizes the information contained in the contact configuration and shows high efficiency. In particular, we formulate this problem as a Partially Observable Markov Decision Process (POMDP) with carefully designed primitives based on an in-depth analysis of the contact configuration's static stability. From the formulated POMDP, we can derive a novel search strategy. Thanks to its simplicity, this search strategy can be incorporated into a Finite-State-Machine (FSM) controller. The behaviors of the FSM controller are realized through a low-level Cartesian Impedance Controller. Our method is based purely on the robot's proprioceptive sensing and does not need visual or tactile sensors. To evaluate the effectiveness of our proposed strategy and control framework, we conduct extensive comparison experiments in simulation, where we compare our method with the baseline approach. The results demonstrate that our proposed method achieves a higher success rate with a shorter search time and search trajectory length compared to the baseline method. Additionally, we show that our method is robust to various initial displacement errors.

The increasing use of autonomous robot systems in hazardous environments underscores the need for efficient search and rescue operations. Despite significant advancements, existing literature on object search often falls short in overcoming the difficulty of long planning horizons and dealing with sensor limitations, such as noise. This study introduces a novel approach that formulates the search problem as a belief Markov decision processes with options (BMDP-O) to make Monte Carlo tree search (MCTS) a viable tool for overcoming these challenges in large scale environments. The proposed formulation incorporates sequences of actions (options) to move between regions of interest, enabling the algorithm to efficiently scale to large environments. This approach also enables the use of customizable fields of view, for use with multiple types of sensors. Experimental results demonstrate the superiority of this approach in large environments when compared to the problem without options and alternative tools such as receding horizon planners. Given compute time for the proposed formulation is relatively high, a further approximated "lite" formulation is proposed. The lite formulation finds objects in a comparable number of steps with faster computation.

We apply Bayesian Additive Regression Tree (BART) principles to training an ensemble of small neural networks for regression tasks. Using Markov Chain Monte Carlo, we sample from the posterior distribution of neural networks that have a single hidden layer. To create an ensemble of these, we apply Gibbs sampling to update each network against the residual target value (i.e. subtracting the effect of the other networks). We demonstrate the effectiveness of this technique on several benchmark regression problems, comparing it to equivalent shallow neural networks, BART, and ordinary least squares. Our Bayesian Additive Regression Networks (BARN) provide more consistent and often more accurate results. On test data benchmarks, BARN averaged between 5 to 20 percent lower root mean square error. This error performance does come at the cost, however, of greater computation time. BARN sometimes takes on the order of a minute where competing methods take a second or less. But, BARN without cross-validated hyperparameter tuning takes about the same amount of computation time as tuned other methods. Yet BARN is still typically more accurate.

We introduce Score identity Distillation (SiD), an innovative data-free method that distills the generative capabilities of pretrained diffusion models into a single-step generator. SiD not only facilitates an exponentially fast reduction in Fr\'echet inception distance (FID) during distillation but also approaches or even exceeds the FID performance of the original teacher diffusion models. By reformulating forward diffusion processes as semi-implicit distributions, we leverage three score-related identities to create an innovative loss mechanism. This mechanism achieves rapid FID reduction by training the generator using its own synthesized images, eliminating the need for real data or reverse-diffusion-based generation, all accomplished within significantly shortened generation time. Upon evaluation across four benchmark datasets, the SiD algorithm demonstrates high iteration efficiency during distillation and surpasses competing distillation approaches, whether they are one-step or few-step, data-free, or dependent on training data, in terms of generation quality. This achievement not only redefines the benchmarks for efficiency and effectiveness in diffusion distillation but also in the broader field of diffusion-based generation. Our PyTorch implementation will be publicly accessible on GitHub.

The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL). A promising approach to addressing this challenge is distributionally robust RL, often framed as a robust Markov decision process (RMDP). In this framework, the objective is to find a robust policy that achieves good performance under the worst-case scenario among all environments within a pre-specified uncertainty set centered around the training environment. Unlike previous work, which relies on a generative model or a pre-collected offline dataset enjoying good coverage of the deployment environment, we tackle robust RL via interactive data collection, where the learner interacts with the training environment only and refines the policy through trial and error. In this robust RL paradigm, two main challenges emerge: managing distributional robustness while striking a balance between exploration and exploitation during data collection. Initially, we establish that sample-efficient learning without additional assumptions is unattainable owing to the curse of support shift; i.e., the potential disjointedness of the distributional supports between the training and testing environments. To circumvent such a hardness result, we introduce the vanishing minimal value assumption to RMDPs with a total-variation (TV) distance robust set, postulating that the minimal value of the optimal robust value function is zero. We prove that such an assumption effectively eliminates the support shift issue for RMDPs with a TV distance robust set, and present an algorithm with a provable sample complexity guarantee. Our work makes the initial step to uncovering the inherent difficulty of robust RL via interactive data collection and sufficient conditions for designing a sample-efficient algorithm accompanied by sharp sample complexity analysis.

We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit trade-off between convergence guarantees and convergence speed, which contrasts with the typical worst-case analysis. Our learned optimization algorithms provably outperform related ones derived from a (deterministic) worst-case analysis. The results rely on PAC-Bayesian bounds for general, possibly unbounded loss-functions based on exponential families. Then, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum. Furthermore, we provide a concrete algorithmic realization of the framework and new methodologies for learning-to-optimize, and we conduct four practically relevant experiments to support our theory. With this, we showcase that the provided learning framework yields optimization algorithms that provably outperform the state-of-the-art by orders of magnitude.

Alzheimer's disease (AD) and sleep disorders exhibit a close association, where disruptions in sleep patterns often precede the onset of Mild Cognitive Impairment (MCI) and early-stage AD. This study delves into the potential of utilizing sleep-related electroencephalography (EEG) signals acquired through polysomnography (PSG) for the early detection of AD. Our primary focus is on exploring semi-supervised Deep Learning techniques for the classification of EEG signals due to the clinical scenario characterized by the limited data availability. The methodology entails testing and comparing the performance of semi-supervised SMATE and TapNet models, benchmarked against the supervised XCM model, and unsupervised Hidden Markov Models (HMMs). The study highlights the significance of spatial and temporal analysis capabilities, conducting independent analyses of each sleep stage. Results demonstrate the effectiveness of SMATE in leveraging limited labeled data, achieving stable metrics across all sleep stages, and reaching 90% accuracy in its supervised form. Comparative analyses reveal SMATE's superior performance over TapNet and HMM, while XCM excels in supervised scenarios with an accuracy range of 92 - 94%. These findings underscore the potential of semi-supervised models in early AD detection, particularly in overcoming the challenges associated with the scarcity of labeled data. Ablation tests affirm the critical role of spatio-temporal feature extraction in semi-supervised predictive performance, and t-SNE visualizations validate the model's proficiency in distinguishing AD patterns. Overall, this research contributes to the advancement of AD detection through innovative Deep Learning approaches, highlighting the crucial role of semi-supervised learning in addressing data limitations.