Large language models are thought to have potential to aid in medical decision making. We investigate this here. We start with the treatment problem, the patient's core medical decision-making task, which is solved in collaboration with a healthcare provider. We discuss approaches to solving the treatment problem, including -- within evidence-based medicine -- trials and observational data. We then discuss the chat problem, and how this differs from the treatment problem -- in particular as it relates to imitation. We then discuss how a large language model might be used to solve the treatment problem and highlight some of the challenges that emerge. We finally discuss how these challenges relate to evidence-based medicine, and how this might inform next steps.

By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these machine learning models using the framework of quantum information theory, leading to the introduction of positive unital circuits (PUnCs), which generalize circuit evaluations over positive real-valued probabilities to circuit evaluations over positive semi-definite matrices. As a consequence, PUnCs strictly generalize probabilistic circuits as well as recently introduced circuit classes such as PSD circuits.

In many real-world planning tasks, agents must tackle uncertainty about the environment's state and variability in the outcomes of any chosen policy. We address both forms of uncertainty as a first step toward safer algorithms in partially observable settings. Specifically, we extend Distributional Reinforcement Learning (DistRL)--which models the entire return distribution for fully observable domains--to Partially Observable Markov Decision Processes (POMDPs), allowing an agent to learn the distribution of returns for each conditional plan. Concretely, we introduce new distributional Bellman operators for partial observability and prove their convergence under the supremum p-Wasserstein metric. We also propose a finite representation of these return distributions via ψ -vectors, generalizing the classical α -vectors in POMDP solvers. Building on this, we develop Distributional Point-Based V alue Iteration (DPBVI), which integrates ψ -vectors into a standard point-based backup procedure-- bridging DistRL and POMDP planning . By tracking return distributions, DPBVI lays the foundation for future risk-sensitive control in domains where rare, high-impact events must be carefully managed. We provide source code to foster further research in robust decision-making under partial observability.

Vision-Language Models (VLMs) learn joint representations by mapping images and text into a shared latent space. However, recent research highlights that deterministic embeddings from standard VLMs often struggle to capture the uncertainties arising from the ambiguities in visual and textual descriptions and the multiple possible correspondences between images and texts. Existing approaches tackle this by learning probabilistic embeddings during VLM training, which demands large datasets and does not leverage the powerful representations already learned by large-scale VLMs like CLIP. In this paper, we propose GroVE, a post-hoc approach to obtaining probabilistic embeddings from frozen VLMs. GroVE builds on Gaussian Process Latent Variable Model (GPLVM) to learn a shared low-dimensional latent space where image and text inputs are mapped to a unified representation, optimized through single-modal embedding reconstruction and cross-modal alignment objectives. Once trained, the Gaussian Process model generates uncertainty-aware probabilistic embeddings. Evaluation shows that GroVE achieves state-of-the-art uncertainty calibration across multiple downstream tasks, including cross-modal retrieval, visual question answering, and active learning.

A Bayesian Deep Restricted Boltzmann-Kohonen architecture for data clustering termed as DRBM-ClustNet is proposed. This core-clustering engine consists of a Deep Restricted Boltzmann Machine (DRBM) for processing unlabeled data by creating new features that are uncorrelated and have large variance with each other. Next, the number of clusters are predicted using the Bayesian Information Criterion (BIC), followed by a Kohonen Network-based clustering layer. The processing of unlabeled data is done in three stages for efficient clustering of the non-linearly separable datasets. In the first stage, DRBM performs non-linear feature extraction by capturing the highly complex data representation by projecting the feature vectors of $d$ dimensions into $n$ dimensions. Most clustering algorithms require the number of clusters to be decided a priori, hence here to automate the number of clusters in the second stage we use BIC. In the third stage, the number of clusters derived from BIC forms the input for the Kohonen network, which performs clustering of the feature-extracted data obtained from the DRBM. This method overcomes the general disadvantages of clustering algorithms like the prior specification of the number of clusters, convergence to local optima and poor clustering accuracy on non-linear datasets. In this research we use two synthetic datasets, fifteen benchmark datasets from the UCI Machine Learning repository, and four image datasets to analyze the DRBM-ClustNet. The proposed framework is evaluated based on clustering accuracy and ranked against other state-of-the-art clustering methods. The obtained results demonstrate that the DRBM-ClustNet outperforms state-of-the-art clustering algorithms.

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic) gradient descent, and related topics into dynamical statements. We also tackle three concrete challenges. First, we consider the process of information propagation through a neural network, i.e., we study the input-output map for different architectures. We explain the universal embedding property for augmented neural ODEs representing arbitrary functions of given regularity, the classification of multilayer perceptrons and neural ODEs in terms of suitable function classes, and the memory-dependence in neural delay equations. Second, we consider the training aspect of neural networks dynamically. We describe a dynamical systems perspective on gradient descent and study stability for overdetermined problems. We then extend this analysis to the overparameterized setting and describe the edge of stability phenomenon, also in the context of possible explanations for implicit bias. For stochastic gradient descent, we present stability results for the overparameterized setting via Lyapunov exponents of interpolation solutions. Third, we explain several results regarding mean-field limits of neural networks. We describe a result that extends existing techniques to heterogeneous neural networks involving graph limits via digraph measures. This shows how large classes of neural networks naturally fall within the framework of Kuramoto-type models on graphs and their large-graph limits. Finally, we point out that similar strategies to use dynamics to study explainable and reliable AI can also be applied to settings such as generative models or fundamental issues in gradient training methods, such as backpropagation or vanishing/exploding gradients.

It has been challenging to model the complex temporal-spatial dependencies between agents for trajectory prediction. As each state of an agent is closely related to the states of adjacent time steps, capturing the local temporal dependency is beneficial for prediction, while most studies often overlook it. Besides, learning the high-order motion state attributes is expected to enhance spatial interaction modeling, but it is rarely seen in previous works. To address this, we propose a lightweight framework, LTMSformer, to extract temporal-spatial interaction features for multi-modal trajectory prediction. Specifically, we introduce a Local Trend-Aware Attention mechanism to capture the local temporal dependency by leveraging a convolutional attention mechanism with hierarchical local time boxes. Next, to model the spatial interaction dependency, we build a Motion State Encoder to incorporate high-order motion state attributes, such as acceleration, jerk, heading, etc. To further refine the trajectory prediction, we propose a Lightweight Proposal Refinement Module that leverages Multi-Layer Perceptrons for trajectory embedding and generates the refined trajectories with fewer model parameters. Experiment results on the Argoverse 1 dataset demonstrate that our method outperforms the baseline HiVT-64, reducing the minADE by approximately 4.35%, the minFDE by 8.74%, and the MR by 20%. We also achieve higher accuracy than HiVT-128 with a 68% reduction in model size.

Research, innovation and practical capital investment have been increasing rapidly toward the realization of autonomous physical agents. This includes industrial and service robots, unmanned aerial vehicles, embedded control devices, and a number of other realizations of cybernetic/mechatronic implementations of intelligent autonomous devices. In this paper, we consider a stylized version of robotic care, which would normally involve a two-level Reinforcement Learning procedure that trains a policy for both lower level physical movement decisions as well as higher level conceptual tasks and their sub-components. In order to deliver greater safety and reliability in the system, we present the general formulation of this as a two-level optimization scheme which incorporates control at the lower level, and classical planning at the higher level, integrated with a capacity for learning. This synergistic integration of multiple methodologies -- control, classical planning, and RL -- presents an opportunity for greater insight for algorithm development, leading to more efficient and reliable performance. Here, the notion of reliability pertains to physical safety and interpretability into an otherwise black box operation of autonomous agents, concerning users and regulators. This work presents the necessary background and general formulation of the optimization framework, detailing each component and its integration with the others.

The limitations of the Poisson process were more evident when modeling high-speed network traffic, particularly real-time data traffic modeling for next-generation networks. For example, Liji et al. [85] demonstrated that the Stationary Poison Increment Process can only model Short Range Dependence (SRD) but not LRD. To address this limitation, the authors proposed using second-order self-similarity models, such as fractional Gaussian noise and fractional ARIMA processes, as a more appropriate approach. In the meantime, researchers also explored modeling data center network traffic using poisson processes. To better simulate realistic traffic in data center environments, the generation of flow-level network traffic matrices based on the poisson shot-noise model is proposed in [172]. By incorporating factors such as flow arrival rates, intra-rack traffic ratios, flow sizes and durations, the poisson shot-noise process offers a more accurate representation of traffic patterns in data centers. B. Weibull distribution As discussed earlier, the limitations of Poisson processes for modeling network traffic led to exploring other distributions. One such promising model was the Weibull distribution, mainly due to its flexibility to model both heavy and non-heavy tailed distributions [11].

Support and resistance (SR) levels are central to technical analysis, guiding traders in entry, exit, and risk management. Despite widespread use, traditional SR identification methods often fail to adapt to the complexities of modern, volatile markets. Recent research has introduced machine learning techniques to address the following challenges, yet most focus on price prediction rather than structural level identification. This paper presents DeepSupp, a new deep learning approach for detecting financial support levels using multi-head attention mechanisms to analyze spatial correlations and market microstructure relationships. Deep-Supp integrates advanced feature engineering, constructing dynamic correlation matrices that capture evolving market relationships, and employs an attention-based autoencoder for robust representation learning. The final support levels are extracted through unsupervised clustering, leveraging DBSCAN to identify significant price thresholds. Comprehensive evaluations on S&P 500 tickers demonstrate that DeepSupp outperforms six baseline methods, achieving state-of-the-art performance across six financial metrics, including essential support accuracy and market regime sensitivity. With consistent results across diverse market conditions, DeepSupp addresses critical gaps in SR level detection, offering a scalable and reliable solution for modern financial analysis. Our approach highlights the potential of attention-based architectures to uncover nuanced market patterns and improve technical trading strategies.