In designing generative models, it is commonly believed that in order to learn useful latent structure, we face a fundamental tension between expressivity and structure. In this paper we challenge this view by proposing a new approach to training arbitrarily expressive generative models that simultaneously learn disentangled latent structure. This is accomplished by adding a simple decoder-only module to the head of an existing decoder block that can be arbitrarily complex. The module learns to process concept information by implicitly inverting linear representations from an encoder. Inspired by the notion of intervention in causal graphical models, our module selectively modifies its architecture during training, allowing it to learn a compact joint model over different contexts. We show how adding this module leads to disentangled representations that can be composed for out-of-distribution generation. To further validate our proposed approach, we prove a new identifiability result that extends existing work on identifying structured representations in nonlinear models.

Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present a general framework of runtime verification of algorithmic fairness for systems whose models are unknown, but are assumed to have a Markov chain structure, with or without full observation of the state space. We introduce a specification language that can model many common algorithmic fairness properties, such as demographic parity, equal opportunity, and social burden. We build monitors that observe a long sequence of events as generated by a given system, and output, after each observation, a quantitative estimate of how fair or biased the system was on that run until that point in time. The estimate is proven to be correct modulo a variable error bound and a given confidence level, where the error bound gets tighter as the observed sequence gets longer. We present two categories of monitoring algorithms, namely ones with a uniform error bound across all time points, and ones with weaker non-uniform, pointwise error bounds at different time points. Our monitoring algorithms use statistical tools that are adapted to suit the dynamic requirements of monitoring and the special needs of the fairness specifications. Using a prototype implementation, we show how we can monitor if a bank is fair in giving loans to applicants from different social backgrounds, and if a college is fair in admitting students while maintaining a reasonable financial burden on the society. In these experiments, our monitors took less than a millisecond to update their verdicts after each observation.

The proliferation of ride-hailing aggregator platforms presents significant growth opportunities for ride-service providers by increasing order volume and gross merchandise value (GMV). On most ride-hailing aggregator platforms, service providers that offer lower fares are ranked higher in listings and, consequently, are more likely to be selected by passengers. This competitive ranking mechanism creates a strong incentive for service providers to adopt coupon strategies that lower prices to secure a greater number of orders, as order volume directly influences their long-term viability and sustainability. Thus, designing an effective coupon strategy that can dynamically adapt to market fluctuations while optimizing order acquisition under budget constraints is a critical research challenge. However, existing studies in this area remain scarce. To bridge this gap, we propose FCA-RL, a novel reinforcement learning-based subsidy strategy framework designed to rapidly adapt to competitors' pricing adjustments. Our approach integrates two key techniques: Fast Competition Adaptation (FCA), which enables swift responses to dynamic price changes, and Reinforced Lagrangian Adjustment (RLA), which ensures adherence to budget constraints while optimizing coupon decisions on new price landscape. Furthermore, we introduce RideGym, the first dedicated simulation environment tailored for ride-hailing aggregators, facilitating comprehensive evaluation and benchmarking of different pricing strategies without compromising real-world operational efficiency. Experimental results demonstrate that our proposed method consistently outperforms baseline approaches across diverse market conditions, highlighting its effectiveness in subsidy optimization for ride-hailing service providers.

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.