Mutual Information (MI) is a crucial measure for capturing dependencies between variables, yet exact computation is challenging in high dimensions with intractable likelihoods, impacting accuracy and robustness. One idea is to use an auxiliary neural network to train an MI estimator; however, methods based on the empirical distribution function (EDF) can introduce sharp fluctuations in the MI loss due to poor out-of-sample performance, thereby destabilizing convergence. We present a Bayesian nonparametric (BNP) solution for training an MI estimator by constructing the MI loss with a finite representation of the Dirichlet process posterior to incorporate regularization in the training process. With this regularization, the MI loss integrates both prior knowledge and empirical data to reduce the loss sensitivity to fluctuations and outliers in the sample data, particularly in small sample settings like mini-batches. This approach addresses the challenge of balancing accuracy and low variance by effectively reducing variance, leading to stabilized and robust MI loss gradients during training and enhancing the convergence of the MI approximation while offering stronger theoretical guarantees for convergence. We explore the application of our estimator in maximizing MI between the data space and the latent space of a variational autoencoder. Experimental results demonstrate significant improvements in convergence over EDF-based methods, with applications across synthetic and real datasets, notably in 3D CT image generation--yielding enhanced structure discovery and reduced overfitting in data synthesis. While this paper focuses on generative models in application, the proposed estimator is not restricted to this setting and can be applied more broadly in various BNP learning procedures.

Recent inductive logic programming (ILP) approaches learn optimal hypotheses. An optimal hypothesis minimises a given cost function on the training data. There are many cost functions, such as minimising training error, textual complexity, or the description length of hypotheses. However, selecting an appropriate cost function remains a key question. To address this gap, we extend a constraint-based ILP system to learn optimal hypotheses for seven standard cost functions. We then empirically compare the generalisation error of optimal hypotheses induced under these standard cost functions. Our results on over 20 domains and 1000 tasks, including game playing, program synthesis, and image reasoning, show that, while no cost function consistently outperforms the others, minimising training error or description length has the best overall performance. Notably, our results indicate that minimising the size of hypotheses does not always reduce generalisation error.

Dynamic Treatment Regimes (DTRs) provide a systematic approach for making sequential treatment decisions that adapt to individual patient characteristics, particularly in clinical contexts where survival outcomes are of interest. Censoring-Aware Tree-Based Reinforcement Learning (CA-TRL) is a novel framework to address the complexities associated with censored data when estimating optimal DTRs. We explore ways to learn effective DTRs, from observational data. By enhancing traditional tree-based reinforcement learning methods with augmented inverse probability weighting (AIPW) and censoring-aware modifications, CA-TRL delivers robust and interpretable treatment strategies. We demonstrate its effectiveness through extensive simulations and real-world applications using the SANAD epilepsy dataset, where it outperformed the recently proposed ASCL method in key metrics such as restricted mean survival time (RMST) and decision-making accuracy. This work represents a step forward in advancing personalized and data-driven treatment strategies across diverse healthcare settings.

We propose a method, funWeightClust, based on a family of parsimonious models for clustering heterogeneous functional linear regression data. These models extend cluster weighted models to functional data, and they allow for multivariate functional responses and predictors. The proposed methodology follows the approach used by the the functional high dimensional data clustering (funHDDC) method. We construct an expectation maximization (EM) algorithm for parameter estimation. Using simulated and benchmark data we show that funWeightClust outperforms funHDDC and several two-steps clustering methods. We also use funWeightClust to analyze traffic patterns in Edmonton, Canada.

Deep reinforcement learning (DRL)-based frameworks, featuring Transformer-style policy networks, have demonstrated their efficacy across various vehicle routing problem (VRP) variants. However, the application of these methods to the multi-trip time-dependent vehicle routing problem (MTTDVRP) with maximum working hours constraints -- a pivotal element of urban logistics -- remains largely unexplored. This paper introduces a DRL-based method called the Simultaneous Encoder and Dual Decoder Attention Model (SED2AM), tailored for the MTTDVRP with maximum working hours constraints. The proposed method introduces a temporal locality inductive bias to the encoding module of the policy networks, enabling it to effectively account for the time-dependency in travel distance or time. The decoding module of SED2AM includes a vehicle selection decoder that selects a vehicle from the fleet, effectively associating trips with vehicles for functional multi-trip routing. Additionally, this decoding module is equipped with a trip construction decoder leveraged for constructing trips for the vehicles. This policy model is equipped with two classes of state representations, fleet state and routing state, providing the information needed for effective route construction in the presence of maximum working hours constraints. Experimental results using real-world datasets from two major Canadian cities not only show that SED2AM outperforms the current state-of-the-art DRL-based and metaheuristic-based baselines but also demonstrate its generalizability to solve larger-scale problems.

We consider the problem of using diffusion models to generate fast, smooth, and temporally consistent robot motions. Although diffusion models have demonstrated superior performance in robot learning due to their task scalability and multi-modal flexibility, they suffer from two fundamental limitations: (1) they often produce non-smooth, jerky motions due to their inability to capture temporally consistent movement dynamics, and (2) their iterative sampling process incurs prohibitive latency for many robotic tasks. Inspired by classic robot motion generation methods such as DMPs and ProMPs, which capture temporally and spatially consistent dynamic of trajectories using low-dimensional vectors -- and by recent advances in diffusion-based image generation that use consistency models with probability flow ODEs to accelerate the denoising process, we propose Fast Robot Motion Diffusion (FRMD). FRMD uniquely integrates Movement Primitives (MPs) with Consistency Models to enable efficient, single-step trajectory generation. By leveraging probabilistic flow ODEs and consistency distillation, our method models trajectory distributions while learning a compact, time-continuous motion representation within an encoder-decoder architecture. This unified approach eliminates the slow, multi-step denoising process of conventional diffusion models, enabling efficient one-step inference and smooth robot motion generation. We extensively evaluated our FRMD on the well-recognized Meta-World and ManiSkills Benchmarks, ranging from simple to more complex manipulation tasks, comparing its performance against state-of-the-art baselines. Our results show that FRMD generates significantly faster, smoother trajectories while achieving higher success rates.

A number of recent studies have focused on developing surgical simulation platforms to train machine learning (ML) agents or models with synthetic data for surgical assistance. While existing platforms excel at tasks such as rigid body manipulation and soft body deformation, they struggle to simulate more complex soft body behaviors like cutting and suturing. A key challenge lies in modeling soft body fracture and splitting using the finite-element method (FEM), which is the predominant approach in current platforms. Additionally, the two-way suture needle/thread contact inside a soft body is further complicated when using FEM. In this work, we use the material point method (MPM) for such challenging simulations and propose new rigid geometries and soft-rigid contact methods specifically designed for them. We introduce CRESSim-MPM, a GPU-accelerated MPM library that integrates multiple MPM solvers and incorporates surgical geometries for cutting and suturing, serving as a specialized physics engine for surgical applications. It is further integrated into Unity, requiring minimal modifications to existing projects for soft body simulation. We demonstrate the simulator's capabilities in real-time simulation of cutting and suturing on soft tissue and provide an initial performance evaluation of different MPM solvers when simulating varying numbers of particles.

A computational ethics framework is essential for AI and autonomous systems operating in complex, real-world environments. Existing approaches often lack the adaptability needed to integrate ethical principles into dynamic and ambiguous contexts, limiting their effectiveness across diverse scenarios. To address these challenges, we outline the necessary ingredients for building a holistic, meta-level framework that combines intermediate representations, probabilistic reasoning, and knowledge representation. The specifications therein emphasize scalability, supporting ethical reasoning at both individual decision-making levels and within the collective dynamics of multi-agent systems. By integrating theoretical principles with contextual factors, it facilitates structured and context-aware decision-making, ensuring alignment with overarching ethical standards. We further explore proposed theorems outlining how ethical reasoners should operate, offering a foundation for practical implementation. These constructs aim to support the development of robust and ethically reliable AI systems capable of navigating the complexities of real-world moral decision-making scenarios.

The softmax function is a fundamental component in deep learning. This study delves into the often-overlooked parameter within the softmax function, known as "temperature," providing novel insights into the practical and theoretical aspects of temperature scaling for image classification. Our empirical studies, adopting convolutional neural networks and transformers on multiple benchmark datasets, reveal that moderate temperatures generally introduce better overall performance. Through extensive experiments and rigorous theoretical analysis, we explore the role of temperature scaling in model training and unveil that temperature not only influences learning step size but also shapes the model's optimization direction. Moreover, for the first time, we discover a surprising benefit of elevated temperatures: enhanced model robustness against common corruption, natural perturbation, and non-targeted adversarial attacks like Projected Gradient Descent. We extend our discoveries to adversarial training, demonstrating that, compared to the standard softmax function with the default temperature value, higher temperatures have the potential to enhance adversarial training. The insights of this work open new avenues for improving model performance and security in deep learning applications.

In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular, we introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form so-called diffusion bridges. We develop a mechanism for combining multiple such constraints so that the resulting multiply-constrained model remains a manual bridge that respects all constraints. We also develop a mechanism for training a diffusion model that respects such multiple constraints while also adapting it to match a data distribution. We develop and extend theory demonstrating the mathematical validity of our mechanisms. Additionally, we demonstrate our mechanism in constrained generative modeling tasks, highlighting a particular high-value application in modeling trajectory initializations for path planning and control in autonomous vehicles.