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It has long been appreciated that transport properties can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target -- the first-passage time (FPT). Although essential to…

Suppose $X$ is a multidimensional diffusion process. Assume that at time zero the state of $X$ is fully observed, but at time $T>0$ only linear combinations of its components are observed. That is, one only observes the vector $L X_T$ for a…

With the advancement of large language models (LLMs), solving complex reasoning tasks has gained increasing attention. Inference-time computation methods (e.g., Best-of-N, beam search, et al.) are particularly valuable as they can enhance…

In this paper, we consider molecular communications in one-dimensional flow-induced diffusion channels with a perfectly absorbing receiver. In such channels, the random propagation delay until the molecules are absorbed follows an inverse…

Generative Bayesian Computation (GBC) methods are developed for Casual Inference. Generative methods are simulation-based methods that use a large training dataset to represent posterior distributions as a map (a.k.a. optimal transport) to…

The meteoric rise in the adoption of deep neural networks as computational models of vision has inspired efforts to "align" these models with humans. One dimension of interest for alignment includes behavioral choices, but moving beyond…

Goal-models (GM) have been used in adaptive systems engineering for their ability to capture the different ways to fulfill the requirements. Contextual GM (CGM) extend these models with the notion of context and context-dependent…

We use a generic framework, namely the gradient discretisation method (GDM), to propose a unified numerical analysis for general time-dependent convection-diffusion-reaction models. We establish novel results for convergence rates of…

The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the…

Diffusion-based world models have demonstrated strong capabilities in synthesizing realistic long-horizon trajectories for offline reinforcement learning (RL). However, many existing methods do not directly generate actions alongside states…

Large Language Models (LLMs) achieve strong performance through extended inference-time deliberation, yet how their reasoning failures arise remains poorly understood. By analyzing model-generated reasoning trajectories, we find that errors…

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static…

We consider the problem of predicting perturbation effects via causal models. In many applications, it is a priori unknown which mechanisms of a system are modified by an external perturbation, even though the features of the perturbation…

As the development of large-scale Generative AI models evolve beyond text (1D) generation to include image (2D) and video (3D) generation, processing spatial and temporal information presents unique challenges to quality, performance, and…

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse…

We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…

For two molecules to react they first have to meet. Yet, reaction times are rarely on par with the first-passage times that govern such molecular encounters. A prime reason for this discrepancy is stochastic transitions between reactive and…

As a dominant force in text-to-image generation tasks, Diffusion Probabilistic Models (DPMs) face a critical challenge in controllability, struggling to adhere strictly to complex, multi-faceted instructions. In this work, we aim to address…

Reinforcement learning (RL) algorithms have been used recently to align diffusion models with downstream objectives such as aesthetic quality and text-image consistency by fine-tuning them to maximize a single reward function under a fixed…

This study investigates human-computer interface generation based on diffusion models to overcome the limitations of traditional template-based design and fixed rule-driven methods. It first analyzes the key challenges of interface…