Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable formulations. In this paper, we present a theory of stochastic optimal control (SOC) tailored to infinite-dimensional spaces, aiming to extend diffusion-based algorithms to function spaces. Specifically, we demonstrate how Doob’s $h$-transform, the fundamental tool for constructing diffusion bridges, can be derived from the SOC perspective and expanded to infinite dimensions. This expansion presents a challenge, as infinite-dimensional spaces typically lack closed-form densities. Leveraging our theory, we establish that solving the optimal control problem with a specific objective function choice is equivalent to learning diffusion-based generative models. We propose two applications: 1) learning bridges between two infinite-dimensional distributions and 2) generative models for sampling from an infinite-dimensional distribution. Our approach proves effective for diverse problems involving continuous function space representations, such as resolution-free images, time-series data, and probability density functions.

A Bayesian pseudocoreset is a small synthetic dataset for which the posterior over parameters approximates that of the original dataset. While promising, the scalability of Bayesian pseudocoresets is not yet validated in large-scale problems such as image classification with deep neural networks. On the other hand, dataset distillation methods similarly construct a small dataset such that the optimization with the synthetic dataset converges to a solution similar to optimization with full data. Although dataset distillation has been empirically verified in large-scale settings, the framework is restricted to point estimates, and their adaptation to Bayesian inference has not been explored. This paper casts two representative dataset distillation algorithms as approximations to methods for constructing pseudocoresets by minimizing specific divergence measures: reverse KL divergence and Wasserstein distance. Furthermore, we provide a unifying view of such divergence measures in Bayesian pseudocoreset construction. Finally, we propose a novel Bayesian pseudocoreset algorithm based on minimizing forward KL divergence. Our empirical results demonstrate that the pseudocoresets constructed from these methods reflect the true posterior even in large-scale Bayesian inference problems.

Challenging behaviors significantly impact learning and socialization of autistic children and can stress and burden their caregivers. Documentation of challenging behaviors is fundamental for identifying what environmental factors influence them, such as how others respond to a child's such behaviors. Caregiver-tracked data on their child's challenging behaviors can help clinical experts make informed recommendations about how to manage such behaviors. To support caregivers in recording their children's challenging behaviors, we developed GeniAuti, a mobile-based data-collection tool built upon a clinical data collection form to document challenging behaviors and other clinically relevant contextual information such as place, duration, intensity, and what triggers such behaviors. Through an open-ended deployment with 19 parent-child pairs and three expert collaborators, caregivers found GeniAuti valuable for (1) becoming more attentive and reflective to behavioral contexts, including their own response strategies, (2) discovering positive aspects of their children's behaviors, and (3) promoting collaboration with clinical experts around the caregiver-tracked data to develop tailored intervention strategies for their children. However, participant experiences surface challenges of logging behaviors in social circumstances, conflicting views between caregivers and clinical experts around the structured recording process, and emotional struggles resulting from recording and reflecting on intensely negative experiences. Considering the complex nature of caregiver-based health tracking and caregiver--clinician collaboration, we suggest design opportunities for facilitating negotiations between caregivers and clinicians and accounting for caregivers' emotional needs.

This paper presents the design and implementation of high frequency resonant converter based on the Class Φ2inverter for inductive power transfer. MHz frequency operation can allow for higher power density than conventional switching frequencies. The converter is based on the Class Φ2inverter, reducing the voltage stress across the switch compared to other resonant topologies. A prototype of converter and a few cm airgap inductive coupling system with resistive load was implemented. We will demonstrate a greater than hundred Watt push-pull resonant converter for inductive power transfer at 13.56MHz.