Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs

We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine learning. While the gradient flow in the task at hand is a parabolic partial differential equation, the momentum-method corresponds to a damped hyperbolic PDE, leading to qualitatively and quantitatively different trajectories. Using a convex-concave splitting-based FISTA-type time discretization, we demonstrate empirically that momentum can lead to faster convergence if the time step size is large but not too large. With large time steps, the PDE analysis offers only limited insight into the geometric behavior of solutions and typical hyperbolic phenomena like loss of regularity are not be observed in sample simulations.

Contextual Evaluation of Large Language Models for Classifying Tropical and Infectious Diseases

While large language models (LLMs) have shown promise for medical question answering, there is limited work focused on tropical and infectious disease-specific exploration. We build on an opensource tropical and infectious diseases (TRINDs) dataset, expanding it to include demographic and semantic clinical and consumer augmentations yielding 11000+ prompts. We evaluate LLM performance on these, comparing generalist and medical LLMs, as well as LLM outcomes to human experts. We demonstrate through systematic experimentation, the benefit of contextual information such as demographics, location, gender, risk factors for optimal LLM response. Finally we develop a prototype of TRINDs-LM, a research tool that provides a playground to navigate how context impacts LLM outputs for health.