arXiv subjects

Oluwatosin Akande

Publications and source records attributed to Oluwatosin Akande.

3 recordsLinked to original sources

arXiv2026

Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations

Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying model or unknown variables. Proximal operators, ubiquitous in nonsmooth optimization, are central to this because they encode priors and yield efficient iterative algorithms. They have also recently become key to modern machine learning methods, e.g., plug-and-play methods with learned denoisers and deep neural architectures for learning priors of proximal operators. The latter was developed partly due to recent work characterizing proximal operators of nonconvex priors as subdifferentials of convex potentials. In this work, we propose to leverage connections between proximal operators and Hamilton--Jacobi partial differential equations (HJ PDEs) to develop deep learning architectures for learning the prior. In contrast to other existing methods, we learn the prior directly without recourse to inverting the prior after training. We present numerical results in dimensions up to $64$, where the recovered prior is evaluated in a single forward pass.

math.NA↗

arXiv2025

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. We obtain the singular limit of the evolution equations as the length parameter of the phase fields tends to zero by formal expansions and numerically confirm its validity for circles in two dimensions. Our analysis is complemented by numerical experiments for planar curves, surfaces in three-dimensional space, and semi-supervised learning tasks on graphs.

math.AP↗

arXiv2025

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.

cs.CL↗