arXiv subjects

Mirabel Reid

Publications and source records attributed to Mirabel Reid.

5 recordsLinked to original sources

arXiv2025

Convergence to Radial Symmetry in Iterative Convolution-Thresholding Dynamics

We study a discrete-time spatially extended dynamical system motivated by the continuum limit of binary neuron networks on geometric random graphs. The model evolves a function $\psi:\mathbb{R}^d\rightarrow[0,1]$ by iterative smoothing and sharpening; that is, $\psi_{t+1} = \gamma_t\circ (g * \psi_t)$, where $g$ is a radial convolution kernel and $\gamma_t$ is a monotone map. Under mild regularity conditions on $g$ and $\gamma_t$, we prove that $\psi_t$ tends toward radial symmetry as $t \rightarrow \infty$. Notably, a special case of this process recovers the Merriman-Bence-Osher (MBO) scheme for the motion of interfaces by mean curvature, and we provide a novel analysis of its behavior. Our results connect the dynamics of spatial binary neuron networks with classical models of interface motion, and we establish general conditions under which spatial dependence drives activity toward radial symmetry.

math.DS↗

arXiv2024

Online Decision Deferral under Budget Constraints

Machine Learning (ML) models are increasingly used to support or substitute decision making. In applications where skilled experts are a limited resource, it is crucial to reduce their burden and automate decisions when the performance of an ML model is at least of equal quality. However, models are often pre-trained and fixed, while tasks arrive sequentially and their distribution may shift. In that case, the respective performance of the decision makers may change, and the deferral algorithm must remain adaptive. We propose a contextual bandit model of this online decision making problem. Our framework includes budget constraints and different types of partial feedback models. Beyond the theoretical guarantees of our algorithm, we propose efficient extensions that achieve remarkable performance on real-world datasets.

cs.LG↗

arXiv2024

Improving Radiography Machine Learning Workflows via Metadata Management for Training Data Selection

Most machine learning models require many iterations of hyper-parameter tuning, feature engineering, and debugging to produce effective results. As machine learning models become more complicated, this pipeline becomes more difficult to manage effectively. In the physical sciences, there is an ever-increasing pool of metadata that is generated by the scientific research cycle. Tracking this metadata can reduce redundant work, improve reproducibility, and aid in the feature and training dataset engineering process. In this case study, we present a tool for machine learning metadata management in dynamic radiography. We evaluate the efficacy of this tool against the initial research workflow and discuss extensions to general machine learning pipelines in the physical sciences.

cs.LG↗

arXiv2024

Does GPT Really Get It? A Hierarchical Scale to Quantify Human vs AI's Understanding of Algorithms

As Large Language Models (LLMs) perform (and sometimes excel at) more and more complex cognitive tasks, a natural question is whether AI really understands. The study of understanding in LLMs is in its infancy, and the community has yet to incorporate well-trodden research in philosophy, psychology, and education. We initiate this, specifically focusing on understanding algorithms, and propose a hierarchy of levels of understanding. We use the hierarchy to design and conduct a study with human subjects (undergraduate and graduate students) as well as large language models (generations of GPT), revealing interesting similarities and differences. We expect that our rigorous criteria will be useful to keep track of AI's progress in such cognitive domains.

cs.AI↗

arXiv2022

The $k$-Cap Process on Geometric Random Graphs

The $k$-cap (or $k$-winners-take-all) process on a graph works as follows: in each iteration, exactly $k$ vertices of the graph are in the cap (i.e., winners); the next round winners are the vertices that have the highest total degree to the current winners, with ties broken randomly. This natural process is a simple model of firing activity in the brain. We study its convergence on geometric random graphs, revealing rather surprising behavior.

math.PR↗