How the local learning coefficient scales with width in the lazy and rich learning regimes, set by NTK and muP parametrization. A network linear in its parameters does not look regular under the LLC: its Jacobian rank is capped by the dataset rather than the parameter count, so the NTK network's LLC is nearly width-invariant while the muP network's falls with width, ending about 4x lower at width 1024.
Jacob Epifano, Ph.D.
Senior Research Scientist · Philadelphia, PA
Machine learning researcher and engineer. Published work on the failure modes of influence-function interpretability and on scaling Bayesian neural networks. Now build production evaluation and observability infrastructure for LLM systems, including the measurement pipelines that distinguish real improvement from apparent improvement, and use them to drive model and prompt iteration. Independent work on singular learning theory, most recently on the conditions under which local learning coefficient estimates do and do not measure what they claim. Looking to apply evaluation and research infrastructure engineering to alignment.
Research
Estimating the LLC means sampling from a posterior held near the trained weights by a spring of stiffness gamma, a number conventionally fixed once and rarely reported. At finite gamma the estimator returns a curvature-weighted count of directions, so fixing gamma across models whose curvature differs by 400x measures each of them differently. Proposes fixing the dimensionless ratio kappa instead and validates the resulting bias against models whose LLC is known exactly.
Publications
Interpretability and Learning Theory
Efficient Scaling of Bayesian Neural Networks
IEEE Access, 2024PDF
Clinical Machine Learning
Deployment of a Robust and Explainable Mortality Prediction Model: The COVID-19 Pandemic and Beyond
Smart Health, 2(1), 14, 2026PDF
A Comparison of Feature Selection Techniques for First-day Mortality Prediction in the ICU
IEEE International Symposium on Circuits & Systems (ISCAS), 2023PDF
Towards an Explainable Mortality Prediction Tool
Machine Learning for Signal Processing (MLSP), 2020PDF
Machine Learning Analysis of Digital Clock Drawing Test Performance for Differential Classification of Mild Cognitive Impairment Subtypes Versus Alzheimer's Disease
Journal of the International Neuropsychological Society (JINS), 2020PDF
Currently
Senior Research Scientist at Sirona Medical, building evaluation and observability infrastructure for production LLM systems. Full history on the CV.