8 papers
Is the Last Layer Sufficient for Uncertainty Quantification?
Joseph Wilson, Chris van der Heide, Liam Hodgkinson +1
Epistemic uncertainty quantification (UQ) for deep neural networks (DNNs) is a requirement for safe adoption of AI in mission-critical settings. Several leading methods for UQ line…
Free Decompression with Algebraic Spectral Curves
Siavash Ameli, Chris van der Heide, Liam Hodgkinson +1
Tools from random matrix theory have become central to deep learning theory, using spectral information to provide mechanisms for modeling generalization, robustness, scaling, and…
The Interpolating Information Criterion for Overparameterized Models
Liam Hodgkinson, Chris van der Heide, Robert Salomone +2
The problem of model selection is considered for the setting of interpolating estimators, where the number of model parameters exceeds the size of the dataset. Classical informatio…
Uncertainty-Aware Diagnostics for Physics-Informed Machine Learning
Mara Daniels, Liam Hodgkinson, Michael Mahoney
Physics-informed machine learning (PIML) integrates prior physical information, often in the form of differential equation constraints, into the process of fitting machine learning…
Determinant Estimation under Memory Constraints and Neural Scaling Laws
Siavash Ameli, Chris van der Heide, Liam Hodgkinson +2
Calculating or accurately estimating log-determinants of large positive definite matrices is of fundamental importance in many machine learning tasks. While its cubic computational…
Spectral Estimation with Free Decompression
Siavash Ameli, Chris van der Heide, Liam Hodgkinson +1
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions,…