3 papers
cs.LG2025
On the Neural Feature Ansatz for Deep Neural Networks
Edward Tansley, Estelle Massart, Coralia Cartis
Understanding feature learning is an important open question in establishing a mathematical foundation for deep neural networks. The Neural Feature Ansatz (NFA) states that after t…
math.OC2025
Random Subspace Cubic-Regularization Methods, with Applications to Low-Rank Functions
Coralia Cartis, Zhen Shao, Edward Tansley
We propose and analyze random subspace variants of the second-order Adaptive Regularization using Cubics (ARC) algorithm. These methods iteratively restrict the search space to som…
math.OC2025
Scalable Second-Order Optimization Algorithms for Minimizing Low-rank Functions
Edward Tansley, Coralia Cartis
We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix…