17 citations · 83 across the 44 of their papers we have counts for
6 papers · 1 filter
Tight Bounds on the Smallest Eigenvalue of the Neural Tangent Kernel for Deep ReLU Networks
Quynh Nguyen, Marco Mondelli, Guido Montufar
A recent line of work has analyzed the theoretical properties of deep neural networks via the Neural Tangent Kernel (NTK). In particular, the smallest eigenvalue of the NTK has bee…
Can neural networks learn persistent homology features?
Guido Montúfar, Nina Otter, Yuguang Wang
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one stu…
Distributed Learning via Filtered Hyperinterpolation on Manifolds
Guido Montúfar, Yu Guang Wang
Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis…
Optimization Theory for ReLU Neural Networks Trained with Normalization Layers
Yonatan Dukler, Quanquan Gu, Guido Montúfar
The success of deep neural networks is in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization a…
Implicit Bias of Gradient Descent for Mean Squared Error Regression with Two-Layer Wide Neural Networks
Hui Jin, Guido Montúfar
We investigate gradient descent training of wide neural networks and the corresponding implicit bias in function space. For univariate regression, we show that the solution of trai…
Wasserstein Distance to Independence Models
Türkü Özlüm Çelik, Asgar Jamneshan, Guido Montúfar +2
An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wa…