6 citations · 6 across the 2 of their papers we have counts for
8 papers
Conditioning of Random Feature Matrices: Double Descent and Generalization Error
Zhijun Chen, Hayden Schaeffer
We provide (high probability) bounds on the condition number of random feature matrices. In particular, we show that if the complexity ratio where is the number o…
Reduced Order Modeling using Shallow ReLU Networks with Grassmann Layers
Kayla Bollinger, Hayden Schaeffer
This paper presents a nonlinear model reduction method for systems of equations using a structured neural network. The neural network takes the form of a "three-layer" network with…
NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data
Yifan Sun, Linan Zhang, Hayden Schaeffer
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-t…
Extending the step-size restriction for gradient descent to avoid strict saddle points
Hayden Schaeffer, Scott G. McCalla
We provide larger step-size restrictions for which gradient descent based algorithms (almost surely) avoid strict saddle points. In particular, consider a twice differentiable (non…
Recovery guarantees for polynomial approximation from dependent data with outliers
Lam Si Tung Ho, Hayden Schaeffer, Giang Tran +1
Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, ma…
Forward Stability of ResNet and Its Variants
Linan Zhang, Hayden Schaeffer
The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to…