1 citations · 1 across the 5 of their papers we have counts for
6 papers
On Parameter Symmetries and Conservation Laws in Gradient Flow
Khang Nguyen, Guido Montúfar
Parameter space symmetries and conservation laws play an important role in understanding the loss landscapes and implicit biases of neural networks. Inspired by Noether's theorem i…
Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse
Shuang Liang, Tom Jacobs, Guido Montúfar
We study the implicit bias of noisy stochastic gradient descent in training wide two-layer ReLU networks for multivariate regression. In a mean-field regime, the training dynamics…
Implicit Bias of Mirror Flow for Shallow Neural Networks in Univariate Regression
Shuang Liang, Guido Montúfar
We examine the implicit bias of mirror flow in univariate least squares error regression with wide and shallow neural networks. For a broad class of potential functions, we show th…
The Real Tropical Geometry of Neural Networks
Marie-Charlotte Brandenburg, Georg Loho, Guido Montúfar
We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReL…
Benign overfitting in leaky ReLU networks with moderate input dimension
Kedar Karhadkar, Erin George, Michael Murray +2
The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two-layer l…
Pull-back Geometry of Persistent Homology Encodings
Shuang Liang, Renata Turkeš, Jiayi Li +2
Persistent homology (PH) is a method for generating topology-inspired representations of data. Empirical studies that investigate the properties of PH, such as its sensitivity to p…