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Found 4 papers, 1 papers with code
Automated Grain Boundary (GB) Segmentation and Microstructural Analysis in 347H Stainless Steel Using Deep Learning and Multimodal Microscopy
We combine scanning electron microscopy (SEM) images of 347H stainless steel as training data and electron backscatter diffraction (EBSD) micrographs as pixel-wise labels for grain boundary detection as a semantic segmentation task.
Algorithmic Determination of the Combinatorial Structure of the Linear Regions of ReLU Neural Networks
We algorithmically determine the regions and facets of all dimensions of the canonical polyhedral complex, the universal object into which a ReLU network decomposes its input space.
Local and global topological complexity measures OF ReLU neural network functions
We apply a generalized piecewise-linear (PL) version of Morse theory due to Grunert-Kuhnel-Rote to define and study new local and global notions of topological complexity for fully-connected feedforward ReLU neural network functions, F: R^n -> R. Along the way, we show how to construct, for each such F, a canonical polytopal complex K(F) and a deformation retract of the domain onto K(F), yielding a convenient compact model for performing calculations.
Linear discriminant initialization for feed-forward neural networks
Informed by the basic geometry underlying feed forward neural networks, we initialize the weights of the first layer of a neural network using the linear discriminants which best distinguish individual classes.
