4 accepted papers
Finding paths with optimal properties is a foundational problem in computer science. The notions of shortest paths (minimal sum of edge costs), minimax paths (minimal maximum edge weight), reliability of a path and many others all arise as special cases of the "algebraic path problem" (APP). Indeed,…
Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we highlight a learning bi…
Training neural networks involves finding minima of a high-dimensional non-convex loss function. Relaxing from linear interpolations, we construct continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100. Surprisingly, the paths are essentially flat in both the…
Learned boundary maps are known to outperform hand-crafted ones as a basis for the watershed algorithm. We show, for the first time, how to train watershed computation jointly with boundary map prediction. The estimator for the merging priorities is cast as a neural network that is convolutional (ov…