Peter Hinz

Peter Hinz

For fixed training data and network parameters in the other layers the L1 loss of a ReLU neural network as a function of the first layer's parameters is a piece-wise affine function. We use the Deep ReLU Simplex algorithm to iteratively minimize the loss monotonically on adjacent vertices and analyze the trajectory of these vertex positions. We empirically observe that in a neighbourhood around a local minimum, the iterations behave differently such that conclusions on loss level and proximity of the local minimum can be made before it has been found: Firstly the loss seems to decay exponentially slow at iterated adjacent vertices such that the loss level at the local minimum can be estimated from the loss levels of subsequently iterated vertices, and secondly we observe a strong increase of the vertex density around local minima. This could have far-reaching consequences for the design of new gradient-descent algorithms that might improve convergence rate by exploiting these facts.

Dominik Alfke, Weston Baines, Jan Blechschmidt et al.

We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of labelled training data, our methodology is capable of predicting the labels of the test data almost always even if the training data is entirely unrelated to the test data. In other words, we prove in a specific setting that as long as one has access to enough data points, the quality of the data is irrelevant.