title: On the Capacity and Superposition of Minima in Neural Network Loss Function Landscapes
abstract: Minima of the loss function landscape of a neural network are locally optimal sets of
  weights that extract and process information from the input data to make outcome predictions. 
  In underparameterised networks, the capacity of the weights may be insufficient to fit all the relevant information. 
  We demonstrate that different local minima specialise in certain aspects of the learning problem, and process the input
  information differently. This effect can be exploited using a meta-network in
  which the predictive power from multiple minima of the LFL is combined to produce a better
  classifier. With this approach, we can increase the area under the receiver operating characteristic curve
  (AUC) by around $20\%$ for a complex learning problem. 
  We propose a theoretical basis for combining minima and show how a meta-network can
  be trained to select the representative that is used for classification of a
  specific data item. Finally, we present an analysis of symmetry-equivalent
  solutions to machine learning problems, which provides a systematic means to improve the
  efficiency of this approach.
authors: Maximilian Paul Niroomand John William Roger Morgan Conor T Cafolla David John Wales
hIndex: Conor T Cafolla 2