A Universal Approximation Result for Difference of log-sum-exp Neural Networks

no code implementations • 21 May 2019 • Giuseppe C. Calafiore, Stephane Gaubert, Member, Corrado Possieri

We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation function in the output node (LSE networks) is a smooth universal approximator of continuous functions over convex, compact sets.

Log-sum-exp neural networks and posynomial models for convex and log-log-convex data

no code implementations • 20 Jun 2018 • Giuseppe C. Calafiore, Stephane Gaubert, Corrado Possieri

Under a suitable exponential transformation, the class of LSET functions maps to a family of generalized posynomials GPOST, which we similarly show to be universal approximators for log-log-convex functions.