Neural Teleportation

Abstract

In this paper, we explore a process called neural teleportation, a mathematical consequence of applying quiver representation theory to neural networks. Neural teleportation teleports a network to a new position in the weight space and preserves its function. This phenomenon comes directly from the definitions of representation theory applied to neural networks and it turns out to be a very simple operation that has remarkable properties. We shed light on the surprising and counter-intuitive consequences neural teleportation has on the loss landscape. In particular, we show that teleportation can be used to explore loss level curves, that it changes the local loss landscape, sharpens global minima and boosts back-propagated gradients at any moment during the learning process.

Artificial Neural Networks Using Quiver Representations of Finite Cyclic Groups

“…This choice becomes especially pertinent when creating a quiver group algebra representation, where we draw connections with neural networks. These representations provide us with the means to compare and contrast various artificial neural networks through the lens of morphisms of quiver representations [3][4][5] .…”