An Algorithm for Training Polynomial Networks
This work addresses efficient training for deep polynomial networks, offering a universal learner with theoretical guarantees, though it appears incremental in the context of existing deep learning methods.
The paper tackles the problem of training deep polynomial networks by introducing the Basis Learner algorithm, which guarantees decreasing training error and can achieve zero error under mild conditions, with preliminary experimental results provided.
We consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of this paper is the derivation of an efficient layer-by-layer algorithm for training such networks, which we denote as the \emph{Basis Learner}. The algorithm is a universal learner in the sense that the training error is guaranteed to decrease at every iteration, and can eventually reach zero under mild conditions. We present practical implementations of this algorithm, as well as preliminary experimental results. We also compare our deep architecture to other shallow architectures for learning polynomials, in particular kernel learning.