THE BIT GENERATOR AND TIME SERIES PREDICTION

TL;DR

This paper analyzes the dynamics of a Bit-Generator perceptron model for time series prediction, revealing finite-time learnability of its cyclical behavior and generalization properties.

Contribution

It introduces a novel perceptron-based Bit-Generator model and characterizes its long-term dynamics and learnability of cycles in finite time.

Findings

Cycle periods scale polynomially with network size

Finite training sets achieve zero generalization error on cycles

Finite-time learning of rule projections is possible

Abstract

Generation and prediction of time series is analyzed for the case of a Bit-Generator: a perceptron where in each time step the input units are shifted one bit to the right with the state of the leftmost input unit set equal to the output unit in the previous time step. The long-time dynamical behavior of the Bit-Generator consists of cycles whose typical period scale polynomially with the size of the network and whose spatial structure is periodic with a typical finite wave length. The generalization erroron a cycle is zero for a finite training set and global dynamical behaviors such as the cycle period can also be learned in a finite time. Hence, a projection of a rule can be learned in a finite time.