Computer generated higher order expansions
Generate an AI Snapshot to get a quick, structured summary of this paper.
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
This article implemented a computer algorithm to generate all necessary analytic terms for the Boltzmann machine partition function thus leading to lower bounds of any order, and it turns out that the extra variational parameters can be optimized analytically.
Abstract
In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann machine partition function thus leading to lower bounds of any order. It turns out that the extra variational parameters can be optimized analytically. We show that bounds upto nineth order are still reasonably calculable in practical situations. The generated terms can also be used as extra correction terms (beyond TAP)in mean field expansions.