A Learning Algorithm for Boltzmann Machines*

TLDR

Massively parallel networks of simple processing elements possess high computational power due to the communication bandwidth of their hardware connections, allowing rapid application of system knowledge to problem instances and making them well suited for large constraint‑satisfaction searches when a suitable parallel search technique and efficient internal representations are identified. The authors aim to develop a general parallel search method based on statistical mechanics that yields a learning rule for adjusting connection strengths to incorporate task‑domain knowledge efficiently. The method employs statistical mechanics to guide the modification of connection strengths, enabling efficient encoding of domain constraints in the network. In simple examples, the learning algorithm produces internal representations that are demonstrably the most efficient use of the preexisting connectivity structure.

Abstract

The computational power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections can allow a significant fraction of the knowledge of the system to be applied to an instance of a problem in a very short time. One kind of computation for which massively parallel networks appear to be well suited is large constraint satisfaction searches, but to use the connections efficiently two conditions must be met: First, a search technique that is suitable for parallel networks must be found. Second, there must be some way of choosing internal representations which allow the preexisting hardware connections to be used efficiently for encoding the constraints in the domain being searched. We describe a general parallel search method, based on statistical mechanics, and we show how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge about a task domain in an efficient way. We describe some simple examples in which the learning algorithm creates internal representations that are demonstrably the most efficient way of using the preexisting connectivity structure.