A Rule Chaining Architecture Using a Correlation Matrix Memory

Abstract

This paper describes an architecture based on superimposed distributed representations and distributed associative memories which is capable of performing rule chaining. The use of a distributed representation allows the system to utilise memory efficiently, and the use of superposition reduces the time complexity of a tree search to O(d), where d is the depth of the tree. Our experimental results show that the architecture is capable of rule chaining effectively, but that further investigation is needed to address capacity considerations.

ENAMeL: A Language for Binary Correlation Matrix Memories

“…The analysis so far performed has been conservative, and so in order to determine any improvement in memory requirements that may actually result from using ENAMeL we have run the same experiments as we described in our previous work [1]. For this work, however, we used ENAMeL instead of MATLAB and recorded the memory required when storing the CMMs using the sparse binary Yale format.…”

“…The experimental methodology is exactly as in our previous work [1]. Briefly, for each value of d, b, and l, we:…”

“…As such, there are a few basic operations that are required-the ability to create vectors and matrices, and to learn and recall associations. Research into complex CMM-based architectures such as the Cellular Associative Neural Network [20] or ARCA [1] has shown that in addition to these basic operations, a number of other operations are also necessary. These are detailed in section 4 below.…”

“…Rule chaining and tree searches are used in many fields, for instance artificial intelligencesearching a set of rules to determine if there is a path from the starting state to the goal state. We have presented the Associative Rule Chaining Architecture (ARCA) as an architecture which performs rule chaining or tree search using correlation matrix memories [1]. This architecture uses superposition of search states in order to allow a depth-first search to be performed with a time complexity of O(d), an exponential improvement over traditional methods such as depth-first search with have a time complexity of O(b d )-where d is the depth of the tree and b is the branching factor, the number of children of a node.…”

“…Our previous results demonstrated that ARCA is able to search multiple branches of a tree simultaneously, while maintaining separation between each of the branches [1]. As the branches are searched simultaneously, the time complexity of this search is reduced from…”