ABSTRACT
An adaptive logic network (ALN) is a multilayer perceptron that accepts vectors of real (or floating point) values as inputs and produces a logic 0 or 1 as output. The ALN has a number of linear threshold units (perceptrons) acting on the network inputs, and their (Boolean) outputs feed into a tree of logic gates of types AND and OR. An ALN represents a real-valued function of real variables by giving a logic 1 response to points on and under the graph of the function, and a logic 0 otherwise. It cannot compute a real-valued function directly, but it can provide information about how to perform that computation in a separate decision-tree-based program. If a function is invertible, then the same ALN can be used to derive a second decision tree to compute an inverse. Another way to look at function synthesis is that linear functions are combined by a tree expression of MAXIMUM and MINIMUM operations. In this way, ALNs can approximate any continuous function defined on a compact set to any degree of precision. The logic tree structure can control qualitative properties of learned functions, for example convexity. Constraints can be imposed on monotonicities and partial derivatives. ALNs can be used for prediction, data analysis, pattern recognition and control applications. They may be particularly useful for extremely large systems, where lazy evaluation allows large parts of a computation to be omitted. A second, earlier type of ALN is also discussed where the inputs are fixed thresholds on variables and the nodes adapt by changing their logical functions.
