An error reducing approach to machine learning using multi-valued functional decomposition

Abstract

This paper considers minimization of incompletely specified multi-valued functions using functional decomposition. While functional decomposition was originally created for the minimization of logic circuits, this paper uses the decomposition process for both machine learning and logic synthesis of multi-valued functions. As it turns out, the minimization of logic circuits can be used in the concept of "learning" in machine learning, by reducing the complexity of a given data set. A main difference is that machine learning problems normally have a large number of output don't cares. Thus, the decomposition technique presented in this paper is focused on functions with a large number of don't cares. There have been several papers that have discussed the topic of using multi-valued functional decomposition for functions with a large number of don't cares.The novelty brought with this paper is that the proposed method is structured to reduce the resulting "error" of the functional decomposer, where "error" is a measure of how well a machine learning algorithm approximates the actual, or true function.

Inductive learning of quantum behaviors

“…It is well-known that logic synthesis methods applied to binary functions with many don't cares (don't knows) are used as a base of various machine learning (ML) approaches [1,2,3]. The learning process creates circuit description and as a byproduct converts don't cares to cares trying to satisfy the Occam Razor Principle of the circuit's simplicity.…”

Learning hardware using multiple-valued logic - Part 1: introduction and approach

“…In past research, we have used and compared (using software) various network structures for learning: two-level AND/OR (sum-of-products or DNFs), 31 decision trees (using C4.5 software and multilevel decomposition structures. [21][22][23]32,33 We have also studied various logic, nonlogic, and mixed optimization methods, for example, search, 13 rule-based, set-covering, maximum clique, graph coloring, genetic algorithm (including mixtures of logic and genetic algorithm approaches), 34,35 genetic programming, 36 ANNs, and simulated annealing. We compared the resulting complexity of our networks (using an approach based on Occam's Razor), as well as various ways of controlling the number of errors in the learning process.…”

“…We compared the resulting complexity of our networks (using an approach based on Occam's Razor), as well as various ways of controlling the number of errors in the learning process. [21][22][23][24] Because of their strong theoretically proven properties, the decomposed function cardinality and its extensions for multiple-valued (MV) logic [20][21][22]33 work well as common measures of network complexity. 22,25 Our conclusion, based on these investigations, is that logic approaches (especially the MV-decomposition techniques) combined with smart heuristic strategies and good data representations usually provide superior results compared to other approaches.…”

“…In our experiments, evolutionary approaches provided especially poor results. 6,21,35,36 Genetic algorithms might perform well in other applications (such as analog circuit design or specific, isolated subproblems in digital circuit design). But our experience and the literature did not identify a single problem in which a genetic algorithm-based approach was superior to using a handcrafted heuristic algorithm for the design of complete binary or MV-logic networks.…”

“…They lead to high-quality learning results that have no overfitting and small learning errors, or those that lead to knowledge generalization or discovery. [20][21][22][23][24][25][26] However, the software realizations of these algorithms use complex data structures (such as binary decision diagrams 26 ) and controls that are difficult to directly realize in hardware. For instance, recursion and decision diagrams are difficult to parallelize or pipeline and, in general, to implement in hardware structures.…”