Learning Large-Alphabet and Analog Circuits with Value Injection Queries

Abstract. We consider the problem of learning an acyclic discrete circuit with n wires, fan-in bounded by k and alphabet size s using value injection queries. For the class of transitively reduced circuits, we develop the Distinguishing Paths Algorithm, that learns such a circuit using (ns)O(k) value injection queries and time polynomial in the number of queries. We describe a generalization of the algorithm to the class of circuits with shortcut width bounded by b that uses (ns)O(k+b) value injection queries. Both algorithms use value injection queries that fix only O(kd) wires, where d is the depth of the target circuit. We give a reduction showing that without such restrictions on the topology of the circuit, the learning problem may be computationally intractable when s = nΘ(1) , even for circuits of depth O(log n). We then apply our largealphabet learning algorithms to the problem of approximate learning of analog circuits whose gate functions satisfy a Lipschitz condition. Fina...

• Type: Conference
• Year: 2007
• Where: COLT
• Authors: Dana Angluin, James Aspnes, Jiang Chen, Lev Reyzin
• Keywords: Acyclic Discrete Circuit, Algorithms, COLT 2007, Machine Learning, Value Injection Queries