Learning large-alphabet and analog circuits with value injection queries

  • Authors:

  • Dana Angluin;James Aspnes;Jiang Chen;Lev Reyzin

  • Affiliations:

  • Computer Science Department, Yale University, New Haven, USA 06511;Computer Science Department, Yale University, New Haven, USA 06511;Center for Computational Learning Systems, Columbia University, New York, USA 10115;Computer Science Department, Yale University, New Haven, USA 06511

  • Venue:
  • Machine Learning
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

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=n 驴(1), even for circuits of depth O(log驴n). We then apply our large-alphabet learning algorithms to the problem of approximate learning of analog circuits whose gate functions satisfy a Lipschitz condition. Finally, we consider models in which behavioral equivalence queries are also available, and extend and improve the learning algorithms of (Angluin in Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, pp. 584---593, 2006) to handle general classes of gate functions that are polynomial time learnable from counterexamples.