Eric Baum to speak on formal results for generalization in neural nets

[Lorien Y. Pratt]

				 Fall, 1988  
		     Neural Networks Colloquium Series 
				 at Rutgers  


		  What Size Net Gives Valid Generalization?
		  -----------------------------------------

				Eric B. Baum
			Jet Propulsion Laboratory
		    California Institute of Technology
			   Pasadena, CA. 91109

		  
		    Room 705 Hill center, Busch Campus  
		    Friday October 28, 1988 at 11:10 am 
		    Refreshments served before the talk

				   Abstract   


      We address the question of when a network can be expected to generalize
      from m random training examples chosen from some arbitrary probability
      distribution, assuming that future test examples are drawn from the
      same distribution. Among our results are the following bounds on
      appropriate sample vs. network size. Assume 0 < e <= 1/8. We show that
      if m >= O( WlogN/e log(1/e)) examples can be loaded on a feedforward
      network of linear threshold functions with N nodes and W weights, so
      that at least a fraction 1 - e/2 of the examples are correctly
      classified, then one has confidence approaching certainty that the
      network will correctly classify a fraction 1 - e of future test
      examples drawn from the same distribution. Conversely, for
      fully-connected feedforward nets with one hidden layer, any learning
      algorithm using fewer than Omega(W/e) random training examples will,
      for some distributions of examples consistent with an appropriate
      weight choice, fail at least some fixed fraction of the time to find a
      weight choice that will correctly classify more than a 1 - e fraction
      of the future test examples.