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Paper:

TR94-017 | 12th December 1994 00:00

Neural Nets with Superlinear VC-Dimension

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TR94-017
Authors:
Publication: 12th December 1994 00:00
Downloads: 1084
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Abstract:

It has been known for quite a while that the Vapnik-Chervonenkis dimension
(VC-dimension) of a feedforward neural net with linear threshold gates is at
most O(w log w), where w is the total number of weights in the neural net.
We show in this paper that this bound is in fact asymptotically optimal.
More precisely, we exhibit for any depth d >= 3 a large class of feedforward
neural nets of depth d with w weights that have VC-dimension Omega(w log w).
This lower bound holds even if the inputs are restricted to boolean values.
The proof of this result relies on a new method that allows us to encode
more "program-bits" in the weights of a neural net than previously thought
possible.



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