ECCC-Report TR94-017https://eccc.weizmann.ac.il/report/1994/017Comments and Revisions published for TR94-017en-usMon, 12 Dec 1994 00:00:00 +0200
Paper TR94-017
| Neural Nets with Superlinear VC-Dimension |
https://eccc.weizmann.ac.il/report/1994/017It 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.
Mon, 12 Dec 1994 00:00:00 +0200https://eccc.weizmann.ac.il/report/1994/017