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The unsupervised aspect of getting things rolling in deep nets definitely seems to be super important. I don't know how to fix this :).halhttps://www.blogger.com/profile/02162908373916390369noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-4083434122023250682009-02-02T11:37:00.000-07:002009-02-02T11:37:00.000-07:00Another work which uses boosting to add units to a...Another work which uses boosting to add units to an MLP is <A HREF="jmlr.csail.mit.edu/papers/volume3/perkins03a/perkins03a.pdf" REL="nofollow">Grafting: Fast, Incremental Feature Selection by Gradient Descent in Function Space</A>.<BR/><BR/>As Yoshua indicated, though, the main difficulty in inducing a deep architecture is that a purely supervised signal does not seem sufficient to guide the optimization to a good minimum.Joseph Turianhttps://www.blogger.com/profile/06249878639857416906noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-81538523194295792392009-02-01T15:33:00.000-07:002009-02-01T15:33:00.000-07:00The connection between boosted linear classifiers ...The connection between boosted linear classifiers and one-hidden-layer neural networks has been studied in the past. See for example the NIPS'2005 paper on Convex Neural Networks <BR/> http://www.iro.umontreal.ca/%7Elisa/publications/index.php?page=publication&kind=single&ID=19<BR/><BR/>which shows that by successively adding the optimal linear classifier (as a weak learner) one could in principle find the global optimum of a 1-hidden layer neural net. Unfortunately, finding the optimal linear classifier is NP-hard. But more importantly, I agree that 1-hidden layer nets are not satisfying because they are too shallow.<BR/><BR/>I'm not sure I really understood your idea with 5 linear models and a 6th one added in such a way as to increase depth. To increase depth, the 6th one should see in its inputs the outputs of the previous ones. As noted by Peter Turney, this would turn the algorithm into something similar to Cascade Correlation. But looking back onto the goals and motivations of deep learning algorithms, something important would be missing: the discovery of intermediate representations that capture the variations in the input. But something else might be missing: the unsupervised component. Purely supervised greedy addition of layers does not work as well as unsupervised addition of layers, according to the experiments described in the NIPS'2006 paper by Bengio et al on Greedy Layerwise Training of Deep Networks (http://www.iro.umontreal.ca/%7Elisa/publications/index.php?page=publication&kind=single&ID=190). The authors conjectured that purely supervised greedy addition of layers was simply too greedy, not keeping enough of the input information (the part that cannot be exploited yet by a linear classifier but could be exploited later when more layers are added).<BR/><BR/><BR/>-- Yoshua BengioYoshua Bengiohttps://www.blogger.com/profile/01024092022366764581noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-1178059381572551612009-01-31T11:44:00.000-07:002009-01-31T11:44:00.000-07:00The algorithm you describe reminds me a bit of Cas...The algorithm you describe reminds me a bit of <A HREF="http://en.wikipedia.org/wiki/Cascade_correlation_algorithm" REL="nofollow">Cascade Correlation</A>.Peter Turneyhttps://www.blogger.com/profile/00074858095036682671noreply@blogger.com