<table><tr><th>From:</th><th>Misha Gromov &lt;</th></tr><tr><td>Sent:</td><td>Wednesday, October 11, 2017 7:47 PM</td></tr><tr><td>To:</td><td>Jeffrey E.</td></tr><tr><td>Subject:</td><td>Re: Fwd:</td></tr></table>

Like Bach's comments:)

On Wed, 11 Oct 2017 20:01:46 +0200, jeffrey E. wrote:

Forwarded <u>message</u>
Fro=: Joscha Bach <
Date: Wed, Oct 11, 2017 at 7:55 PM
Subject: Re:
To: Jeffrey Eps=ein <jeevacation@gmail.com <mailto:jeevacation@gmail.com> =gt;

After skimming their paper, the idea seemed unexcitin= to me at first: basically, if we have enough feature dimensions we can al=ost always find a linear separation. This is also related to how Support V=ctor Machines work: they project the data into an extremely high-dimension=l space, find a separating hyperplane with linear regression, and then pro=ect that plane back into the original space as the separator. A similar id=a is behind Echo State networks, which use a randomly wired recurrent neur=l network and then only train the output layer with a single linear regres=ion.

The authors take an existing trained neural network, and whenev=r it makes a mistake, they train a linear classifier on the network state =nd data, i.e. they try to find out when the network goes wrong. Instead of=improving the network (which is also likely to make it worse in other case=), they add an additional layer to it. For engineering, this makes a lot o= sense, because large neural networks are cheap to use and deploy but expe=sive to train.

On a more philosophical level, it is tempting t= ask if that might be a general learning principle for brains: when you do='t perform well, add more control structure on top. It probably makes sens= whenever you are confident that training the existing structure won't imp=ove it that much, but unless training the weights in an existing network, =t also adds quite a few milliseconds to the processing time. There is prob=bly an optimal tradeoff for this. The other thing is that the new layer is=a linear classifier only (at least in this paper), and it is creating a lo=al override on the system's results, instead of integrating with it, somew=at similar to how reasoning might override our subconscious behavior. One =f the drawbacks is that this won't allow us to use the new layer for simul=ting/understanding the structure of the domain modeled by the rest of the =etwork.

– Joscha

On Oct 10, 2017, at 09:43, jeffrey E. <jeevacat=on@gmail.com <mailto:jeevacation@gmail.com> wrote:
> 
> h=tps://www.sciencedaily.com/releases/2017/08/170821102725.htm
<https://www=2sciencedaily.com/releases/2017/08/170821102725.htm>

>=

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