<p><em>I thank all the commenters for the valuable feedback. I'm trying to improve this question (which I had long ago -- omg I'm getting old).</em></p>

<p>Is there a way to simply derive the generalization bounds for the classical perceptron model? More specifically, how to derive the maximum number of patterns that a N-large perceptron can store? And in the case of an NxN network of neurons, how to derive the number of patterns (or memories) and their basins of attractions? Are there simple methods, other than the ones invoking replica theory, as it's done in Gardner's works?</p>

<p>More details:</p>

<p>I'm basically referring to the great work of Elizabeth Gardner in this matter. I find that her work is often overlooked in the field of neuroscience, arguably because it is too difficult to understand its mathematical derivation. Yet, her results are so fundamental that many in the field are aware of them.</p>

<p>I couldn't find anywhere a simple explanation of her derivation and the implications of her results, in a terminology that also undergrads could also understand. Of course, I couldn't come up with one myself either. I suppose "Field Theory for Dummies" applied to theoretical neuroscience is what I'm really asking for...</p>

<p>See: <a href="http://iopscience.iop.org/0305-4470/21/1/030" rel="nofollow noreferrer">Gardner, E. "The space of interactions in neural network models." Journal of physics A: Mathematical and general 21.1 (1988): 257.</a></p>

CC BY-SA 3.0
2015-02-09T18:25:56.653Z
Title of your question is misleading. You mean the number of stable fixed points in a recurrent neural network? This is definitely not the classical perceptron model.
Memming
CC BY-SA 3.0
2016-08-08T17:58:05.567Z
I agree with @Memming. Voted for closing the question since "Field Theory for Dummies" is too broad of a question for this site. Even an explanation of the whole paper would be out of scope. So fabioedoardoluigialberto, if you could specify your question in more detail, maybe even quoting equations or figures from the paper, your chances of getting help would substantially increase :)
awakenting
CC BY-SA 3.0
2016-08-09T12:56:33.787Z
also, since you're mostly talking about the mathematical properties of neural networks, I'm convinced (once this question is narrowed down) that it would be more appropriate for cs.stackexchange.com
Seanny123
CC BY-SA 3.0
2017-09-21T14:44:12.787Z
Also, adding an actual question (ending with a question mark) might make things more clear. I realize a question is implied when you say _"I couldn't find anywhere a simple explanation of her derivation and the implications of her results, in a terminology that also undergrads could also understand."_, ... but writing a question might be a good exercise. ;) It might also make it more clear you are asking for quite a broad topic. Also consider narrowing it down as per the previous comments.
Steven Jeuris
<theoretical-neuroscience><neural-network>
How to derive the generalization bounds for the classical perceptron model?
fabioedoardoluigialberto
# How to derive the generalization bounds for the classical perceptron model?

(Asked by: username_0 on 2015-02-06)

*I thank all the commenters for the valuable feedback. I'm trying to improve this question (which I had long ago -- omg I'm getting old).*

Is there a way to simply derive the generalization bounds for the classical perceptron model? More specifically, how to derive the maximum number of patterns that a N-large perceptron can store? And in the case of an NxN network of neurons, how to derive the number of patterns (or memories) and their basins of attractions? Are there simple methods, other than the ones invoking replica theory, as it's done in Gardner's works?

More details:

I'm basically referring to the great work of Elizabeth Gardner in this matter. I find that her work is often overlooked in the field of neuroscience, arguably because it is too difficult to understand its mathematical derivation. Yet, her results are so fundamental that many in the field are aware of them.

I couldn't find anywhere a simple explanation of her derivation and the implications of her results, in a terminology that also undergrads could also understand. Of course, I couldn't come up with one myself either. I suppose "Field Theory for Dummies" applied to theoretical neuroscience is what I'm really asking for...

See: [Gardner, E. "The space of interactions in neural network models." Journal of physics A: Mathematical and general 21.1 (1988): 257.](http://iopscience.iop.org/0305-4470/21/1/030)

**Tags:** theoretical-neuroscience, neural-network

> **Comments:**
> **username_1**: Title of your question is misleading. You mean the number of stable fixed points in a recurrent neural network? This is definitely not the classical perceptron model.  
> **username_2**: I agree with @username_1. Voted for closing the question since "Field Theory for Dummies" is too broad of a question for this site. Even an explanation of the whole paper would be out of scope. So username_0, if you could specify your question in more detail, maybe even quoting equations or figures from the paper, your chances of getting help would substantially increase :)  
> **username_3**: also, since you're mostly talking about the mathematical properties of neural networks, I'm convinced (once this question is narrowed down) that it would be more appropriate for cs.stackexchange.com  
> **username_4**: Also, adding an actual question (ending with a question mark) might make things more clear. I realize a question is implied when you say _"I couldn't find anywhere a simple explanation of her derivation and the implications of her results, in a terminology that also undergrads could also understand."_, ... but writing a question might be a good exercise. ;) It might also make it more clear you are asking for quite a broad topic. Also consider narrowing it down as per the previous comments.  

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