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There seems to be general agreement that theoretical Hopfield networks (consisting of artifical neurons, namely McCulloch-Pitts neurons) are biologically rather implausible, among other reasons because of their (rather strictly) symmetric synaptic weights. On the other side, some authors claim that there are neural assemblies in the brain that qualitatively behave like Hopfield networks, i.e.

  • they are strongly interconnected
  • they synaptically store a limited number of (activity) patterns
  • which they reach as attractors when fed with noisy or incomplete input patterns
  • they "learn" (mainly) by the Hebb rule

The system of hippocampal CA3 neurons is suggested to be one such assembly.

My questions:

  1. Is there an agreement among experts that hippocampal CA3 neurons really behave similar to a Hopfield network?

  2. Which other assemblies (possibly nuclei?) are believed to behave similar to a Hopfield network, too? (Some examples would be welcome.)

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  • $\begingroup$ For the benefit of others coming across the question, could you include a brief explanation of what a Hopfield neural net is? $\endgroup$ – arboviral Aug 21 '17 at 15:22
  • $\begingroup$ "Is there an agreement among experts that hippocampal CA3 neurons really behave similar to a Hopfield network?" - The difficulty with such agreement is that behave similar is very non-specific. Probably no expert will say either CA3 behaves nothing like a Hopfield network, nor CA3 behaves totally like a Hopfield network; rather, in some (perhaps many) circumstances or for some functions, Hopfield networks are sufficient to replicate CA3-like behavior. $\endgroup$ – Bryan Krause Aug 21 '17 at 16:52
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I think it really depends on the level of detail and accuracy needed.

Giving a quick look on Google Scholar, it appears that indeed there is (or at least was) a belief that hippocampal networks could be reasonably modelled by Hopfield networks (e.g. see Neuromodulatory control of hippocampal function: towards a model of Alzheimer’s disease by Menschik and Finkel, and its references). However, many of these papers are somewhat old (though this certainly does not invalidate them!) and computational neuroscience moves fairly fast. So yes, to a certain extent, after reading some papers that corroborate it, it might appear that some macroscopic behaviour of CA3 neurons can be reproduced by Hopfield networks.

That being said, in more recent works, I have personally never seen anyone model biological neurons with such simple neurons, when cellular level accuracy is required (often it isn't). At least stochastic Hodgkin-Huxley or integrate-and-fire, for instance, are used, even if as point processes (so that it is a system of ODEs/SDEs, not PDEs/SPDEs). Even the neurons used in today's deep neural networks (which make no effort towards biophysical plausibility) are (or at least can be) more complex than sigmoiding a linear combination of inputs! Also, for slightly larger scales, as you note, the connectivity structure is extremely unrealistic. (Just look at the histology!)

So anyway, it depends on the goal. For simple macroscopic, qualitative similarities it may suffice. But if the goal is biophysical accuracy of simulation then I would look at newer papers and see what they do. Check out Synaptic mechanisms of pattern completion in the hippocampal CA3 network by Guzman et al.

As for your second question, just searching for papers on Hopfield networks finds a number of them. However, they appear to be largely computational or mathematical, rather than neuroscientific modelling papers. Maybe others can find better ones though!

Disclaimer: I am not in the field of hippocampal modelling nor have I worked much with Hopfield networks, so take my thoughts with a grain of salt. My suggestion is to do an extensive literature search, and post what you find as an answer here :)

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