# Serializing and deserializing stable states of Hopfield networks

I am looking for simple artificial neural networks that may perform the following serializing task.

Consider two identical Hopfield networks, one being at rest, the other being in a stable state of acitivity (a subset of its neurons firing synchronously).

The task is to connect these two networks to a serializer and a deserializer network with the serializer passing only a sequence of signals to the deserializer (along one single line) such that the stable state of the first network will be reconstructed in the second network, just by the specific sequence of signals.

Can be seen at a glance that this task cannot be solved with (de)serializers made out of McCulloch-Pitts neurons alone?

If it can not be solved: which kind of neurons would be needed?

If it can be solved: how (in the most simple way)? (For simplicity's sake you may consider two Hopfield networks of only three MP neurons each.)

Note, that not the total of $n$ (e.g. 3) bits (to describe completely the state of network A) has to be transferred (because of the reconstruction abilities of the identical network B). The other way around: network B might reach the copied state earlier than the end of message arrived.

• Given that Hopfield networks are content-addressable memories would it be acceptable for me to post an answer using a different form of content-addressable memory, such as a NEF/SPA associative memory? Additionally, why are you using a Hopfield network? May I ask what the greater context of this extremely interesting question is? – Seanny123 Sep 14 '17 at 16:51
• Of course it would. And I used Hopfield networks only because I know them quite well (having attractors and the like). Concerning the greater context: I'll do my best to provide it in an addendum. – Hans-Peter Stricker Sep 14 '17 at 17:01
• Hopfield networks consist of McCulloch-Pitts neurons (which are good approximations of integrate-and-fire neurons), they are content-addressable memories, they have stable attractors,... That's why I started with them. – Hans-Peter Stricker Sep 14 '17 at 17:13
• To distill your question further, are you just trying to transfer knowledge between two content-addressable memories or are you also trying to change the state? – Seanny123 Sep 14 '17 at 23:43
• After having understood how the former works I definitely would also try the latter. But starting with transfer seems more tractable, doesn't it. – Hans-Peter Stricker Sep 15 '17 at 5:24