On Hopfield Networks. From the general model to a special… | by Arun Jagota | Oct, 2024

From the final mannequin to a particular case

The 2024 Nobel Prize in Physics went to John Hopfield and Geoffrey Hinton, John Hopfield on his work on the so-called Hopfield Community.

Just a few a long time again, my PhD thesis was on Hopfield-style Networks. I figured this was time to put in writing this put up.

I’ll concentrate on Hopfield networks. I’ll start with the best instance and illustrate the way it works, then deliver within the idea of an power perform and minimizing it domestically, then cowl the particular case launched in my PhD thesis, then come again to the extra normal case and focus on associative recollections and optimization use instances, then come again to the particular case to instantiate these purposes in a extra particular setting.

Let’s start at first. First off, what’s a Hopfield Community?

Contemplate the image beneath.

Interpret it as follows. We now have two neurons, every can tackle a worth of 1 (suppose “firing”) or -1 (suppose “not firing”). The 2 neurons are linked by a optimistic weight, denoting a synapse of optimistic affect. Which means that, from the attitude of any one of many neurons, say the primary one, it desires the opposite one to be in the identical state as it’s — “firing” or “not firing”.