<p>After doing some additional research, I think the answer is yes. It just means using a fixed timestep for the continuous-time activation equation (as described <a href="http://www.scholarpedia.org/article/Hopfield_network#Graded_neuron_response_and_continuous_variables">here</a>). Since this is a differential equation, implementing it in software requires implementing a numerical integration method. I recommend the <a href="http://www.genesis-sim.org/BABEL/gum-tutorials/cornelis/doc/html/node9.html">Exponential Euler Method</a> as a starting point, because it's relatively simple and it's designed for differential equations of the sort that's used for the continuous Hopfield network.</p>

CC BY-SA 3.0
2012-12-20T22:15:27.477Z
2012-12-20T22:15:27.477Z
visual-kinetic
<p>I've found plenty of resources on <a href="http://en.wikipedia.org/wiki/Hopfield_network" rel="nofollow">Hopfield networks</a> that use either discrete variables for both activation level and time or continuous variables for both activation level and time. <strong>Is it possible to construct a Hopfield neural network that uses a continuous variable for activation level and a discrete variable for time?</strong> If it is possible, can anyone offer resources and/or tips on how to construct one in software?</p>

CC BY-SA 3.0
2012-12-18T22:21:57.627Z
I don't know, but here is the reverse: [continuous time with binary neurons](http://users.ics.aalto.fi/orponen/papers/nc2000.pdf) Orponen, P., & Šıma, J. (2000)
Jeff
<neural-network>
Is a Hopfield network with a continuous activation variable and a discrete time variable possible?
visual-kinetic
# Is a Hopfield network with a continuous activation variable and a discrete time variable possible?

(Asked by: username_0 on 2012-12-18)

I've found plenty of resources on [Hopfield networks](http://en.wikipedia.org/wiki/Hopfield_network) that use either discrete variables for both activation level and time or continuous variables for both activation level and time. **Is it possible to construct a Hopfield neural network that uses a continuous variable for activation level and a discrete variable for time?** If it is possible, can anyone offer resources and/or tips on how to construct one in software?

**Tags:** neural-network

> **Comments:**
> **username_1**: I don't know, but here is the reverse: [continuous time with binary neurons](http://users.ics.aalto.fi/orponen/papers/nc2000.pdf) Orponen, P., & Šıma, J. (2000)  

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## 1 answers

### Answer by username_0 on 2012-12-20. Score: 5 | Accepted answer

After doing some additional research, I think the answer is yes. It just means using a fixed timestep for the continuous-time activation equation (as described [here](http://www.scholarpedia.org/article/Hopfield_network#Graded_neuron_response_and_continuous_variables)). Since this is a differential equation, implementing it in software requires implementing a numerical integration method. I recommend the [Exponential Euler Method](http://www.genesis-sim.org/BABEL/gum-tutorials/cornelis/doc/html/node9.html) as a starting point, because it's relatively simple and it's designed for differential equations of the sort that's used for the continuous Hopfield network.


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