<p><strong>Short answer</strong><br>
In artificial neural networks currents are not involved, other than those flowing <em>in silico</em> in your pc. Instead, those currents are represented by weighted mathematical functions.</p>

<p><strong>Background</strong><br>
Artificial neural networks as applied in machine learning (<em>e.g.</em>, <a href="https://machinelearningmastery.com/what-is-deep-learning/" rel="nofollow noreferrer">deep learning</a>) perform stuff like automatic feature extraction from raw data, also called feature learning. These models are algorithms that have little to do with the basic physiology of neurons. Hence, current/current density is not a matter of interest. It's the coupling between elements that matters, namely which cells couple to which cells and how strong that interaction is (Fig. 1).</p>

<blockquote>
  <p>A given node [(Fig. 1)] takes the weighted sum of its inputs, and
  passes it through a non-linear activation function. This is the output
  of the node, which then becomes the input of another node in the next
  layer. The signal flows from left to right, and the final output is
  calculated by performing this procedure for all the nodes. Training
  this deep neural network means learning the weights associated with
  all the edges.</p>
</blockquote>

<p><sup>source: <a href="https://towardsdatascience.com/applied-deep-learning-part-1-artificial-neural-networks-d7834f67a4f6" rel="nofollow noreferrer">Towards Science</a></sup></p>

<p>In other words, there is no current involved, only weighted functions.</p>

<p><a href="https://i.sstatic.net/TL8Ix.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/TL8Ix.png" alt="ANN"></a>
<sup>Artificial neural network. source: <a href="https://towardsdatascience.com/applied-deep-learning-part-1-artificial-neural-networks-d7834f67a4f6" rel="nofollow noreferrer">Towards Science</a></sup></p>

CC BY-SA 4.0
2018-09-07T14:37:12.357Z
So what's the mathematical/physics formalism to study the interactions?
0x90
CC BY-SA 4.0
2018-09-07T15:48:30.460Z
@0x90 I think you need to do a bunch of your own research here before asking such broad questions. Especially because it sounds like you want to approach this with a research interest.
Bryan Krause
CC BY-SA 4.0
2018-09-07T15:50:15.657Z
@BryanKrause I have something in mind, but I couldn't find the standard approach while googling stuff. That's why I think it's a legit question.
0x90
CC BY-SA 4.0
2018-09-07T15:51:27.923Z
There is no such thing as 'the standard approach' here, and the content of your original question also suggests you have a bit to learn first.
Bryan Krause
CC BY-SA 4.0
2018-09-07T12:24:00.127Z
2018-09-13T09:09:44.523Z
2018-09-13T09:09:44.523Z
AliceD
<p>How do neuroscientists define current/current densities in artificial neural networks? </p>

<p>Assume I have some deep network and I would like to study its dynamic/evolution in time during the training session what kind of model are there to study the flow?  </p>

<p>Maybe there is some information I can extract from the PDE's of back-propagation? or some evolution of the Graph <span class="math-container">$G=(V,E)$</span> in time. </p>

CC BY-SA 4.0
2018-09-08T16:49:46.777Z
Related: https://psychology.stackexchange.com/q/16269/4397
Seanny123
<theoretical-neuroscience>
How to define "current" in artificial neural network?
0x90
# How to define "current" in artificial neural network?

(Asked by: username_0 on 2018-09-07)

How do neuroscientists define current/current densities in artificial neural networks?

Assume I have some deep network and I would like to study its dynamic/evolution in time during the training session what kind of model are there to study the flow?

Maybe there is some information I can extract from the PDE's of back-propagation? or some evolution of the Graph $G=(V,E)$ in time.

**Tags:** theoretical-neuroscience

> **Comments:**
> **username_1**: Related: https://psychology.stackexchange.com/q/16269/4397  

---

## 1 answers

### Answer by username_2 on 2018-09-07. Score: 4

**Short answer**  
In artificial neural networks currents are not involved, other than those flowing *in silico* in your pc. Instead, those currents are represented by weighted mathematical functions.

**Background**  
Artificial neural networks as applied in machine learning (*e.g.*, [deep learning](https://machinelearningmastery.com/what-is-deep-learning/)) perform stuff like automatic feature extraction from raw data, also called feature learning. These models are algorithms that have little to do with the basic physiology of neurons. Hence, current/current density is not a matter of interest. It's the coupling between elements that matters, namely which cells couple to which cells and how strong that interaction is (Fig. 1).

> A given node [(Fig. 1)] takes the weighted sum of its inputs, and
> passes it through a non-linear activation function. This is the output
> of the node, which then becomes the input of another node in the next
> layer. The signal flows from left to right, and the final output is
> calculated by performing this procedure for all the nodes. Training
> this deep neural network means learning the weights associated with
> all the edges.

source: [Towards Science](https://towardsdatascience.com/applied-deep-learning-part-1-artificial-neural-networks-d7834f67a4f6)

In other words, there is no current involved, only weighted functions.

[![ANN](https://i.sstatic.net/TL8Ix.png)](https://i.sstatic.net/TL8Ix.png)
Artificial neural network. source: [Towards Science](https://towardsdatascience.com/applied-deep-learning-part-1-artificial-neural-networks-d7834f67a4f6)

> **Comments:**
> **username_0**: So what's the mathematical/physics formalism to study the interactions?  
> **username_3**: @username_0 I think you need to do a bunch of your own research here before asking such broad questions. Especially because it sounds like you want to approach this with a research interest.  
> **username_0**: @BryanKrause I have something in mind, but I couldn't find the standard approach while googling stuff. That's why I think it's a legit question.  
> **username_3**: There is no such thing as 'the standard approach' here, and the content of your original question also suggests you have a bit to learn first.  

---

