<p>When the system grows matrix notation is used, as <strong>a</strong>=<strong>Wx</strong>, being <strong>a</strong> (input to activation function in hidden layer) and <strong>x</strong> (values from input layer) column vectors, transpose of (a1,a2,...a_m) and (x1,x2,...,x_n), and <strong>W</strong> a m-by-n matrix of dimensions m rows and n columns. The standard way to denote matrix elements is w(i,j) where "i" is the row number and "j" column number:</p>

<p><a href="https://i.sstatic.net/XL9H4.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/XL9H4.png" alt="enter image description here"></a>
(from <a href="https://en.wikipedia.org/wiki/Matrix_(mathematics)" rel="nofollow noreferrer">wiki</a>)</p>

<p>For this reason, the weight that applies to h4 from x3 is element in row 4 column 3 of the matrix W, that is, W(4,3) ( as your teachers advocates but with a sad lack of ability to explain ).</p>

<p>In your example:</p>

<p><a href="https://i.sstatic.net/NNVMu.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NNVMu.gif" alt="enter image description here"></a></p>

<p>Note: things are a few more complex when x1, x2, ... are itself vectors, but final conclusion is the same.</p>

<p>( PS: URGENT to allow latex notation on this stack exchange ! )</p>

CC BY-SA 3.0
2018-03-07T15:49:07.903Z
Indeed there seems to be a naming convention but a more elaborate and clear explanation would be appreciated. Even the author here has not explained the reason properly http://neuralnetworksanddeeplearning.com/chap2.html
Nav
CC BY-SA 3.0
2018-03-07T16:03:00.517Z
Which part of current explanation do you think must be expanded?
pasaba por aqui
CC BY-SA 3.0
2018-03-07T16:26:16.263Z
Depicting the weights of the ANN in my question as matrices could make it more intuitive. Thanks.
Nav
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2018-03-07T16:36:37.733Z
@Nav: answer edited
pasaba por aqui
CC BY-SA 3.0
2018-03-08T08:32:28.207Z
Lovely! That's a lot clearer now. Thanks Pasaba.
Nav
CC BY-SA 3.0
2018-03-06T07:57:56.087Z
2018-03-07T16:36:08.127Z
2018-03-07T16:36:08.127Z
pasaba por aqui
<p>In the diagram below, although the flow of information happens from the input to output layer, the labeling of weights appears reverse. Eg: For the arrow flowing from X3 to the fourth hidden layer node has the weight labeled as W(1,0) and W(4,3) instead of W(0,1) and W(3,4) which would indicate data flowing from the 3rd node of the 0'th layer to the 4th node of the 1st layer.  </p>

<p><a href="https://i.sstatic.net/YyD9E.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YyD9E.png" alt="enter image description here"></a></p>

<p>One of my neural networks teachers did not emphasize on this convention at all. Another teacher made it a point to emphasize on it.  </p>

<p>Is there a reason there is such an un-intuitive convention and is there really a convention?</p>

CC BY-SA 3.0
2018-03-06T08:30:25.620Z
@DuttaA: it should be always welcome student who thinks about things and arise questions to himself or publicly.
pasaba por aqui
CC BY-SA 3.0
2018-03-06T09:24:38.757Z
@pasabaporaqui Humans,lets get serious here.someone in Microsoft is working on ai project,however if it requires him/her to query through SE knowledge base,then we shouldn't bring here students course work but rather world real problems to solve, out of school.Humans,hope this can save your planetary civilisation.
quintumnia
CC BY-SA 3.0
2018-03-06T10:03:02.140Z
@quintumnia: If I must choice help students or Mycrosoft ... . But, being serious, taken into account that first comment has been similar to "it is a personal choice" ', I think the question is on-topic and  deserves an answer explaining the motivation under usual notation.
pasaba por aqui
CC BY-SA 3.0
2018-03-06T10:08:51.360Z
@pasabaporaqui If you analyze and comprehend this question very well,then it's right fit in cross validated community for effective feedback.Try to analyze it !
quintumnia
CC BY-SA 3.0
2018-03-06T12:19:14.170Z
@DuttaA: What is, according to you, a personal preference in my answer? Say that matrix notation is used in NN design ? The math notation for matrix elements ?
pasaba por aqui
CC BY-SA 3.0
2018-03-06T12:50:22.677Z
Guys, students are the ones going to spread false info in the professional world if concepts and standards are not clear. I am a seasoned StackExchange user and a working professional doing a part time course. A proper answer to this question will ensure that anyone Googling this question in future wont end up with a nonsensical concept. I wanted to know if it is a standard notation uniformly used and recognized across the world.
Nav
CC BY-SA 3.0
2018-03-06T12:59:03.043Z
@Nav: yes, there are a standard/common/usual/recommended notation, the one that your teachers are using, for the reason I've explain in my answer.
pasaba por aqui
<neural-networks>
Is there a naming convention for network weights for multilayer networks?
Nav
# Is there a naming convention for network weights for multilayer networks?

(Asked by: username_0 on 2018-03-06)

In the diagram below, although the flow of information happens from the input to output layer, the labeling of weights appears reverse. Eg: For the arrow flowing from X3 to the fourth hidden layer node has the weight labeled as W(1,0) and W(4,3) instead of W(0,1) and W(3,4) which would indicate data flowing from the 3rd node of the 0'th layer to the 4th node of the 1st layer.

[![enter image description here](https://i.sstatic.net/YyD9E.png)](https://i.sstatic.net/YyD9E.png)

One of my neural networks teachers did not emphasize on this convention at all. Another teacher made it a point to emphasize on it.

Is there a reason there is such an un-intuitive convention and is there really a convention?

**Tags:** neural-networks

> **Comments:**
> **username_1**: @DuttaA: it should be always welcome student who thinks about things and arise questions to himself or publicly.  
> **username_2**: @pasabaporaqui Humans,lets get serious here.someone in Microsoft is working on ai project,however if it requires him/her to query through SE knowledge base,then we shouldn't bring here students course work but rather world real problems to solve, out of school.Humans,hope this can save your planetary civilisation.  
> **username_1**: @username_2: If I must choice help students or Mycrosoft ... . But, being serious, taken into account that first comment has been similar to "it is a personal choice" ', I think the question is on-topic and  deserves an answer explaining the motivation under usual notation.  
> **username_2**: @pasabaporaqui If you analyze and comprehend this question very well,then it's right fit in cross validated community for effective feedback.Try to analyze it !  
> **username_1**: @DuttaA: What is, according to you, a personal preference in my answer? Say that matrix notation is used in NN design ? The math notation for matrix elements ?  
> **username_0**: Guys, students are the ones going to spread false info in the professional world if concepts and standards are not clear. I am a seasoned StackExchange user and a working professional doing a part time course. A proper answer to this question will ensure that anyone Googling this question in future wont end up with a nonsensical concept. I wanted to know if it is a standard notation uniformly used and recognized across the world.  
> **username_1**: @username_0: yes, there are a standard/common/usual/recommended notation, the one that your teachers are using, for the reason I've explain in my answer.  

---

## 1 answers

### Answer by username_1 on 2018-03-06. Score: 2 | Accepted answer

When the system grows matrix notation is used, as **a**=**Wx**, being **a** (input to activation function in hidden layer) and **x** (values from input layer) column vectors, transpose of (a1,a2,...a\_m) and (x1,x2,...,x\_n), and **W** a m-by-n matrix of dimensions m rows and n columns. The standard way to denote matrix elements is w(i,j) where "i" is the row number and "j" column number:

[![enter image description here](https://i.sstatic.net/XL9H4.png)](https://i.sstatic.net/XL9H4.png)
(from [wiki](https://en.wikipedia.org/wiki/Matrix_(mathematics)))

For this reason, the weight that applies to h4 from x3 is element in row 4 column 3 of the matrix W, that is, W(4,3) ( as your teachers advocates but with a sad lack of ability to explain ).

In your example:

[![enter image description here](https://i.sstatic.net/NNVMu.gif)](https://i.sstatic.net/NNVMu.gif)

Note: things are a few more complex when x1, x2, ... are itself vectors, but final conclusion is the same.

( PS: URGENT to allow latex notation on this stack exchange ! )

> **Comments:**
> **username_0**: Indeed there seems to be a naming convention but a more elaborate and clear explanation would be appreciated. Even the author here has not explained the reason properly http://neuralnetworksanddeeplearning.com/chap2.html  
> **username_1**: Which part of current explanation do you think must be expanded?  
> **username_0**: Depicting the weights of the ANN in my question as matrices could make it more intuitive. Thanks.  
> **username_1**: @username_0: answer edited  
> **username_0**: Lovely! That's a lot clearer now. Thanks Pasaba.  

---

