Body: <p>I have read <a href="https://arxiv.org/pdf/2002.10857.pdf" rel="nofollow noreferrer">the paper about circle loss</a> for neural networks. I may have missed something, but I didn't find the way to compute the positive similarity and the negative similarity in the case of circle loss.</p>
  <p>The paper gives the equations for AM-SoftMax and Triplet loss, that can be computed from a unified loss function:</p>
  <p><a href="https://i.sstatic.net/VvSYP.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VvSYP.png" alt="Loss Function" /></a></p>
  <p>For example, in the case of AM-SoftMax, the positive and negative similarities are computed by the following way, <code>w</code> being the weights of the last fully connected layer, and <code>x</code> being the inputs of this last layer:</p>
  <p><a href="https://i.sstatic.net/TLXCt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/TLXCt.png" alt="positive similarity" /></a></p>
  <p><a href="https://i.sstatic.net/V495C.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/V495C.png" alt="negative similarity" /></a></p>
  <p>So my questions are:</p>
  <ol>
  <li><p>Should I compute the similarities for circle loss by the same way the paper compute them for AM-SoftMax ?</p>
  </li>
  <li><p>Should I compute the forward pass of the last fully connected layer with a standard product: <code>output[j] += weight[i][j] * input[i]</code>, followed by a standard SoftMax function ? Or by another way ?</p>
  </li>
  </ol>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-03-05T23:50:46.253Z
Comments.Text: Hello. Welcome to AISE. In general, each post should contain exactly one question. As a rule of thumb, if you can't put your **specific question** in the title (because maybe you have more than 1), then your post might be too broad. Moreover, note that programming questions are off-topic. However, if you're only trying to understand how the theory is connected to the code, then your questions are fine for our site.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-03-06T03:43:17.650Z
Comments.Text: I have reformulated my question, focalizing on the two problems I have with circle loss computation.
Comments.UserDisplayName: Bertrand125
Tags: <neural-networks><loss>
Title: How to compute circle loss?
UserDisplayName: Bertrand125
ThreadText: # How to compute circle loss?
  
  (Asked by: username_0 on 2022-03-05)
  
  I have read [the paper about circle loss](https://arxiv.org/pdf/2002.10857.pdf) for neural networks. I may have missed something, but I didn't find the way to compute the positive similarity and the negative similarity in the case of circle loss.
  
  The paper gives the equations for AM-SoftMax and Triplet loss, that can be computed from a unified loss function:
  
  [![Loss Function](https://i.sstatic.net/VvSYP.png)](https://i.sstatic.net/VvSYP.png)
  
  For example, in the case of AM-SoftMax, the positive and negative similarities are computed by the following way, `w` being the weights of the last fully connected layer, and `x` being the inputs of this last layer:
  
  [![positive similarity](https://i.sstatic.net/TLXCt.png)](https://i.sstatic.net/TLXCt.png)
  
  [![negative similarity](https://i.sstatic.net/V495C.png)](https://i.sstatic.net/V495C.png)
  
  So my questions are:
  
  1. Should I compute the similarities for circle loss by the same way the paper compute them for AM-SoftMax ?
  2. Should I compute the forward pass of the last fully connected layer with a standard product: `output[j] += weight[i][j] * input[i]`, followed by a standard SoftMax function ? Or by another way ?
  
  **Tags:** neural-networks, loss
  
  > **Comments:**
  > **username_1**: Hello. Welcome to AISE. In general, each post should contain exactly one question. As a rule of thumb, if you can't put your **specific question** in the title (because maybe you have more than 1), then your post might be too broad. Moreover, note that programming questions are off-topic. However, if you're only trying to understand how the theory is connected to the code, then your questions are fine for our site.  
  > **username_0**: I have reformulated my question, focalizing on the two problems I have with circle loss computation.  
  
  ---
  
  ## 0 answers
  
  