Body: <p>I'm trying to understand <a href="https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&amp;arnumber=7958570" rel="nofollow noreferrer">the paper by Carlini and Wagner on deep neural networks adversarial attacks</a>. On page 44, in Section V-A, it is explained how the loss function to the described problem was designed. One part of this loss function is called &quot;objective function&quot;.</p>
  <p>There are 7 such functions proposed on which experiments are made, but there is no information provided on where they came from and why those are chosen.</p>
  <p>Is this some commonly known thing in the Deep Learning area? Do you recognize them and can tell me where they came from and why they were chosen?</p>
  <p><span class="math-container">\begin{align}
  f_{1}\left(x^{\prime}\right) &amp;= -\operatorname{loss}_{F, t}\left(x^{\prime}\right)+1 \\
  f_{2}\left(x^{\prime}\right) &amp;= \left(\max _{i \neq t}\left(F\left(x^{\prime}\right)_{i}\right)-F\left(x^{\prime}\right)_{t}\right)^{+} \\
  f_{3}\left(x^{\prime}\right) &amp;= \operatorname{softplus}\left(\max _{i \neq t}\left(F\left(x^{\prime}\right)_{i}\right)-F\left(x^{\prime}\right)_{t}\right)-\log (2) \\
  f_{4}\left(x^{\prime}\right) &amp;= \left(0.5-F\left(x^{\prime}\right)_{t}\right)^{+} \\
  f_{5}\left(x^{\prime}\right) &amp;= -\log \left(2 F\left(x^{\prime}\right)_{t}-2\right) \\
  f_{6}\left(x^{\prime}\right) &amp;= \left(\max _{i \neq t}\left(Z\left(x^{\prime}\right)_{i}\right)-Z\left(x^{\prime}\right)_{t}\right)^{+} \\
  f_{7}\left(x^{\prime}\right)&amp;= \operatorname{softplus}\left(\max _{i \neq t}\left(Z\left(x^{\prime}\right)_{i}\right)-Z\left(x^{\prime}\right)_{t}\right)-\log (2)
  \end{align}</span></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-11-20T21:39:06.077Z
Comments.Text: Hello. Welcome to Artificial Intelligence Stack Exchange! It seems that you're asking us about the origin of multiple functions. I would recommend that you focus on 1 (objective) function for each post. If you have multiple questions, ask each of them in a separate post (note that asking us to explain a full paper and say it's only one question is not the correct approach).
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-11-20T21:39:37.720Z
Comments.Text: Having said that, I just opened the pdf you're linking us to, but it has only 19 pages (while you point us to the 44 page). In this linked paper, the page should be 6. I would also recommend that you tell us what you read from the paper and briefly tell us what you know about the topic and/or machine learning in general. Finally, in the paper, they tell us in the paper why they enumerate these functions, i.e. they should meet the requirements that they talk about in the paper just before these equations. So, what exactly are you asking here?
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-11-20T22:21:09.270Z
Comments.Text: ok, so my guess was that functions used here are from some set of functions used in machine learning for this specific task. Just like we've got a few different loss functions (cross entropy, MSE, MAE), a few different activation functions (sigmoid, ReLU) etc. So maybe those presented on image also have some common name?
Comments.UserDisplayName: Piotrek
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-11-20T22:22:50.447Z
Comments.Text: so in other words I'm not asking about 7 functions separately. I am interested in what the whole collection represents, not the individual elements. Btw: you have page numbers written at the bottom of each page
Comments.UserDisplayName: Piotrek
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-11-20T22:26:42.563Z
Comments.Text: In the paper, they write "_We define an objective function $f$ such that [this constraint is met]. There are many possible choices for..._".
Comments.UserDisplayName: nbro
Tags: <deep-learning><objective-functions><adversarial-ml>
Title: Where do the objective functions proposed in this paper by Carlini-Wagner attack come from?
UserDisplayName: Piotrek
ThreadText: # Where do the objective functions proposed in this paper by Carlini-Wagner attack come from?
  
  (Asked by: username_0 on 2021-11-20)
  
  I'm trying to understand [the paper by Carlini and Wagner on deep neural networks adversarial attacks](https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7958570). On page 44, in Section V-A, it is explained how the loss function to the described problem was designed. One part of this loss function is called "objective function".
  
  There are 7 such functions proposed on which experiments are made, but there is no information provided on where they came from and why those are chosen.
  
  Is this some commonly known thing in the Deep Learning area? Do you recognize them and can tell me where they came from and why they were chosen?
  
  \begin{align}
  f\_{1}\left(x^{\prime}\right) &= -\operatorname{loss}\_{F, t}\left(x^{\prime}\right)+1 \\
  f\_{2}\left(x^{\prime}\right) &= \left(\max \_{i \neq t}\left(F\left(x^{\prime}\right)\_{i}\right)-F\left(x^{\prime}\right)\_{t}\right)^{+} \\
  f\_{3}\left(x^{\prime}\right) &= \operatorname{softplus}\left(\max \_{i \neq t}\left(F\left(x^{\prime}\right)\_{i}\right)-F\left(x^{\prime}\right)\_{t}\right)-\log (2) \\
  f\_{4}\left(x^{\prime}\right) &= \left(0.5-F\left(x^{\prime}\right)\_{t}\right)^{+} \\
  f\_{5}\left(x^{\prime}\right) &= -\log \left(2 F\left(x^{\prime}\right)\_{t}-2\right) \\
  f\_{6}\left(x^{\prime}\right) &= \left(\max \_{i \neq t}\left(Z\left(x^{\prime}\right)\_{i}\right)-Z\left(x^{\prime}\right)\_{t}\right)^{+} \\
  f\_{7}\left(x^{\prime}\right)&= \operatorname{softplus}\left(\max \_{i \neq t}\left(Z\left(x^{\prime}\right)\_{i}\right)-Z\left(x^{\prime}\right)\_{t}\right)-\log (2)
  \end{align}
  
  **Tags:** deep-learning, objective-functions, adversarial-ml
  
  > **Comments:**
  > **username_1**: Hello. Welcome to Artificial Intelligence Stack Exchange! It seems that you're asking us about the origin of multiple functions. I would recommend that you focus on 1 (objective) function for each post. If you have multiple questions, ask each of them in a separate post (note that asking us to explain a full paper and say it's only one question is not the correct approach).  
  > **username_1**: Having said that, I just opened the pdf you're linking us to, but it has only 19 pages (while you point us to the 44 page). In this linked paper, the page should be 6. I would also recommend that you tell us what you read from the paper and briefly tell us what you know about the topic and/or machine learning in general. Finally, in the paper, they tell us in the paper why they enumerate these functions, i.e. they should meet the requirements that they talk about in the paper just before these equations. So, what exactly are you asking here?  
  > **username_0**: ok, so my guess was that functions used here are from some set of functions used in machine learning for this specific task. Just like we've got a few different loss functions (cross entropy, MSE, MAE), a few different activation functions (sigmoid, ReLU) etc. So maybe those presented on image also have some common name?  
  > **username_0**: so in other words I'm not asking about 7 functions separately. I am interested in what the whole collection represents, not the individual elements. Btw: you have page numbers written at the bottom of each page  
  > **username_1**: In the paper, they write "_We define an objective function $f$ such that [this constraint is met]. There are many possible choices for..._".  
  
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  ## 0 answers
  
  