Answers.Body: <p>a TLDR of all the questions would be the following:</p>
  <p><strong>1.) which token pays most attention to which other token, is that the same asking as which token attends to which other token?</strong></p>
  <p>Not exactly. The operation isn’t scalar but vectorial. When working with vectors, all weights and outputs influence the final output token. A single token doesn’t attend to another token directly; rather, all tokens attend to each other, and all their outputs contribute to the final output. It’s not only about the one with the highest value but about the entire vector's influence. Remember that transformers have various layers and multiple attention heads. You also have to consider the attention  matrix for the different heads to really know the final influence two tokens have with each other.</p>
  <p><strong>2.)  What exactly does that mean? Do I have to look it from the Keys perspective or the Queries perspective?</strong></p>
  <p>It doesnt mean anything in self-attention.The important part is not to have a Q or K matrix. Becuase we could have the same Linear Projections for Q or K and it woulnt mean that much in terms of Architecture( Graph Attention Models uses the same Projection Matrix, so theres no difference between Q and K in that case).
  because at the end they use the same tokens for attention. The most important part is the they use the same tokens for self-attention becuase you want that the final output is a square matrix. all the tokens attends to all the other ones.</p>
  <p><strong>3.) Which token pays the most attention to token X?</strong></p>
  <p>If we define attention as the operation  <span class="math-container">$\space \text{Softmax}(\frac{QK^T}{\sqrt{d}})$</span>, then the argmax of the softmax function can indicate the most attention given to a token pair. However, this doesn’t mean the other outputs don’t contribute to the final result; it just indicates which has the highest contribution weight.</p>
  <p><strong>Extra Comments:</strong></p>
  <p>The challenge with Transformers and these types of questions is that while the model works very well empirically, it lacks an extensive theoretical background . Therefore, I wouldn’t focus too much on the meaning and semantics of each operation,because there isnt a mathematical theory we can rely on.
  I wouldn’t worry too much about the meaning of “paying attention” to a token, as this can vary based on interpretation. Instead, it’s best to rely on the mathematical definition of the attention mechanism,that is just an operation that has proven effective for sequential data in a empirical way. Additionally, there’s an interesting field called Mechanistic Interpretability that seeks to make Transformers interpretable across various tasks. It maps which operations contribute to the model’s final output. There are hypotheses, like <a href="https://transformer-circuits.pub/2022/in-context-learning-and-induction-heads/index.html" rel="nofollow noreferrer">Induction Heads for In-Context Learning</a>, but in my opinion many results rely heavily on the model architecture, training data, and human pattern recognition, rather than on a deep or intrinsic understanding of how the operations translate to behaviors. Ultimately, the attention mechanism is only one part of the full Transformer model,you still need to interpret the impact of Value weights, concatenation, linear projections, deep layers, positional encoding, and more that also affects on the final 'attention' that one token pays to another.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-11-05T23:32:41.073Z
Answers.LastActivityDate: 2024-11-05T23:32:41.073Z
Answers.UserDisplayName: Cesar Ruiz
Answers.Body: <p>During inference time in an autoregressive model like GPT or Llama, at each step the attention matrix is a strictly lower triangular. Each row represents the attention distribution for a particular token as query attending to all previous tokens' keys including the said particular token itself since each row sums to <span class="math-container">$1$</span> due to the <span class="math-container">$\text{Softmax}$</span> function as you correctly claimed. If the question is &quot;<em>Which token pays the most attention to 'good'?</em>&quot;, then no previous tokens like &quot;I&quot; or &quot;am,&quot; can attend to &quot;good&quot; during prediction because they were generated without any knowledge of it. You need to look at the column for 'good' (the third column in your example) and have to find the latter row generated after the token &quot;good&quot; with the highest value in that column of your attention weight matrix.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-11-05T23:11:21.580Z
Answers.LastActivityDate: 2024-11-05T23:11:21.580Z
Answers.UserDisplayName: cinch
Body: <p>If the question is: which token pays most attention to which other token, is that the same asking as which token attends to which other token?</p>
  <p>What exactly does that mean? Do I have to look it from the Keys perspective or the Queries perspective?</p>
  <p>Suppose I performed: <span class="math-container">$\text{softmax}(\frac{QK^T}{\sqrt{d_k}})$</span></p>
  <p>Each row will sum up to 1.
  If I have the sentence: I am good and attention weight matrix is <span class="math-container">$3 \times 3$</span>.
  If I want to know which token pays most attention to 'good', where do I have to look?</p>
  <p>There are exactly two answers and I can't figure out which because I'm not sure if I'm not familiar with the lingo or if I'm confusing myself.</p>
  <p>Each row sums up to 1. So we know that if you have the highest value in a row, then that is somewhat meaningful and attention is put on there. For vectors, it just means the value vectors is scaled strongly by those weights and less by others.</p>
  <p>What that means for tokens is ambigious. I assume it means that if the model reads that token, it pays attention to the those tokens that have highest values in the row and that can in turn help it to figue out what the next token is. The idea is to use the context surrounding the token to figure out what the next token should be. Attention helps the model to pull this off.</p>
  <p>On the other hand, if the question is: <em>Which token pays most attention to token X?</em>. Then it's more about which token does the model have to read to consider token X the most when predicting the next word. I think? So then you look at the columns but again, columns do not sum up to 1, so I could be very off here too. Could someone clarify?</p>
  <p>TL;DR:
  What does 'attend to' mean and is it related to 'token A pays attention to token B'?
  How do I have to read the attention weight matrix to answer these questions?</p>
  
Tags: <attention>
Title: Who attends to whom in Attention Weight Matrix? (Transformers)
UserDisplayName: Yuirike
ThreadText: # Who attends to whom in Attention Weight Matrix? (Transformers)
  
  (Asked by: username_0 on 2024-11-05)
  
  If the question is: which token pays most attention to which other token, is that the same asking as which token attends to which other token?
  
  What exactly does that mean? Do I have to look it from the Keys perspective or the Queries perspective?
  
  Suppose I performed: $\text{softmax}(\frac{QK^T}{\sqrt{d\_k}})$
  
  Each row will sum up to 1.
  If I have the sentence: I am good and attention weight matrix is $3 \times 3$.
  If I want to know which token pays most attention to 'good', where do I have to look?
  
  There are exactly two answers and I can't figure out which because I'm not sure if I'm not familiar with the lingo or if I'm confusing myself.
  
  Each row sums up to 1. So we know that if you have the highest value in a row, then that is somewhat meaningful and attention is put on there. For vectors, it just means the value vectors is scaled strongly by those weights and less by others.
  
  What that means for tokens is ambigious. I assume it means that if the model reads that token, it pays attention to the those tokens that have highest values in the row and that can in turn help it to figue out what the next token is. The idea is to use the context surrounding the token to figure out what the next token should be. Attention helps the model to pull this off.
  
  On the other hand, if the question is: *Which token pays most attention to token X?*. Then it's more about which token does the model have to read to consider token X the most when predicting the next word. I think? So then you look at the columns but again, columns do not sum up to 1, so I could be very off here too. Could someone clarify?
  
  TL;DR:
  What does 'attend to' mean and is it related to 'token A pays attention to token B'?
  How do I have to read the attention weight matrix to answer these questions?
  
  **Tags:** attention
  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_1 on 2024-11-05. Score: 3
  
  a TLDR of all the questions would be the following:
  
  **1.) which token pays most attention to which other token, is that the same asking as which token attends to which other token?**
  
  Not exactly. The operation isn’t scalar but vectorial. When working with vectors, all weights and outputs influence the final output token. A single token doesn’t attend to another token directly; rather, all tokens attend to each other, and all their outputs contribute to the final output. It’s not only about the one with the highest value but about the entire vector's influence. Remember that transformers have various layers and multiple attention heads. You also have to consider the attention matrix for the different heads to really know the final influence two tokens have with each other.
  
  **2.) What exactly does that mean? Do I have to look it from the Keys perspective or the Queries perspective?**
  
  It doesnt mean anything in self-attention.The important part is not to have a Q or K matrix. Becuase we could have the same Linear Projections for Q or K and it woulnt mean that much in terms of Architecture( Graph Attention Models uses the same Projection Matrix, so theres no difference between Q and K in that case).
  because at the end they use the same tokens for attention. The most important part is the they use the same tokens for self-attention becuase you want that the final output is a square matrix. all the tokens attends to all the other ones.
  
  **3.) Which token pays the most attention to token X?**
  
  If we define attention as the operation $\space \text{Softmax}(\frac{QK^T}{\sqrt{d}})$, then the argmax of the softmax function can indicate the most attention given to a token pair. However, this doesn’t mean the other outputs don’t contribute to the final result; it just indicates which has the highest contribution weight.
  
  **Extra Comments:**
  
  The challenge with Transformers and these types of questions is that while the model works very well empirically, it lacks an extensive theoretical background . Therefore, I wouldn’t focus too much on the meaning and semantics of each operation,because there isnt a mathematical theory we can rely on.
  I wouldn’t worry too much about the meaning of “paying attention” to a token, as this can vary based on interpretation. Instead, it’s best to rely on the mathematical definition of the attention mechanism,that is just an operation that has proven effective for sequential data in a empirical way. Additionally, there’s an interesting field called Mechanistic Interpretability that seeks to make Transformers interpretable across various tasks. It maps which operations contribute to the model’s final output. There are hypotheses, like [Induction Heads for In-Context Learning](https://transformer-circuits.pub/2022/in-context-learning-and-induction-heads/index.html), but in my opinion many results rely heavily on the model architecture, training data, and human pattern recognition, rather than on a deep or intrinsic understanding of how the operations translate to behaviors. Ultimately, the attention mechanism is only one part of the full Transformer model,you still need to interpret the impact of Value weights, concatenation, linear projections, deep layers, positional encoding, and more that also affects on the final 'attention' that one token pays to another.
  
  
  ---
  
  ### Answer by username_2 on 2024-11-05. Score: 2
  
  During inference time in an autoregressive model like GPT or Llama, at each step the attention matrix is a strictly lower triangular. Each row represents the attention distribution for a particular token as query attending to all previous tokens' keys including the said particular token itself since each row sums to $1$ due to the $\text{Softmax}$ function as you correctly claimed. If the question is "*Which token pays the most attention to 'good'?*", then no previous tokens like "I" or "am," can attend to "good" during prediction because they were generated without any knowledge of it. You need to look at the column for 'good' (the third column in your example) and have to find the latter row generated after the token "good" with the highest value in that column of your attention weight matrix.
  
  
  ---
  
  