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@@ -160,16 +160,16 @@ We use the following _statistical-based metrics_:
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  - **Image F1 Score** is the harmonic mean of Precision and Recall, providing an overall evaluation of the image quality in the multimodal answer.
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  It is calculated as:
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- \[
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  \text{Image F1 Score} = 2 \times \frac{\text{Image Precision} \times \text{Image Recall}}{\text{Image Precision} + \text{Image Recall}}
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- \]
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  - **Image Ordering Score** evaluates whether the order of images inserted into the multimodal answer matches the order of images in the ground truth.
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  Specifically, we compute the weighted edit distance between the two image sequences to reflect the difference in their order.
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  - **Data Format** (For lifestyle datasets):
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- - **Ground-truth**: \( A = a_1 \rightarrow a_2 \rightarrow \cdots \rightarrow a_n \), where \( a_i \) represents the image at the \( i \)-th position in the order.
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- - **Answer**: \( B = b_1 \rightarrow b_2 \rightarrow \cdots \rightarrow b_m \), where \( b_j \) is not necessarily in \(\{a_i\}\), and \( m \) is not necessarily equal to \( n \).
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  - **Scoring Formula**:
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@@ -181,13 +181,13 @@ We use the following _statistical-based metrics_:
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  - \( \frac{|A \cap B|}{n} \): Normalization factor.
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  - **Details**:
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- - Here, \( \text{dist}(A, B) \) represents the weighted edit distance between string \( A \) and string \( B \), i.e., the minimum total cost to transform string \( B \) into string \( A \) through the following three operations:
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- - **String Insertion**: If \( B \) is missing certain images, insert an image from \( A \) into a specific position in \( B \)
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- . The operation cost is \( p_1 \).
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- - **String Deletion**: If \( B \) contains extra irrelevant images, delete them. The operation cost is \( p_2 \).
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- - **String Substitution**: If the positions of images in \( B \) do not match \( A \), substitute the image in \( B \) with the corresponding image from \( A \). The operation cost is \( p_3 \).
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- - The weights generally satisfy \( p_1 > p_2 > p_3 \), and \( p \geq p_1 \) ensures the final score falls within the range \([0, 1]\).
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- - Weighted edit distance can be computed using dynamic programming, with a time complexity of \( O(mn) \).
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  - **Rouge-L** is a text generation evaluation metric based on the longest common subsequence, measuring the structural similarity between the answer and the ground truth.
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  - **BERTScore** is a text generation evaluation metric based on the pre-trained language model BERT, used to assess the semantic similarity between the text in the generated multimodal answer and the ground truth.
@@ -205,6 +205,7 @@ We use the following _LLM-based metrics_:
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  ## Prompts
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  ### Generation Prompts
 
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  #### Answer Generation Prompt for LLM-Based Method
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  #Input
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  Query: {}
 
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  - **Image F1 Score** is the harmonic mean of Precision and Recall, providing an overall evaluation of the image quality in the multimodal answer.
161
  It is calculated as:
162
 
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+ ![\[
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  \text{Image F1 Score} = 2 \times \frac{\text{Image Precision} \times \text{Image Recall}}{\text{Image Precision} + \text{Image Recall}}
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+ \]](https://cdn-uploads.huggingface.co/production/uploads/67571051d39ac252085797ca/9Y1NtxXcyUoLay9mln2GR.png)
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  - **Image Ordering Score** evaluates whether the order of images inserted into the multimodal answer matches the order of images in the ground truth.
168
  Specifically, we compute the weighted edit distance between the two image sequences to reflect the difference in their order.
169
 
170
  - **Data Format** (For lifestyle datasets):
171
+ - **Ground-truth**: A = a_1 -> a_2 -> ... -> a_n, where a_i represents the image at the i-th position in the order.
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+ - **Answer**: B = b_1 -> b_2 -> ... -> b_m, where b_j is not necessarily in A, and m is not necessarily equal to n.
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  - **Scoring Formula**:
175
 
 
181
  - \( \frac{|A \cap B|}{n} \): Normalization factor.
182
 
183
  - **Details**:
184
+ - Here, dist(A, B) represents the weighted edit distance between string A and string B , i.e., the minimum total cost to transform string B into string A through the following three operations:
185
+ - **String Insertion**: If B is missing certain images, insert an image from A into a specific position in B
186
+ . The operation cost is p_1.
187
+ - **String Deletion**: If B contains extra irrelevant images, delete them. The operation cost is p_2.
188
+ - **String Substitution**: If the positions of images in B do not match A, substitute the image in B with the corresponding image from A. The operation cost is p_3.
189
+ - The weights generally satisfy p_1 > p_2 > p_3, and p >= p_1 ensures the final score falls within the range \[0, 1\].
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+ - Weighted edit distance can be computed using dynamic programming, with a time complexity of O(mn).
191
 
192
  - **Rouge-L** is a text generation evaluation metric based on the longest common subsequence, measuring the structural similarity between the answer and the ground truth.
193
  - **BERTScore** is a text generation evaluation metric based on the pre-trained language model BERT, used to assess the semantic similarity between the text in the generated multimodal answer and the ground truth.
 
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  ## Prompts
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  ### Generation Prompts
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+
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  #### Answer Generation Prompt for LLM-Based Method
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  #Input
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  Query: {}