SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Proof. Equation (2) demonstrates that the attention score for each instance ranges between 0 and 1. After normalizing by  $\frac{1}{\sum_{j=1}^{n_i} a_{i,j}}$ , the sum of attention scores for all instances within a multi-instance bag becomes equal to 1. When the normalized attention score of an instance  $x_{i,j'}$  is approach 1, the normalized attention scores of the remaining instances  $\{\pmb{x}_{i,1}, \pmb{x}_{i,2}, \dots, \pmb{x}_{i,n_i}\} \setminus \{\pmb{x}_{i,j'}\}$  approach 0. Based on Equation (3), the aggregated bag-level vector representation  $z_i = \frac{1}{\sum_{j=1}^{n_i} a_{i,j}} \sum_{j=1}^{n_i} a_{i,j} h_{i,j} \approx h_{i,j'} = h(x_{i,j'})$ . Therefore, it is confirmed that instances with higher attention scores contribute significantly to the bag-level predictions, underlining the significance of attention mechanisms in multi-instance partial-label learning.
Theorem 1 suggests that high attention scores of individual instances can play a crucial role in determining the bag-level class prediction, emphasizing the significance of accurately capturing and interpreting attention scores in multi-instance partial-label learning scenarios.
A.4 Image Bag Generator
We utilize four image bag generators to extract multi-instance features from the CRC-MIPL dataset. The detailed descriptions of these image bag generators are provided below:
- Row Generator: It treats each row of the image as an individual instance. To extract the feature for each instance, the Row generator computes the average RGB color value of the row and the color differences in the rows above and below it.
- SBN Generator: It considers each  $2 \times 2$  blob within the image and includes the RGB color values of the blob itself and its four neighboring blobs as features for each instance. It generates instances by iteratively moving one pixel at a time. However, it should be noted that the SBN generator ignores the feature information at the four corners of the image.
- KMeansSeg Generator: It divides the image into  $K$  segments or partition blocks. For each segment, it generates a 6-dimensional feature. The first three dimensions represent color values in the YCbCr color space, while the last three dimensions represent values obtained by applying the wavelet transform to the luminance (Y) component of the image.
- SIFT Generator: It applies the scale-invariant feature transform (SIFT) algorithm to extract features, which partitions each instance into multiple  $4 \times 4$  subregions and assigns the gradients of the pixels within these subregions to 8 bins. Consequently, the SIFT generator produces a 128-dimensional feature vector for each instance.
The implementations of the four image bag generators are available at http://www.lamda.nju.edu.cn/code_MIL-BG.ashx.
A.5 Data and Code Availability
The implementations of the compared algorithms are publicly available. MIPLGP and PLAGGD are implemented at http://palm.seu.edu.cn/zhangml/. PRODEN is implemented at https://github.com/Lvcrezia77/PRODEN. RC is implemented at https://lfeng-ntu.github.io/codedata.html. LWS is implemented at https://github.com/hongwei-wen/LW-loss-for-partial-label. Additionally, the code of DEMIPL, the benchmark datasets, and the real-world dataset are publicly available at http://palm.seu.edu.cn/zhangml/.