SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Compared to PLL algorithms, DEMIPL outperforms them on all benchmark datasets. This superiority can be attributed to two main factors. First, PLL algorithms cannot directly handle multi-instance bags, whereas the original multi-instance features possess better discriminative power than the degenerated features obtained through the Mean and MaxMin strategies. Second, the proposed momentum-based disambiguation strategy is more robust than the disambiguation strategies of the compared algorithms. It should be noted that although these PLL algorithms achieve satisfactory results in PLL tasks, their performance in addressing MIPL problems is inferior to dedicated MIPL algorithms, namely DEMIPL and MIPLGP. This observation emphasizes the greater challenges posed by MIPL problems, which involve increased ambiguity in supervision compared to PLL problems, and highlights the necessity of developing specialized algorithms for MIPL.
Additionally, we experiment with another extension of applying PLL algorithms to MIPL data by directly assigning a bag-level candidate label set as the candidate label set for each instance within the bag. However, all of them perform worse than MIPL. Moreover, the majority of the compared PLL algorithms fail to produce satisfactory results. This is likely caused by the fact that the ground-truth labels for most instances are absent from their respective candidate label sets. Consequently, the absences of ground-truth labels impede the disambiguation ability of MIPL algorithms.
3.3 Experimental Results on the Real-World Dataset
The classification accuracy of DEMIPL and the compared algorithms on the CRC-MIPL dataset is presented in Table 3, where the symbol - indicates that MIPLGP encounters memory overflow issues on our V100 GPUs. DEMIPL demonstrates superior performance compared to MIPLGP on the CRC-MIPL-SBN and CRC-MIPL-KMeansSeg datasets, while only falling behind MIPLGP on the CRC-MIPL-Row dataset. When compared to the PLL algorithms, DEMIPL achieves better results in 28 out of 32 cases, and only underperforms against PL-AGGD in 2 cases on CRC-MIPL-Row and CRC-MIPL-SBN.
Table 2: Classification accuracy (mean±std) of each comparing algorithm on the benchmark datasets in terms of the different number of false positive labels  $[r \in \{1,2,3\}]$ .  $\bullet/\circ$  indicates whether the performance of DEMIPL is statistically superior/inferior to the compared algorithm on each dataset.
Algorithm	r	MNIST-MIPL	FMNIST-MIPL	Birdsong-MIPL	SIVAL-MIPL
DEMIIPL	1	0.976±0.008	0.881±0.021	0.744±0.016	0.635±0.041
2	0.943±0.027	0.823±0.028	0.701±0.024	0.554±0.051
3	0.709±0.088	0.657±0.025	0.696±0.024	0.503±0.018
MIPLGP	1	0.949±0.016	0.847±0.030	0.716±0.026	0.669±0.019
2	0.817±0.030	0.791±0.027	0.672±0.015	0.613±0.026
3	0.621±0.064	0.670±0.052	0.625±0.015	0.569±0.032
Mean
PRODEN	1	0.605±0.023	0.697±0.042	0.296±0.014	0.219±0.014
2	0.481±0.036	0.573±0.026	0.272±0.019	0.184±0.014
3	0.283±0.028	0.345±0.027	0.211±0.013	0.166±0.017
RC	1	0.658±0.031	0.753±0.042	0.362±0.015	0.279±0.011
2	0.598±0.033	0.649±0.028	0.335±0.011	0.258±0.017
3	0.392±0.033	0.401±0.063	0.298±0.009	0.237±0.020
LWS	1	0.463±0.048	0.726±0.031	0.265±0.010	0.240±0.014
2	0.209±0.028	0.720±0.025	0.254±0.010	0.223±0.008
3	0.205±0.013	0.579±0.041	0.237±0.005	0.194±0.026
PL-AGGD	1	0.671±0.027	0.743±0.026	0.353±0.019	0.355±0.015
2	0.595±0.036	0.677±0.028	0.314±0.018	0.315±0.019
3	0.380±0.032	0.474±0.057	0.296±0.015	0.286±0.018
MaxMin
PRODEN	1	0.508±0.024	0.424±0.045	0.387±0.014	0.316±0.019
2	0.400±0.037	0.377±0.040	0.357±0.012	0.287±0.024
3	0.345±0.048	0.309±0.058	0.336±0.012	0.250±0.018
RC	1	0.519±0.028	0.731±0.027	0.390±0.014	0.306±0.023
2	0.469±0.035	0.666±0.027	0.371±0.013	0.288±0.021
3	0.380±0.048	0.524±0.034	0.363±0.010	0.267±0.020
LWS	1	0.242±0.042	0.435±0.049	0.225±0.038	0.289±0.017
2	0.239±0.048	0.406±0.040	0.207±0.034	0.271±0.014
3	0.218±0.017	0.318±0.064	0.216±0.029	0.244±0.023
PL-AGGD	1	0.527±0.035	0.391±0.040	0.383±0.014	0.397±0.028
2	0.439±0.020	0.371±0.037	0.372±0.020	0.360±0.029
3	0.321±0.043	0.327±0.028	0.344±0.011	0.328±0.023
Table 3: Classification accuracy (mean±std) of each comparing algorithm on the CRC-MIPL dataset.
Algorithm	CRC-MIPL-Row	CRC-MIPL-SBN	CRC-MIPL-KMeansSeg	CRC-MIPL-SIFT
DEMIPL	0.408±0.010	0.486±0.014	0.521±0.012	0.532±0.013
MIPLGP	0.432±0.005°	0.335±0.006●	0.329±0.012●	-
Mean
PRODEN	0.365±0.009●	0.392±0.008●	0.233±0.018●	0.334±0.029●
RC	0.214±0.011●	0.242±0.012●	0.226±0.009●	0.209±0.007●
LWS	0.291±0.010●	0.310±0.006●	0.237±0.008●	0.270±0.007●
PL-AGGD	0.412±0.008	0.480±0.005●	0.358±0.008●	0.363±0.012●
MaxMin
PRODEN	0.401±0.007	0.447±0.011●	0.265±0.027●	0.291±0.011●
RC	0.227±0.012●	0.338±0.010●	0.208±0.007●	0.246±0.008●
LWS	0.299±0.008●	0.382±0.009●	0.247±0.005●	0.230±0.007●
PL-AGGD	0.460±0.008○	0.524±0.008○	0.434±0.009●	0.285±0.009●
The above results indicate that DEMIPL achieves the best performance when combined with stronger bag generators such as CRC-MIPL-KMeansSeg and CRC-MIPL-SIFT. This combination enables the disambiguation attention mechanism to learn meaningful embeddings. This aligns with the fact that CRC-MIPL-Row and CRC-MIPL-SBN use classic multi-instance bag generators that only consider pixel colors, and lack the ability to extract any of the content information. In contrast, CRC-MIPL-KMeansSeg and CRC-MIPL-SIFT are content-aware generators that are capable of producing semantically meaningful features. Both CRC-MIPL-Row and CRC-MIPL-SBN segment images using fixed grids, and represents instances based on their pixel-level colors and the colors of their adjacent rows or grids. Consequently,
Table 4: Classification accuracy (mean±std) of DEMIPL-MD and DEMIPL.
Algorithm	FMNIST-MIPL	SIVAL-MIPL
r=1	r=2	r=3	r=1	r=2	r=3
DEMIPL-MD	0.744±0.273	0.784±0.018	0.586±0.101	0.607±0.024	0.530±0.021	0.499±0.035
DEMIPL	0.881±0.021	0.823±0.028	0.657±0.025	0.635±0.041	0.554±0.051	0.503±0.018
Figure 3: The frequency distribution of attention scores on MNIST-MiPL dataset  $(r = 1)$
instances in CRC-MIPL-Row and CRC-MIPL-SBN exhibit similar feature representations, and possess limited discriminative power when distinguishing positive and negative instances. With more powerful bag generators such as CRC-MIPL-KMeansSeg and CRC-MIPL-SIFT, which generate content-aware features that are more informative and discriminative, the disambiguation power of DEMIPL can be fully utilized as demonstrated by the significant performance advantages against all compared baselines.
Furthermore, the CRC-MIPL dataset exhibits distinct differences between tissue cells and the background in each image. The Mean strategy diminishes the disparities and discriminations, leading to superior outcomes for the Maxmin strategy in most cases when compared to the Mean strategy.
3.4 Further Analysis
Effectiveness of the Attention Loss To validate the effectiveness of the attention loss, we introduce a degenerated variant named DEMIPL-MD, which excludes the attention loss from DEMIPL. Table 4 verifies that DEMIPL achieves superior accuracy compared to DEMIPL-MD on both the FMNIST-MIPL and SIVAL-MIPL datasets. Notably, the difference is more pronounced on the FMNIST-MIPL dataset than that on the SIVAL-MIPL dataset. This can be attributed to the fact that the feature representation of each instance in the FMNIST-MIPL dataset solely comprises self-contained information, enabling clear differentiation between positive and negative instances. Conversely, the feature representation of each instance in the SIVAL-MIPL dataset encompasses both self- and neighboring information, leading to couplings between the feature information of positive instances and negative instances.
To further investigate the scores learned by the attention loss, we visualize the frequency distribution of attention scores throughout the training process. As illuminated in Figure 3, the top row corresponds to DEMIPL-MD, while the bottom row corresponds to DEMIPL. At epoch=10, attention scores generated by DEMIPL show higher dispersion, suggesting that DEMIPL trains faster than DEMIPL-MD. At epoch=50 and 100, attention scores computed by DEMIPL tend to converge towards two extremes: attention scores for negative instances gravitate towards zero, while attention scores for positive instances approach one. In conclusion, the attention loss is conducive to calculating appropriate attention scores for positive and negative instances, thereby improving accuracy.
Effectiveness of the Momentum-based Disambiguation Strategy To further investigate the momentum-based disambiguation strategy, the performance of DEMIPL is compared with its two degenerated versions denoted as DEMIPL-PR and DEMIPL-AV. DEMIPL-PR is obtained by setting the momentum parameter  $\lambda^{(t)} = 0$  in Equation (7), which corresponds to progressively updating the weights based on the current output of the classifier. In contrast, DEMIPL-AV is obtained by setting the momentum parameter  $\lambda^{(t)} = 1$ , resulting in uniform weights throughout the training process.
Figure 4 illustrates the performance comparison among DEMIPL, DEMIPL-PR, and DEMIPL-AV on the MNIST-MIPL, FMNIST-MIPL, and Birdsong-MIPL datasets. When the number of false positive labels is small, DEMIPL-PR and DEMIPL-AV demonstrate similar performance to DEMIPL. However,
Figure 4: Classification accuracy of DEMIPL, DEMIPL-PR, and DEMIPL-AV with varying  $r$ .
Figure 5: Performance of DEMIPL with varying weight  $\lambda_{a}$ .
as the number of false positive labels increases, DEMIPL consistently outperforms DEMIPL-PR and DEMIPL-Av by a significant margin. This observation suggests that the momentum-based disambiguation strategy is more robust in handling higher levels of disambiguation complexity. Furthermore, it can be observed that DEMIPL-PR generally outperforms DEMIPL-Av across various scenarios. However, when  $r = 3$  in the MNIST-MIPL and FMNIST-MIPL datasets, DEMIPL-Av surpasses DEMIPL-PR. We believe this can be attributed to the following reason: having three false positive labels within the context of five classifications represents an extreme case. DEMIPL-PR likely assigns higher weights to false positive labels, whereas DEMIPL-Av uniformly assigns weights to each candidate label, adopting a more conservative approach to avoid assigning excessive weights to false positive labels. In a nutshell, the proposed momentum-based disambiguation strategy demonstrates superior robustness compared to existing methods for disambiguation.
Parameter Sensitivity Analysis The weight  $\lambda_{a}$  in Equation (8) is the primary hyperparameter in DEMIPL. Figure 5 illustrates the sensitivity analysis of the weight  $\lambda_{a}$  on the MNIST-MIPL and CRC-MIPL-SIFT datasets. The learning rates on the MNIST-MIPL dataset are set to 0.01, 0.01, 0.05 for  $r = 1$ , 2, 3, respectively, while on the CRC-MIPL-SIFT dataset, the learning rate is set to 0.01. As illuminated in Figure 5, DEMIPL demonstrates insensitivity to changes in the weight  $\lambda_{a}$ . In the experiments involving DEMIPL and its variants, the weight  $\lambda_{a}$  is chosen from a set of  $\{0.0001, 0.001\}$ .
In this paper, we propose DEMIPL, the first deep learning-based algorithm for multi-instance partial-label learning, accompanied by a real-world dataset. Specifically, DEMIPL utilizes the disambiguation attention mechanism to aggregate each multi-instance bag into a single vector representation, which is further used in conjunction with the momentum-based disambiguation strategy to determine the ground-truth label from the candidate label set. The disambiguation attention mechanism and momentum-based strategy synergistically facilitate disambiguation in both the instance space and label space. Extensive experimental results indicate that DEMIPL outperforms the compared algorithms in  $96.3\%$  of cases on benchmark datasets and  $85.7\%$  of cases on the real-world dataset.
Despite DEMIPL's superior performance compared to the well-established MIPL and PLL approaches, it exhibits certain limitations and there are several unexplored research avenues. For example, DEMIPL assumes independence among instances within each bag. A promising avenue for future research involves considering dependencies between instances. Moreover, akin to MIL algorithms grounded in the embedded-space paradigm [13], accurately predicting instance-level labels poses a challenging endeavor. One possible approach entails the introduction of an instance-level classifier.
The authors wish to thank the anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Science Foundation of China (62225602, 62206047), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX23_0317), and the Big Data Computing Center of Southeast University.
[1] Bo Han, Quanming Yao, Xingrui Yu, Gang Niu, Miao Xu, Weihua Hu, Ivor W. Tsang, and Masashi Sugiyama. Co-teaching: Robust training of deep neural networks with extremely noisy labels. In Advances in Neural Information Processing Systems 31, Montréal, Canada, pages 8536-8546, 2018.
[2] David Berthelot, Nicholas Carlini, Ian J. Goodfellow, Nicolas Papernot, Avital Oliver, and Colin Raffel. Mixmatch: A holistic approach to semi-supervised learning. In Advances in Neural Information Processing Systems 32, Vancouver, BC, Canada, pages 5050-5060, 2019.
[3] Takashi Ishida, Gang Niu, Weihua Hu, and Masashi Sugiyama. Learning from complementary labels. In Advances in Neural Information Processing Systems 30, Long Beach, CA, pages 5639-5649, 2017.
[4] Yi Wei, Mei Xue, Xin Liu, and Pengxiang Xu. Data fusing and joint training for learning with noisy labels. Frontiers of Computer Science, 16(6):166338:1-8, 2022.
[5] Ming-Kun Xie and Sheng-Jun Huang. Partial multi-label learning with noisy label identification. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(7):3676-3687, 2022.
[6] Gengyu Lyu, Songhe Feng, Yi Jin, Tao Wang, Congyan Lang, and Yidong Li. Prior knowledge regularized self-representation model for partial multi-label learning. IEEE Transactions on Cybernetics, 53(3):1618-1628, 2023.
[7] Zhi-Hua Zhou. A brief introduction to weakly supervised learning. National Science Review, 5 (1):44-53, 2018.
[8] Jaume Amores. Multiple instance classification: Review, taxonomy and comparative study. Artificial Intelligence, 201:81-105, 2013.
[9] Marc-Andre Carbonneau, Veronika Cheplygina, Eric Granger, and Ghyslain Gagnon. Multiple instance learning: A survey of problem characteristics and applications. Pattern Recognition, 77:329–353, 2018.
[10] Zhi-Hua Zhou, Yu-Yin Sun, and Yu-Feng Li. Multi-instance learning by treating instances as non-i.i.d. samples. In Proceedings of the 26th International Conference on Machine Learning, Montreal, Quebec, Canada, pages 1249-1256, 2009.
[11] Xiu-Shen Wei, Han-Jia Ye, Xin Mu, Jianxin Wu, Chunhua Shen, and Zhi-Hua Zhou. Multi-instance learning with emerging novel class. IEEE Transactions on Knowledge and Data Engineering, 33(5):2109-2120, 2019.
[12] Xinggang Wang, Yongluan Yan, Peng Tang, Xiang Bai, and Wenyu Liu. Revisiting multiple instance neural networks. Pattern Recognition, 74:15-24, 2018.
[13] Maximilian Ilse, Jakub M. Tomczak, and Max Welling. Attention-based deep multiple instance learning. In Proceedings of the 35th International Conference on Machine Learning, Stockholm, Sweden, pages 2132-2141, 2018.
[14] Xiaoshuang Shi, Fuyong Xing, Yuanpu Xie, Zizhao Zhang, Lei Cui, and Lin Yang. Loss-based attention for deep multiple instance learning. In Proceedings of the 34th AAAI Conference on Artificial Intelligence, New York, NY, USA, pages 5742-5749, 2020.
A.1 Pseudo-Code of DEMIPL
Given an unseen multi-instance bag  $\mathbf{X}_{*} = [\pmb{x}_{*,1},\pmb{x}_{*,2},\dots,\pmb{x}_{*,n_{*}}]$  with  $n_*$  instances, DEMIPL initially utilizes the feature extractor to obtain the instance-level representation as follows:
$$
\boldsymbol {H} _ {*} = h \left(\boldsymbol {X} _ {*}\right) = \left\{\boldsymbol {h} _ {* , 1}, \boldsymbol {h} _ {* , 2}, \dots , \boldsymbol {h} _ {* , n _ {*}} \right\}. \tag {9}
$$
Subsequently, DEMIPL maps the instance-level representation  $H_{*}$  into a vector representation  $z_{*}$  using the disambiguation attention mechanism, which is described as follows:
$$
a _ {*, j} = \frac {1}{1 + \exp \left\{- \boldsymbol {W} ^ {\top} \left(\tanh  \left(\boldsymbol {W} _ {v} ^ {\top} \boldsymbol {h} _ {*, j} + \boldsymbol {b} _ {v}\right) \odot \operatorname {s i g m} \left(\boldsymbol {W} _ {u} ^ {\top} \boldsymbol {h} _ {*, j} + \boldsymbol {b} _ {u}\right)\right) \right\}}, \tag {10}
$$
$$
\boldsymbol {z} _ {*} = \frac {1}{\sum_ {j = 1} ^ {n _ {*}} a _ {*, j}} \sum_ {j = 1} ^ {n _ {*}} a _ {*, j} \boldsymbol {h} _ {*, j}. \tag {11}
$$
Finally, we employ the trained classifier  $\mathbf{f}$  to predict the label of  $X_{*}$  by:
$$
Y _ {*} = \underset {c \in \mathcal {Y}} {\arg \max } f _ {c} \left(\boldsymbol {z} _ {*}\right), \tag {12}
$$
where  $f_{c}(\cdot)$  is the  $c$ -th element of  $\mathbf{f}(\cdot)$ , and the normalized function  $f_{c}(\cdot)$  represents the probability of class label  $c$  being the ground-truth label.
Algorithm 1 summarizes the complete procedure of DEMIPL. First, the algorithm uniformly initializes the weights of the momentum-based disambiguation loss (Step 1). Next, the model training can be divided into two sub-steps (Steps 2-13). The initial sub-step involves extracting features for each mini-batch and aggregating them into bag-level vector representations (Steps 5-7). The subsequent sub-step encompasses calculating the loss function and updating the model (Steps 8-11). Finally, for an unseen multi-instance bag, instance-level features are extracted and aggregated into a bag-level vector representation, which is used to predict the label (Steps 14-16).
Algorithm 1  $Y_{*} = \mathrm{DEMIPL}$ $(\mathcal{D},\lambda_a,T,\boldsymbol {X}_*)$
Inputs:   
 $\mathcal{D}$  : the multi-instance partial-label training set  $\{(X_i,\mathcal{S}_i)\mid 1\leq i\leq m\}$  , where  $X_{i} =$ $\{\pmb {x}_{i,1},\pmb {x}_{i,2},\dots ,\pmb {x}_{i,n_i}\} ,\pmb {x}_{i,j}\in \mathcal{X},\mathcal{X} = \mathbb{R}^d,\mathcal{S}_i\subset \mathcal{Y},\mathcal{Y} = \{l_1,l_2,\dots ,l_q\}$ $\lambda_{a}$  : the weight for the attention loss   
 $T$  : the number of iterations   
 $X_{*}$  : the unseen multi-instance bag with  $n_*$  instances   
Outputs:   
 $Y_{*}$  : the predicted label for  $X_{*}$    
Process:   
1: Initialize uniform weights  $\boldsymbol{w}^{(0)}$  as stated by Equation (6)   
2: for  $t = 1$  to  $T$  do   
3: Shuffle training set  $\mathcal{D}$  into  $B$  mini-batches   
4: for  $b = 1$  to  $B$  do   
5: Extract the instance-level features of  $X$  according to Equation (1)   
6: Calculate the attention scores as stated by Equation (2)   
7: Map the instance-level features into a single vector representation according to Equation (3)   
8: Update weights  $\boldsymbol{w}^{(t)}$  according to Equation (7)   
9: Calculate  $\mathcal{L}$  according to Equation (8)   
10: Set gradient -  $\nabla_{\Phi}\mathcal{L}$    
11: Update  $\Phi$  by the optimizer   
12: end for   
13: end for   
14: Extract the instance-level features of  $X_{*}$  according to Equation (9)   
15: Calculate the attention scores and map the instance-level features into a single vector representa. tion according to Equations (10) and (11)   
16: Return  $Y_{*}$  according to Equation (12)
A.2 Additional Experiment Results
Table 5: Classification accuracy (mean±std) of each comparing algorithm on the benchmark datasets in terms of the different number of false positive labels  $[r \in \{1,2,3\}]$ .  $\bullet/\circ$  indicates whether the performance of DEMIPL is statistically superior/inferior to the compared algorithm on each dataset (pairwise t-test at a significance level of 0.05).
Algorithm	r	MNIST-MIPL	FMNIST-MIPL	Birdsong-MIPL	SIVAL-MIPL
DEMIPL	1	0.976±0.008	0.881±0.021	0.744±0.016	0.635±0.041
2	0.943±0.027	0.823±0.028	0.701±0.024	0.554±0.051
3	0.709±0.088	0.657±0.025	0.696±0.024	0.503±0.018
Mean
PRODEN	1	0.555±0.033●	0.652±0.033●	0.303±0.016●	0.303±0.020●
2	0.372±0.038●	0.463±0.067●	0.287±0.017●	0.274±0.022●
3	0.285±0.032●	0.288±0.039●	0.278±0.006●	0.242±0.009●
RC	1	0.660±0.031●	0.697±0.166●	0.329±0.014●	0.344±0.014●
2	0.577±0.039●	0.684±0.029●	0.301±0.014●	0.299±0.015●
3	0.362±0.029●	0.414±0.050●	0.288±0.019●	0.256±0.013●
LWS	1	0.605±0.030●	0.702±0.033●	0.344±0.018●	0.346±0.014●
2	0.431±0.024●	0.547±0.040●	0.310±0.014●	0.312±0.015●
3	0.335±0.029●	0.411±0.033●	0.289±0.021●	0.286±0.018●
MaxMin
PRODEN	1	0.465±0.023●	0.358±0.019●	0.339±0.010●	0.322±0.018●
2	0.338±0.031●	0.315±0.023●	0.329±0.016●	0.295±0.021●
3	0.260±0.037●	0.265±0.031●	0.305±0.015●	0.244±0.018●
RC	1	0.518±0.022●	0.421±0.016●	0.379±0.014●	0.304±0.015●
2	0.462±0.028●	0.363±0.018●	0.359±0.015●	0.268±0.023●
3	0.366±0.039●	0.294±0.053●	0.332±0.024●	0.244±0.014●
LWS	1	0.457±0.028●	0.346±0.033●	0.349±0.013●	0.345±0.013●
2	0.351±0.043●	0.323±0.031●	0.336±0.013●	0.314±0.019●
3	0.274±0.037●	0.267±0.034●	0.307±0.016●	0.268±0.019●
Table 6: Classification accuracy (mean±std) of each comparing algorithm on the real-world dataset.
Algorithm	CRC-MIPL-Row	CRC-MIPL-SBN	CRC-MIPL-KMeansSeg	CRC-MIPL-SIFT
DEMIPL	0.408±0.010	0.486±0.014	0.521±0.012	0.532±0.013
Mean
PRODEN	0.405±0.012	0.515±0.010	0.512±0.014	0.352±0.015
RC	0.290±0.010	0.394±0.010	0.304±0.017	0.248±0.008
LWS	0.360±0.008	0.440±0.009	0.422±0.035	0.338±0.009
MaxMin
PRODEN	0.453±0.009	0.529±0.010	0.563±0.011	0.294±0.008
RC	0.347±0.013	0.432±0.008	0.366±0.010	0.204±0.008
LWS	0.381±0.011	0.442±0.009	0.335±0.049	0.287±0.009
In Section 3.2 and Section 3.3, we report the results of PRODEN, RC, and LWS using linear models. In this section, we supplement the results of the compared PLL algorithms with multi-layer perceptrons (MLPs) as described in the respective literature. Table 5 and Table 6 present the experimental results of DEMIPL compared to PLL algorithms on the benchmark and real-world datasets, respectively. It is noteworthy that DEMIPL employs a two-layer CNN network for feature extraction on the MNIST-MIPL and FMNIST-MIPL datasets, while on the remaining datasets, DEMIPL only utilizes linear models.
On the benchmark datasets, DEMIPL consistently outperforms the compared algorithms in almost all cases. Moreover, the compared algorithms using MLPs do not consistently yield superior results compared to those using linear models, especially when the benchmark datasets exhibit relatively simple features. This suggests that linear models are sufficient to achieve satisfactory results given the benchmark datasets, while MLPs might introduce unnecessary complexity.
On the real-world dataset, DEMIPL outperforms the compared algorithms in 19 out of 24 cases. When combined with complex image bag generators such as CRC-MIPL-KMeansSeg and CRC-MIPL-SIFT, DEMIPL outperforms the compared algorithms in 11 out of 12 cases. In the majority of cases, the compared algorithms using MLPs demonstrate better performance than those using linear models.
However, on the CRC-MIPL-SIFT dataset, the improvement provided by MLPs is not particularly evident and sometimes even leads to a decline in performance. Therefore, when dealing with complex multi-instance features, the bag features obtained through the Mean or MaxMin strategies do not accurately reflect the characteristics of multi-instance bags. This highlights the need for specialized MIPL algorithms to accurately capture the features of multi-instance bags.
A.3 Theoretical Analysis
Theorem 1. In a multi-instance bag  $X_{i}$ , when the normalized attention score of an instance  $x_{i,j'}$  approaches 1, e.g.,  $\frac{a_{i,j'}}{\sum_{j=1}^{n_i} a_{i,j}} \to 1$ , the probability of the multi-instance bag  $X_{i}$  being classified as the c-th class is approximately equal to that of the instance  $x_{i,j'}$  belonging to the c-th class.