SlowGuess/NeurIPS_2023_OCR huggingface dataset:
[39] S. Pal, A. Valkanas, F. Regol, and M. Coates, “Bag graph: Multiple instance learning using bayesian graph neural networks,” Proceedings of the AAAI Conference on Artificial Intelligence, vol. 36, no. 7, pp. 7922–7930, Jun. 2022. [Online]. Available: https://ojs(aaai.org/index.php/AAAI/article/view/20762
[40] Y. Yan, X. Wang, X. Guo, J. Fang, W. Liu, and J. Huang, “Deep multi-instance learning with dynamic pooling,” in Proceedings of The 10th Asian Conference on Machine Learning, ser. Proceedings of Machine Learning Research, J. Zhu and I. Takeuchi, Eds., vol. 95. PMLR, 14-16 Nov 2018, pp. 662-677. [Online]. Available: https://proceedings.mlr.press/v95/yan18a.html
[41] Y. Lin, M. Moosaei, and H. Yang, "OutfitNet: Fashion outfit recommendation with attention-based multiple instance learning," in Proceedings of The Web Conference 2020. ACM, apr 2020. [Online]. Available: https://doi.org/10.1145%2F3366423.3380096
[42] X. Shi, F. Xing, Y. Xie, Z. Zhang, L. Cui, and L. Yang, “Loss-based attention for deep multiple instance learning,” Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, no. 04, pp. 5742–5749, apr 2020. [Online]. Available: https://doi.org/10.1609%2Faaaiv34i04.6030
[43] K. Thandiackal, B. Chen, P. Pati, G. Jaume, D. F. K. Williamson, M. Gabrani, and O. Goksel, "Differentiable zooming for multiple instance learning on whole-slide images," in Lecture Notes in Computer Science. Springer Nature Switzerland, 2022, pp. 699-715. [Online]. Available: https://doi.org/10.1007%2F978-3-031-19803-8_41
[44] W. Zhang, X. Zhang, h. deng, and M.-L. Zhang, “Multi-instance causal representation learning for instance label prediction and out-of-distribution generalization,” in Advances in Neural Information Processing Systems, S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, Eds., vol. 35. Curran Associates, Inc., 2022, pp. 34940-34953. [Online]. Available: https://proceedings.neurips.cc/paper_files/paper/2022/file/e261e92e1cfb820da930ad8c38d0aead-Paper-Conference.pdf
[45] W. Zhang, L. Liu, and J. Li, Robust Multi-Instance Learning with Stable Instances. IOS Press, 2020, p. 1682–1689, citation Key: zhangRobustMultiInstanceLearning2020. [Online]. Available: https://ebooks.iopress.nl/doi/10.3233/FAIA200280
[46] T. G. Dietterich, R. H. Lathrop, and T. Lozano-Pérez, "Solving the multiple instance problem with axis-parallel rectangles," Artificial Intelligence, vol. 89, no. 1-2, pp. 31-71, jan 1997. [Online]. Available: https://doi.org/10.1016%2Fs0004-3702%2896%2900034-3
[47] N. Weidmann, E. Frank, and B. Pfahringer, “A two-level learning method for generalized multi-instance problems,” in Machine Learning: ECML 2003. Springer Berlin Heidelberg, 2003, pp. 468–479. [Online]. Available: https://doi.org/10.1007%2F978-3-540-39857-8_42
Proof of Theorem 2:
Proof.  $g(\{\emptyset, c_1, c_2\}) = c_1 \geq 1 \land c_2 \geq 1$  is the target function. Using  $\emptyset_p$  to represent the background poison signal and  $\emptyset_B$  to represent the indiscriminate background noise, The training distribution contains negative samples ( $y = -1$ ) of the form  $\{\emptyset_p = 1, \emptyset_B \geq 1, c_1 = 1\}$  and  $\{\emptyset_p = 1, \emptyset_B \geq 1, c_2 = 1\}$ , and positive samples ( $y = 1$ ) of the form  $\{\emptyset_B \geq 1, c_1 = 1, c_2 = 1\}$ .
By exhaustive enumeration, only two possible logic rules can distinguish the positive and negative bags. Either the (MIL) rule  $c_{1} \geq 1 \wedge c_{2} \geq 1$ , and the non-MIL rule  $\varnothing_{p} = 0$ . However, a MIL model cannot respect the MIL hypothesis and learn to use  $\varnothing_{p}$  simultaneously, because  $\varnothing_{p}$  occurs only in negative bags.
By changing the test distribution to evaluate the sample  $\varnothing_B = 1, c_1 = 1, c_2 = 1$  and observing the model produce the negative label  $y = -1$ , the only possible conclusion is it has learned the non-MIL hypothesis.
Proof of Theorem 3:
Proof.  $g(\{\emptyset, c_1, c_2\}) = c_1 \geq 1 \land c_2 \geq 1$  is the target function. Using  $\varnothing_B$  to represent the indiscriminate background noise, The training distribution contains negative samples ( $y = -1$ ) of the form  $\{\emptyset_B \in [1, 10], c_1 \in [1, 2]\}$  and  $\{\emptyset_B \in [1, 10], c_2 \in [1, 2]\}$ , and positive samples ( $y = 1$ ) of the form  $\{\emptyset_B \in [1, 10], c_1 \in [1, 2], c_2 \in [1, 2]\}$ .
By exhaustive enumeration, only two possible logic rules can distinguish the positive and negative bags:  $c_{1} \geq 1 \land c_{2} \geq 1$ . However, there is a naive MIL rule that can obtain non-random, but not perfect accuracy,  $c_{1} + c_{2} \geq 3$ .
By changing the test distribution to evaluate the samples  $\varnothing_B = 1, c_1 \geq 35$  and  $\varnothing_B = 1, c_2 \geq 35$  and observing the model produce the positive label  $y = 1$ , the only possible conclusion is it has learned the non-threshold MIL hypothesis.