In this paper we present a deep Multiple Instance Learning (MIL) method that can be trained end-to-end to perform classification from weak supervision. Our MIL method is implemented as a two stream neural network, specialized in tasks of instance classification and weighting. Our instance weighting stream makes use of Gaussian radial basis function to normalize the instance weights by comparing instances locally within the bag and globally across bags. The final classification score of the bag is an aggregate of all instance classification scores. The instance representation is shared by both instance classification and weighting streams. The Gaussian instance weighting allows us to regularize the representation learning of instances such that all positive instances to be closer to each other w.r.t. the instance weighting function. We evaluate our method on five standard MIL datasets and show that our method outperforms other MIL methods. We also evaluate our model on two datasets where all models are trained end-to-end. Our method obtain better bag-classification and instance classification results on these datasets. We conduct extensive experiments to investigate the robustness of the proposed model and obtain interesting insights.
This paper described an approach of performing multiple instance learning (MIL) by using a network branch to weight instances and then using a Gaussian normalization layer on top of it, where the weightings are predicted based on in-bag variances. The instance weighting scheme, a classic in MIL, has been proposed in deep networks by [3]. Hence, I don't see much novelty here except that there is a Gaussian normalization layer after the instance weighting in the MIL framework. 
I'm a bit worried that sigma seems to be unnormalized in the first case -- what would happen if the bag score distribution is non-Gaussian? GP1T1 seems more sensible by learning all these weights.
However, I see significant issues in terms of evaluation which makes hard to accept this paper.
I firmly believe that 22 years after the (Dietterich 1997) paper, it's no longer enough to only use the original MIL datasets and classification datasets such as the CIFAR-10 bags to evaluate MIL. I may be alone here which is open to discussions, but the original motivation for MIL is for the problem to be weakly-supervised where we only know a high-level label but no low-level labels. There exist many realistic image problems that are similar to this (e.g. weakly-supervised detection and semantic segmentation) and have received a plethora of work, hence it's unclear to me whether still using these arbitrarily generated CIFAR-10 bags and the 5 old datasets would still apply to MIL as an approach. After all, MIL is almost dying and "weakly-supervised learning" has risen in popularity with almost being the same problem as MIL. I think for MIL to work its way back, it should first start by using the right datasets to test (e.g. the datasets in [3] would be a great starting point) and comparing with other weakly-supervised detection approaches that do not use additional information.
Besides the philosophical point, a practical issue is that the numbers seem to be bold arbitrarily according to the authors' whim. In table 3, MI-Net DS is better than every other method in the last 2 columns, but not bold, and also it seems that no t-test was performed to determine the significance of differences. This also happens in Table 1, where I think WSDN should be equivalent with the proposed method in the last 2 rows.
Finally, the choice of excluding MI-Net in the CIFAR experiments is dubious as well, given its performance in the simple datasets. Why is MI-Net not tested on the CIFAR experiments?