Neural Expectation Maximization
Many real world tasks such as reasoning and physical interaction require identification and manipulation of conceptual entities. A first step towards solving these tasks is the automated discovery of distributed symbol-like representations. In this paper, we explicitly formalize this problem as inference in a spatial mixture model where each component is parametrized by a neural network. Based on the Expectation Maximization framework we then derive a differentiable clustering method that simultaneously learns how to group and represent individual entities. We evaluate our method on the (sequential) perceptual grouping task and find that it is able to accurately recover the constituent objects. We demonstrate that the learned representations are useful for next-step prediction.
The paper presents two related deep neural networks for clustering entities together into roughly independant components.  In their implementations the entities are always pixels in an image.  The first technique they brand as neural expectation maximization, and show how the network is performing an unrolled form of generalized EM.  The E-step predicts the probability that a given pixel was generated by each of the components.  The M-step, then updates the parameters of each component using these probabilities.  This is neural, because each of these steps relies on a neural network which maps from the parameters of a component to the pixel values. By unrolling this process they can train this network in an end-to-end basis.  They also proposed a related model which modifies this process by updating the parameters of the components at each step in the unrolling using an RNN-style update.  This allows them to extend the model to sequential/video data where the image is changing at each step.
	The show results only on toy datasets consisting of a small number of shapes or MNIST images (3-5) superimposed on top of each other.  Their neural EM approach performs significantly worse than recent work on Tagger for static data, however the RNN version of their model slightly out performs Tagger.  However Tagger significantly outperforms even the RNN version of their work if Tagger is trained with batch normalization.  In the video setting, their model performs significantly better, which is not surprising given the additional information available in video.  They show both higher scores for predicting the pixel to component mapping, but also much better reconstruction MSE than a standard  (fully entangled) autoencoder model (which is the same a their model with 1 component).
	Overall these seems like a solid paper with solid results on a toy dataset.
	My main concern is that the technique may not work on messier real world data, since they only show results on relatively toy datasets where the components are completely independant, and the component boundaries are relatively clear when they are not overlapping.  Results in a more realistic domain would make the paper much strong, but even in the current state I believe both the technique and the results are interesting.