Wecanseethis as the slope of the update function changes (middle row of Figure 1), these green lines correspond tothelocations givenbythearrowsinthetoprow.

Learning object-centric representations of complex scenes is a promising step towards enabling efficient abstract reasoning from low-levelperceptual features. Yet, most deep learning approaches learn distributed representations that do not capture the compositional properties of natural scenes.

We represent a higher-order logic formula as a graph that is invariant to variable renaming but still fully preserves syntactic and semantic information.

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A.1 Multiple data matrices A combinatorial optimization problem can be presented with multiple ( f) relationship features between two groups of items. In FFSP, for example, a production cost could be different for each process that one has to take into account for scheduling in addition to the processing time for each pair of the job and the machine. "Trainable element-wise function" block in Figure A.1 is now an MLP with f + 1 input nodes and 1 output node. The bold line indicates the change from the original. A.3 Alternatives to one-hot initial node embeddings For initial node representations of nodes in group B, one only needs mutually distinct-enough N We have chosen to present our model with one-hot vectors because it is the simplest to implement this way.