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Recent works on machine learning for combinatorial optimization have shownthat learning based approaches can outperform heuristic methods in terms ofspeed and performance. In this paper, we consider the problem of finding anoptimal topological order on a directed acyclic graph with focus on the memoryminimization problem which arises in compilers. We propose an end-to-endmachine learning based approach for topological ordering using anencoder-decoder framework. Our encoder is a novel attention based graph neuralnetwork architecture called \emph{Topoformer} which uses different topologicaltransforms of a DAG for message passing. The node embeddings produced by theencoder are converted into node priorities which are used by the decoder togenerate a probability distribution over topological orders. We train our modelon a dataset of synthetically generated graphs called layered graphs. We showthat our model outperforms, or is on-par, with several topological orderingbaselines while being significantly faster on synthetic graphs with up to 2knodes. We also train and test our model on a set of real-world computationgraphs, showing performance improvements.

Neural Topological Ordering for Computation Graphs