Asynchronous Algorithmic Alignment with Cocycles
This addresses a bottleneck in neural algorithmic reasoning for researchers and practitioners, offering an incremental improvement over existing GNN methods.
The paper tackles the inefficiency of synchronous message passing in graph neural networks (GNNs) when learning dynamic programming algorithms, where only a few nodes need updates, by separating node state updates from message function invocation, resulting in scalable GNN layers that are provably invariant under asynchrony.
State-of-the-art neural algorithmic reasoners make use of message passing in graph neural networks (GNNs). But typical GNNs blur the distinction between the definition and invocation of the message function, forcing a node to send messages to its neighbours at every layer, synchronously. When applying GNNs to learn to execute dynamic programming algorithms, however, on most steps only a handful of the nodes would have meaningful updates to send. One, hence, runs the risk of inefficiencies by sending too much irrelevant data across the graph. But more importantly, many intermediate GNN steps have to learn the identity functions, which is a non-trivial learning problem. In this work, we explicitly separate the concepts of node state update and message function invocation. With this separation, we obtain a mathematical formulation that allows us to reason about asynchronous computation in both algorithms and neural networks. Our analysis yields several practical implementations of synchronous scalable GNN layers that are provably invariant under various forms of asynchrony.