Dataflow Graphs as Matrices and Programming with Higher-order Matrix Elements

We consider dataflow architecture for two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We improve the earlier technique of almost continuous program transformations by adopting a discipline of bipartite graphs linking nodes obtained via general transformations and nodes obtained via linear transformations which makes it possible to develop and evolve dataflow programs over these classes of computations by continuous program transformations. The use of bipartite graphs allows us to represent the dataflow programs from this class as matrices of real numbers and evolve and modify programs by continuous change of these numbers. We develop a formalism for higher-order dataflow programming for this class of dataflow graphs based on the higher-order matrix elements. Some of our software experiments are briefly discussed.