Generally disclosed herein is a hardware/software interface for asynchronous data movement between an off-core memory and a core-local memory, referred to as “stream transfers”, and a stream ordering model. The stream transfers allow software to more efficiently express common data-movement patterns, specifically ones seen in sparse workloads. Direct stream instructions that belong to a stream are processed in-order. For indirect stream instructions, offset elements in an offset list are processed in order. A sync flag is updated to indicate monotonic incremental progress for the stream.