Computing gradients is a crucial task in many domains, including machine learning, physics simulations, and scientific computing. Automatic differentiation (AD) computes gradients for arbitrary imperative code. In reverse mode AD, an auxiliary structure, the tape, is used to transfer intermediary values required for gradient computation. The challenge is how to organize the tape in the memory hierarchy since it has a high reuse distance, lacks temporal locality, and inflates working set by 2 — 4×. We introduce Tapeflow, a compiler framework to orchestrate and manage the gradient tape. We make three key contributions. i) We introduce the concept of regions, which transforms the tape layout into an array-of-structs format to improve spatial reuse. ii) We schedule the execution into layers and explicitly orchestrate the tape operands using a scratchpad. This reduces the required cache size and on-chip energy. iii) Finally, we stream the tape from the DRAM by organizing it into a FIFO of tiles. The tape operands arrive just-in-time for each layer. Tapeflow, running on the same hardware, outperforms Enzyme, the state-of-the-art compiler, by 1.3—2.5×, reduces on-chip SRAM usage by 5— 40×, and saves 8× on-chip energy. We demonstrate Tapeflow on a wide range of algorithms written in general-purpose language.
Index Terms—Automatic differentiation, Gradients, Streaming Algorithms, Back propagation