Dynamic automatic differentiation of GPU broadcast kernels

We show how forward-mode automatic differentiation (AD) can be employed within larger reverse-mode computations to dynamically differentiate broadcast operations in a GPU-friendly manner. Our technique fully exploits the broadcast Jacobian's inherent sparsity structure, and unlike a pure reverse-mode approach, this "mixed-mode" approach does not require a backwards pass over the broadcasted operation's subgraph, obviating the need for several reverse-mode-specific programmability restrictions on user-authored broadcast operations. Most notably, this approach allows broadcast fusion in primal code despite the presence of data-dependent control flow. We discuss an experiment in which a Julia implementation of our technique outperformed pure reverse-mode TensorFlow and Julia implementations for differentiating through broadcast operations within an HM-LSTM cell update calculation

Dynamic Control Flow in Large-Scale Machine Learning

Many recent machine learning models rely on fine-grained dynamic control flow for training and inference. In particular, models based on recurrent neural networks and on reinforcement learning depend on recurrence relations, data-dependent conditional execution, and other features that call for dynamic control flow. These applications benefit from the ability to make rapid control-flow decisions across a set of computing devices in a distributed system. For performance, scalability, and expressiveness, a machine learning system must support dynamic control flow in distributed and heterogeneous environments. This paper presents a programming model for distributed machine learning that supports dynamic control flow. We describe the design of the programming model, and its implementation in TensorFlow, a distributed machine learning system. Our approach extends the use of dataflow graphs to represent machine learning models, offering several distinctive features. First, the branches of conditionals and bodies of loops can be partitioned across many machines to run on a set of heterogeneous devices, including CPUs, GPUs, and custom ASICs. Second, programs written in our model support automatic differentiation and distributed gradient computations, which are necessary for training machine learning models that use control flow. Third, our choice of non-strict semantics enables multiple loop iterations to execute in parallel across machines, and to overlap compute and I/O operations. We have done our work in the context of TensorFlow, and it has been used extensively in research and production. We evaluate it using several real-world applications, and demonstrate its performance and scalability.Comment: Appeared in EuroSys 2018. 14 pages, 16 figure

Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used differential equation solver library in a high-level language (Julia's DifferentialEquations.jl) and enables GPU acceleration without requiring code changes by the user. Our approach achieves state-of-the-art performance compared to hand-optimized CUDA-C++ kernels, while performing $20-100\times$ faster than the vectorized-map (\texttt{vmap}) approach implemented in JAX and PyTorch. Performance evaluation on NVIDIA, AMD, Intel, and Apple GPUs demonstrates performance portability and vendor-agnosticism. We show composability with MPI to enable distributed multi-GPU workflows. The implemented solvers are fully featured, supporting event handling, automatic differentiation, and incorporating of datasets via the GPU's texture memory, allowing scientists to take advantage of GPU acceleration on all major current architectures without changing their model code and without loss of performance.Comment: 11 figure