DeepBench
September 26, 2016
 Sharan Narang Baidu sharan@baidu.com

## 1. DeepBench

DeepBench is an open source benchmarking tool that measures the performance of basic operations involved in training deep neural networks. These operations are executed on different hardware platforms using neural network libraries. Deepbench is available as a repository on github.

The primary purpose of DeepBench is to benchmark operations that are important to deep learning on different hardware platforms. Although the fundamental computations behind deep learning are well understood, the way they are used in practice can be surprisingly diverse. For example, a matrix multiplication may be compute-bound, bandwidth-bound, or occupancy-bound, based on the size of the matrices being multiplied and the kernel implementation. Because every deep learning model uses these operations with different parameters, the optimization space for hardware and software targeting deep learning is large and underspecified.

DeepBench attempts to answer the question, “Which hardware provides the best performance on the basic operations used for training deep neural networks?”. We specify these operations at a low level, suitable for use in hardware simulators for groups building new processors targeted at deep learning.

### 1.1. Where does DeepBench fit in?

The Deep Learning ecosystem consists of several different pieces. We wanted to highlight where DeepBench fits into this ecosystem. The diagram below describes the software and hardware components involved with deep learning. At the very top, deep learning frameworks like Baidu's PaddlePaddle, Theano, TensorFlow, Torch etc. allow us to build deep learning models. They include basic building blocks like layers which can be connected in different ways to create a model. In order to train these models, the frameworks use underlying neural network libraries such as NVIDIA's cuDNN and Intel's MKL. These libraries implement operations such as matrix multiply that are required to train deep learning models. Finally, the models are trained on hardware like NVIDIA GPUs or Intel's Xeon Phi processor.

DeepBench uses the neural network libraries to benchmark the performance of basic operations on different hardware. It does not work with deep learning frameworks or deep learning models built for applications. We cannot measure the time required to train an entire model using DeepBench. The performance characteristics of models built for different applications are very different from each other. Therefore, we are benchmarking the underlying operations involved in training a deep learning model. Benchmarking these operations will help raise awareness amongst hardware vendors and software developers about the bottlenecks in deep learning training.

### 1.2. Methodology

DeepBench consists of a set of basic operations (dense matrix multiplications, convolutions and communication) as well as some recurrent layer types. There is an Excel spreadsheet (DeepBenchKernels.xlsx) in the DeepBench repository that describes all of the sizes.

Both forward and backward operations are tested. This first version of the benchmark will focus on training performance in 32-bit floating-point arithmetic. Future versions may expand to focus on inference workloads as well as lower precision arithmetic.

We will use vendor supplied libraries even if faster independent libraries exist or faster results have been published. Most users will default to the vendor supplied libraries and as such the vendor supplied libraries are most representative of users' experience.

### 1.3. Entry

We are releasing with results for four hardware platforms, NVIDIA's TitanX, M40, TitanX Pascal and Intel's Knights Landing. Hardware vendors or independent users can run the appropriate benchmarks and input the results into the spreadsheet. We provide an overview of the results and all results are available in the DeepBench repository. We will gladly accept pull requests for new hardware platforms.

## 2. Types of Operations

### 2.1. Dense Matrix Multiplies

Dense matrix multiplies exist in almost all deep neural networks today. They are used to implement fully connected layers and vanilla RNNs and are building blocks for other types of recurrent layers. Sometimes they are also used as a quick way to implement novel layer types for which custom code doesn't exist.

When performing the GEMM operation A * B = C, either or both of A and B can be optionally transposed. Common terminology to describe a matrix problem is the triple (M, N, K), which describes the sizes of the matrices involved, and the “op” which tells us which matrices (if any) are transposed. The figure below describes how the triple (M, N, K) correspond to the sizes of the matrices being multiplied.

The variant where both matrices are transposed is not used in neural networks. The other three variants are used, but they need not be implemented as a call to SGEMM with those transpose descriptors. Sometimes it can be faster to perform an in-place transpose followed by the appropriate multiplication and a transpose back.

### 2.2. Convolutions

Convolutions make up the vast majority of flops in networks that operate on images and videos and form important parts of networks such as speech and natural language modeling making them, perhaps, the single most important layer from a performance perspective.

Convolutions have 4 or 5 dimensional inputs and outputs giving rise to a large number of possible orderings for these dimensions. For the first version of the benchmark we are only concerned with performance in NCHW format i.e. data is presented in image, feature maps, rows and columns.

There are many techniques for computing convolutions that are optimal for different sizes of the filter and image, including: direct, matrix-multiply -based, FFT-based, and Winograd-based approaches. In the first version of this benchmark, we are not concerned about the accuracy of the different approaches since the general consensus is that 32-bit floating point is accurate enough for each of them.

### 2.3. Recurrent Layers

Recurrent layers are usually made up of some combination of the above operations and also simpler operations such as unary or binary operations which aren't very compute intensive and generally are a small percentage of overall runtime. However, the GEMM and convolution operations are relatively small in recurrent layers, so the cost of these smaller operations can become significant. This is especially true if there is a high fixed overhead associated with starting a computation. It is also possible to use alternate storage formats for the recurrent matrices because the cost of converting to a new storage format can be amortized over the many steps of the recurrent computation. If this is done the time to convert to and from the custom format should be included in the overall time.

These factors lead to many optimization possibilities both within a time step and across a sequence of time steps such that measuring the raw performance of the operations is not necessarily representative of the performance of an entire recurrent layer. In this benchmark we focus on only one recurrent layer, even though there are even more optimization opportunities if one considers stacks of them.

The calculation of the inputs should not be included in the time for the recurrent layer calculation since it can be calculated as one large multiply and then consumed by the actual recurrent calculation. So in: h_t = g(Wx_t + Uh_t-1) the time for the calculation of Wx_t for all t should not be included in the time for the recurrent layer.

The backward calculation should calculate the updates with respect to the weights but not the inputs. All the recurrent work is done to calculate the weight updates, so calculating the updates with respect to the inputs as well just obscures what we are trying to measure.

The non-linearity for vanilla RNNs should be a ReLU. The internal non-linearities of the LSTM should be the standard operations - sigmoid for the gates and tanh for the activations. The LSTM should not have peephole connections.

### 2.4. All-Reduce

Neural networks are today often trained across multiple GPUs or even multiple systems each with multiple GPUs. There are two main categories of techniques for doing this: synchronous and asynchronous. Synchronous techniques rely on keeping the parameters on all instances of the model synchronized, usually by making sure all instances of the model have the same copy of the gradients before taking an optimization step. The Message Passing Interface (MPI) primitive usually used to perform this operation is called All-Reduce. There are many ways to implement All-Reduce based on the number of ranks, the size of the data, and the topology of the network. This benchmark places no constraints on the implementation other than that it should be deterministic. Asynchronous methods are quite varied and in this version of the benchmark we will not be attempting to test these methods.

In order to evaluate All-Reduce, we use the following libraries and benchmarks:  NVIDIA's NCCL  Ohio State University (OSU) Benchmarks

The NCCL library contains a set of standard communication routines. The library supports any number of GPUs in a single node and can be run in single process or multi-process (MPI). The NCCL routines don't support All-Reduce across multiple nodes. In order to evaluate All-Reduce across multiple nodes, we use the benchmarks from OSU. We report the shortest latency achieved from all three implementations (NCCL single process, NCCL MPI, OpenMPI).

##### Topology for NVIDIA 8 GPU System

Each node has two CPU sockets, and each socket has a PCIe root complex. For each socket there are two PLX switches that are each connected to the CPU socket via 16 lanes of PCIe v3. There are two GPUs on each PLX switch. All pairs of GPUs communicate simultaneously over 16 lanes of PCIe v3. The two CPU sockets are connected via Intel QPI. The interconnect across nodes is InfiniBand FDR. The figure below shows a schematic diagram of one our nodes, where all devices connected by the same PCI root complex are encapsulated in a dotted box

##### Topology for Intel Xeon Phi and Omni-Path System

The MPI_AllReduce time is measured on Intel Xeon Phi processor 7250 on Intel’s internal Endeavor cluster with Intel® Omni-Path Architecture (Intel® OPA) series 100 fabric with fat-tree topology, using Intel MPI 5.1.3.181.

## 3. Results

In this section, we are documenting the performance for a few operations. These are picked at random and are only meant to demonstrate the performance for a few applications. The results below only include the time and TeraFLOPS for the fastest processor for the particular operation and parameters. The full results can be found in the repository.

The software libraries (e.g. cuDNN, OpenMPI) and some details of the hardware system are also available in the repository on github. Please feel free to ask us any clarifying questions.

Results on more hardware platforms will be added once they are available. We welcome contributions from all hardware vendors.

### 3.1. GEMM Results

Kernel A Transpose B Transpose Application Time (ms) TeraFLOPS Processor
M=1760, N=128, K=1760 N N Speech Recognition 0.17 4.66 TitanX Pascal
M=7860, N=64, K=2560 N N Speech Recognition 0.42 5.94 TitanX Pascal
M=2560, N=64, K=2560 N N Speech Recognition 0.28 3.02 TitanX Pascal
M=5124, N=9124, K=2560 T N Speech Recognition 55.17 4.34 Xeon Phi 7250
M=3072, N=128, K=1024 T N Speech Recognition 0.28 2.87 TitanX Pascal

### 3.2. Convolution Results

Input Size Filter Size # of Filters Padding (h, w) Stride (h, w) Application Total Time (ms) Fwd TeraFLOPS Processor
W = 700, H = 161, C = 1, N = 32 R = 5, S = 20 32 0, 0 2, 2 Speech Recognition 2.98 6.63 TitanX Pascal
W = 54, H = 54, C = 64, N = 8 R = 3, S = 3 64 1, 1 1, 1 Face Recognition 0.63 10.55 TitanX Pascal
W = 224, H = 224, C = 3, N = 16 R = 3, S = 3 64 1, 1 1, 1 Computer Vision 3.99 3.6 TitanX Pascal
W = 7, H = 7, C = 512, N = 16 R = 3, S = 3 512 1, 1 1, 1 Computer Vision 2.93 5.88 TitanX Pascal
W = 28, H = 28, C = 192, N = 16 R = 5, S = 5 32 2, 2 1, 1 Computer Vision 1.57 6.59 TitanX Pascal

### 3.3. Recurrent Ops Results

The recurrent op kernels are only run on NVIDIA hardware. The recurrent benchmarks will be run on Intel hardware shortly. Results should be available in October.

Hidden Units Batch Size TimeSteps Recurrent Type Application Total Time (ms) Fwd TeraFLOPS Processor
1760 64 50 Vanilla Speech Recognition 8.48 1.14 TitanX Pascal
2560 32 50 Vanilla Speech Recognition 24.69 1.69 TitanX Pascal
1024 128 25 LSTM Machine Translation 16.90 5.41 TitanX Pascal

### 3.4. All-Reduce Results

We couldn't run the All-Reduce benchmark on NVIDIA's TitanX Pascal GPU since we only had a single Pascal GPU.

Size (# of floats) Number of Processors Application Time (ms) Bandwidth (GB/s) Processor
16777216 8 Speech Recognition 22.06 24.34 TitanX Maxwell with InfiniBand FDR
16777216 16 Speech Recognition 53.76 19.97 Xeon Phi 7250 with Intel® Omni-Path
16777216 32 Speech Recognition 55.68 38.57 Xeon Phi 7250 with Intel® Omni-Path

## 4. Get Involved

We welcome contributions from the community to DeepBench. You can contribute in two ways:

1. Deep Learning Researchers/Engineers: If you are deep learning researcher or engineer working on a new deep learning application, you may have different operations and/or workloads involved in training your model. We are interested in learning more about the underlying operations that are adversely impacting the performance (speed) of your model. Please contribute these operations and workloads!
2. Hardware Vendors: We would gladly accept contributions from other hardware vendors. We're open to accepting benchmark results from large companies or smaller startups building hardware for training deep learning models. Please contribute benchmark results for your hardware!

## 5. Acknowledgments

I would like to thank Greg Diamos, Erich Elsen, Bryan Catanzaro and Patrick LeGresley for their contributions to DeepBench and Shubho Sengputa for his guidance.