A Study of BFLOAT16 for Deep Learning Training

A Study of BFLOAT16 for Deep Learning Training
Dhiraj Kalamkar1
, Dheevatsa Mudigere2
, Naveen Mellempudi∗1
, Dipankar Das1
,
Kunal Banerjee1
, Sasikanth Avancha1
, Dharma Teja Vooturi †1
, Nataraj Jammalamadaka‡1
,
Jianyu Huang2
, Hector Yuen2
, Jiyan Yang2
, Jongsoo Park2
, Alexander Heinecke1
,
Evangelos Georganas1
, Sudarshan Srinivasan1
, Abhisek Kundu1
,
Misha Smelyanskiy2
, Bharat Kaul1
, and Pradeep Dubey1
1
Parallel Computing Lab, Intel Labs
2
Facebook, 1 Hacker Way, Menlo Park, CA
Abstract
This paper presents the first comprehensive empirical study demonstrating the
efficacy of the Brain Floating Point (BFLOAT16) half-precision format for Deep
Learning training across image classification, speech recognition, language model-
ing, generative networks and industrial recommendation systems. BFLOAT16 is
attractive for Deep Learning training for two reasons: the range of values it can
represent is the same as that of IEEE 754 floating-point format (FP32) and conver-
sion to/from FP32 is simple. Maintaining the same range as FP32 is important to
ensure that no hyper-parameter tuning is required for convergence; e.g., IEEE 754
compliant half-precision floating point (FP16) requires hyper-parameter tuning.
In this paper, we discuss the flow of tensors and various key operations in mixed
precision training, and delve into details of operations, such as the rounding modes
for converting FP32 tensors to BFLOAT16. We have implemented a method to
emulate BFLOAT16 operations in Tensorflow, Caffe2, IntelCaffe, and Neon for
our experiments. Our results show that deep learning training using BFLOAT16
tensors achieves the same state-of-the-art (SOTA) results across domains as FP32
tensors in the same number of iterations and with no changes to hyper-parameters.
1 Introduction
The spectacular success of Deep Learning has come riding on the ready availability of data and a
tremendous growth in compute capability of deep learning systems. In recent years, compute growth
has been driven by specialized architectures for GEMM (General Matrix Multiply) acceleration,
and the shift to low precision compute. Inference has witnessed a proliferation of mixed precision
compute [19, 33, 27, 25] where different operations execute at different precision, all the way from
binary/ternary operands to 16b floating point. Similarly, training has also witnessed its share of mixed
precision methods, where a combination of half- and single-precision compute is used.
There are at least three half-precision formats in the domain of mixed precision training of large neural
networks: FP16 [28], 16-bit Integer based [9], and BFLOAT16 [10, 4, 3]. All these methods have 16-
bit input operands and 32-bit accumulators for all the computations. Of the three formats, only the first
two have publicly available description of training methodology and experimental results on a wide
variety of neural networks although BFLOAT16 was originally conceived for deep learning training.
BFLOAT16 data format was first introduced as part of distributed training frameworks DistBelief [10]
and Tensorflow [4] as a low precision storage format used to reduce communication volumes of
∗
corresponding author {naveen.k.mellempudi}@intel.com
†
IIIT Hyderabad, ‡
Lab126 Amazon, work done while at at Intel
Preprint. Under review.
arXiv:1905.12322v3
[cs.LG]
13
Jun
2019

weights and activations shared between compute nodes during distributed parallel training3
. It has
since become an alternative numeric format specifically targeted towards accelerating deep leaning
training (mainly within the Google ecosystem [3]), because of its wider dynamic range and smaller
footprint. In this work, we present a detailed mixed precision methodology using BFLOAT16 and
demonstrate coverage by training a variety of workloads from image processing (including GANs),
to speech/language processing, and recommendation systems. For our experiments we employ a
method, where FP32 operations emulate the behavior of BFLOAT16 operations by appropriately
zeroing out the lower 16 bits and appropriately rounding the input operands.
We have developed a library called Quantlib to implement the emulation in multiple deep learning
frameworks such as IntelCaffe, Caffe2, Neon and Tensorflow. One of the functions Quantlib provides
is appropriately modifying the elements of an input FP32 tensor to emulate the behavior of BFLOAT16.
Specifically, it zeroes out the lower 16 bits of the FP32 elements and performs RNE (Round to Nearest
Even) rounding based on those bits. This modification ensures that the tensor possesses FP32 precision
(so that FP32-hardware and FP32-libraries can operate on it), and also provides the exact precision
and rounding as would be afforded by BFLOAT16 hardware. Quantlib is called prior to GEMM
operations (or other operations which are planned to be implemented in BFLOAT16) to emulate
the behavior of BFLOAT16 input operands, while FP32 output of the GEMM naturally fits into the
“BFLOAT16-input, FP32-accumulator” schema of this training methodology.
Using multiple deep learning frameworks modified to insert appropriate Quantlib calls, we provide
SOTA results for: AlexNet [24], ResNet-50 [20], DC-GAN [32], SR-GAN [26], DeepSpeech2
[5], GNMT [40], and two industrial workloads namely: a Deep and Cross Network, and a DNN
Recommendation System. We also qualitatively compare and contrast the training methodologies
using BFLOAT16, FP16 and INT16. We observe that FP16-based training requires tuning an
additional hyper-parameter for loss scaling to achieve SOTA results; INT16-based training requires
fine grained block-quantization and maintaining block-level scaling factors to achieve SOTA results.
In comparison all BFLOAT16 experiments are performed without any hyperparameter changes and
BFLOAT16 kernels are expected to be relatively straightforward.
The rest of the paper is organized as follows. Section 2 provides a survey of the literature and
describes various attempts at half-precision based training. Section 3 discusses the BFLOAT16
format, operations and data flow in detail. Section 4 describes our experimental results in detail.
Section 5 discusses our concluding thoughts.
2 Related Work
Application of low precision datatype in deep learning is a well explored topic in research. Literature
shows that various different reduced precision data representations have been investigated which can
be broadly classified into two types: the more standard floating-point based formats [28, 15, 12] and
custom fixed point based formats [37, 7, 18, 22, 23].
Custom fixed point representations may offer more flexibility than typical floating point based ones
in terms of both increased precision and dynamic range by maintaining separate integer values
for precision and range. Consequently, fixed point representations may provide more robust and
accurate training of an underlying application. The work reported in [37] leverages the dynamically
scaled fixed point representation proposed in [39] to speed up convolution neural networks by 4×
over an optimized floating point implementation on general purpose CPU hardware. In [18], the
authors present a comprehensive study on the effect of low precision fixed point computation for
deep learning. They also train smaller networks using 16-bit fixed point on specialized hardware.
Researchers have ventured into less than 16-bit precision as well and almost all of them use custom
fixed point schemes. Reference [7] uses a dynamical fixed point format with low precision multipli-
cations with up to 12-bit operations. This idea is further advanced in [8] where the authors showcase
training with only binary weights while keeping all other tensors and operations in full precision.
Another extension [21] uses binary activations as well; however, the gradients and the weights are
maintained in full precision. Another related work [22] uses activations and weights quantized into
6-bits for neural network training with gradients in full precision. The method described in [33]
uses binary representation for all components including gradients. However, all the aforementioned
3
special thanks to Jeff Dean for pointing this out
2

methods are shown to work for smaller benchmark model/data-sets only and invariably result in
a non-trivial drop in accuracy with larger ImageNet data-set [11] and classification task [35]. The
authors of [23] advocate for a fixed point numerical format called Flexpoint that is specifically
tailored for executing deep neural networks on a specialized hardware; this datatype is shown to
outperform FP16 and achieve numerical parity with FP32 across a diverse set of workloads. A more
general dynamic fixed point representation and associated compute primitives are presented in [9],
which leverages general purpose hardware using the integer-compute pipeline to match FP32 baseline
accuracy across state of the art convolution neural networks.
The disadvantage of these integer based representations in contrast to floating point is the additional
overheads of handling shared exponents and managing accumulator overflow. Köster et al.[23]
proposed an algorithm that predicts the shared exponent ahead of time to eliminate some of these
overheads. However this solution requires collection of additional statistics at each layer, which
cannot be efficiently computed on general purpose hardware.
A mixed precision training methodology using FP16 and FP32 is reported in [28]. This work employs
FP16 for storing activations, weights and gradients. The computations during forward pass and
back propagation use FP16 datatype while results are accumulated into FP32. A master copy of
the FP32 weights are preserved for the update operation. The authors successfully perform deep
learning training on a wide range of applications encompassing deep networks and larger data-sets
(ILSVRC-class problems) at the expense of minimal loss compared to baseline FP32 results. This
work, however, underlines that FP16/FP32 mixed precision training entails loss scaling [15] to attain
near-SOTA results. Loss scaling, basically, ensures that back-propagated gradient values are shifted
into a range which can be represented by FP16 and therefore the small magnitude (negative exponent)
values which are critical for accuracy are preserved.
The need for loss scaling can be avoided by using BFLOAT16 datatype. The hardware numerics
of BFLOAT16 on Intel architecture is available at [1]. BFLOAT16 has been underlined to be a
crucial ingredient for achieving peta-FLOPS scale on image classification task in [42]. In [3], Google
notes the speed ups achieved on using this datatype over FP32 for TensorFlow models for various
tasks, such as, image classification, image segmentation, object detection, machine translation. It
may be noted that the benefits of BFLOAT16 are not only restricted to machine learning paradigm,
the recently published work [41] uses this representation for performing Monte Carlo simulations
of Ising model which is an important model is statistical physics. In fact, the authors of [41]
mention BFLOAT16 “provides better training and model accuracy than the IEEE half-precision
representation”. The Julia language [6], which is designed to provide high-performance without
sacrificing ease of programming, has also been shown to be benefited from BFLOAT16 [13]. OpenAI
has also mentioned that optimizing kernels targeting BFLOAT16 is “in active development” [17].
3 Training with Brain Floating Point
Numerous studies have shown that 16-bits of precision is sufficient for training deep neural
networks[18],[28],[23],[9]. Researchers have experimented with various numeric formats to op-
timize training platforms for power and performance. State-of-the-art training platforms today have
chosen IEEE-754 half-precision floating point as the preferred numeric format for deep leaning
training. However, the narrow dynamic range of half-precision floating point is not sufficient to
represent error gradients during back propagation. To mitigate this, training methods use loss scaling
techniques[28] to shift gradients into expressible range supported by half-precision floats. While this
is easier to implement for certain feed-forward networks as a simple multiplication of loss with a
constant scaling factor, others (e.g. recurrent) require a more sophisticated approach to determine
the right scaling parameter. This process is often iterative and requires significant time and resource
investment from data scientists to optimize it to their network. These software overheads become a
hindrance for seamless migration of new deep learning applications to take advantage of the low-
precision hardware. Recent developments in software tools such as “automatic mixed precision” [30]
are aimed at easing some of this burden from data scientists. However, these tools in their current
form also require changes in the original model code and are not guaranteed to result in sufficient
performance gains.
The values are represented as truncated full precision floating point values with 8 bits of mantissa and
the dynamic range comparable to FP32 (Table 1). The extended dynamic range can now represent
3

smaller gradient values without applying complicated loss scaling methods, which enables easier
migration of deep learning workloads to BFLOAT16 hardware. There are some additional benefits to
adopting BFLOAT16 numeric format to build hardware for deep learning. Core compute primitives
such as FMA can be built using 8-bit multipliers which lead to significant area and power savings
while preserving the full dynamic range of FP32. Table 1 shows the comparison of BFLOAT16 with
other standard IEEE floating point formats.
Table 1: Comparison BFLOAT16 numeric format with IEEE-754 FP32 and FP16 formats.
Data Type Bit Format Max Min Min Acc.
(s, e, m) Normal Normal Subnormal Size
FP32 1, 8, 23 3.40e38 1.17e−38 1.40e−45 float32
FP16 1, 5, 10 6.55e4 6.10e−5 5.96e−8 float32
BFLOAT16 1, 8, 7 3.38e38 1.17e−38 N/A float32
Figure 1: Mixed precision data flow used for training DNNs with BFLOAT16 data format
Figure 1 shows the mixed precision data flow used to train deep neural networks using BFLOAT16
numeric format. The core compute kernels represented as GEMM operations accept inputs as
BFLOAT16 tensors and accumulate the output to FP32 tensors. Quantlib (shown as Q in Figure 1)
modifies these output tensors to BFLOAT16 format before passing them to the next layer. Quantlib
is also employed to modify a copy of the FP32 weights to BFLOAT16 for the forward pass. Error
gradients with respect to the inputs also in BFLOAT16 format. Non-GEMM compute operations
including batch-normalization, and activation functions such as ReLU, tanh and sigmoid also accept
BFLOAT16 tensors as inputs. Bias tensors are always maintained in FP32. The weight update step
(e.g., in SGD solver) uses the FP32 copy of the weights to maintain model accuracy.
4 Results
Our evaluation of BFLOAT16 consists of the aforementioned deep learning models from different
application domains and frameworks, using the tensor modification method via Quantlib discussed in
section 1.
4.1 Convolution Neural Networks
Convolutional neural networks (CNN) have been primarily used for computer vision applications such
as image classification, object detection and semantic segmentation. CNNs have been extensively
studied both in academia and industry, primarily driven by public benchmarks such as the ImageNet
Large Scale Visual Recognition Competition (ILSVRC). Over the past few years the CNNs which
have won the ILSVRC competition, have become well established benchmarks. Here we choose
AlexNet (ILSVRC 2012) [24] and ResNet-50 (ILSVRC 2015) [20] as representative models for
4

the BFLOAT16 evaluation. In addition to Convolution and InnerProduct layers (which contributes
to majority of the computations), we use BFLOAT16 emulations for ReLU, BatchNorm, Pooling,
Dropout and EltWise layers as well. This ensures that the full training pipeline uses BFLOAT16, not
necessitating the use of higher precision for the intermediate tensor outputs.
4.1.1 AlexNet
For AlexNet, we used a global minibatch of 1024 running data parallel on 16 nodes for 88 epochs and
achieved 57.4% top-1 and 80.7% top-5 accuracy. As shown in Figure 2, our BFLOAT16 emulation
follows very closely to the actual FP32 run and achieves 57.2% top-1 and 80.1% top-5 accuracy.
57.4%
57.2%
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#Epochs
Top-1 FP32 Top-1 BFP16 Top-5 FP32 Top-5 BFP16
(a) AlexNet
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#Epochs
Top-1 FP32 Top-1 BFP16 Top-5 FP32 Top-5 BFP16
(b) ResNet-50
Figure 2: Imagenet-1K training, top-1 and top-5 validation accuracy plots for CNNs
4.1.2 ResNet
Our Resnet-50 experiments are with a global minibatch of 1024 running data parallel on 32 nodes
using SGD with Nestrov momentum. We trained for 90 epochs with learning rate warm up for first
5 epochs. Baseline FP32 run achieved top-1 accuracy of 74.7% and top-5 accuracy of 92.0% and
as shown in Figure 2, our BFLOAT16 emulation follows the baseline almost exactly and achieving
the same top-1 and top-5 accuracy. During training we use local batch statistics for the batch
normalization to compute validation accuracy after every epoch. The fully trained BFLOAT16 model,
achieves 75.7% top-1 test accuracy with global sample statistics, matching the baseline FP32 results.
4.2 Recurrent Neural Networks
Recurrent neural networks (RNN) unlike the feedforward networks allows for capturing temporal
information due to its feedback connections. These models have been popularly used for applications
such as automatic speech recognition (ASR) and language processing, which primarily involve
sequence-based learning. RNNs have been observed to have more demanding numerical range
requirements [28] and are more sensitive to the half precision datatype. For this class of networks we
identify Baidu’s DeepSpeech2 [5] and Google’s neural machine translation (GNMT) model [40] as
representative candidates for the BFLOAT16 evaluation.
4.2.1 DeepSpeech2
The Deep speech 2 (DS2) topology, consists of two convolution layers followed by 3 bi-directional
gated recurrent unit (GRU) layers with 2048 cells and a final inner-product layer as a classifier. We
use Adam optimizer to compute connectionist temporal classification loss (CTC) [16]. We use a
batch size of 64 and a learning rate of 0.0005. The aforementioned model is trained on the librispeech
dataset [31], which consists of 460 hour corpus.
4.2.2 Neural Machine Translation
Google’s Neural Machine Translation (GNMT) is the SOTA neural machine translation model using
a recurrent network. It uses stack of long short-term memory (LSTM) layers, along with an attention
model for language modeling and translation. Table 2 compares translation accuracy in terms of
achieved BLEU scores for baseline FP32 and BFLOAT16 emulation. We use the small Vietnamese
5

(a) DeepSpeech2 (b) GNMT
Figure 3: RNN training using BFLOAT16 data type.
(VI) to English (EN) model and big German (DE) to English (EN) model. BFLOAT16 emulation
achieves same or better accuracy than baseline. Figure 3 shows how closely BFLOAT16 emulation
run follows the baseline FP32 run.
Table 2: GNMT BLEU scores for De→En and Vi→En on WMT’16 and IWSLT’15 datasets.
TASK FP32 BFLOAT16
DE→EN, WMT’16 29.3 29.3
VI→EN, IWSLT’15 + ATTENTION 17.1 18.3
4.3 Generative Adversarial Networks (GANs)
Generative Adversarial Networks (GANs) have become a very important class of networks, they can
be used to learn and mimic any arbitrary distribution of data. GANs achieve this by using two separate
generator and discriminators networks in a tightly coupled way. Because GANs combine regression
and discrimination tasks during training they tend to have different requirements for numerical
precision and range. For the BFLOAT16 evaluation we consider DC-GAN[32] and SR-GAN [26]
models.
4.3.1 DC-GAN
DC-GAN [32] represents a critical step in designing GAN architectures which were earlier known
to be notoriously difficult to train. This consists of fractionally-strided convolutions with ReLU
activations in the generator, whereas convolutions with leaky ReLU activations are used in the
discriminator; batch normalization layers are used in both the generator and the discriminator. We have
implemented DC-GAN in Caffe and for our experiments all the input tensors (activations, weights)
are converted to BFLOAT16 for convolution layers (in both the generator and the discriminator),
while only the input activations are converted to BFLOAT16 for batch normalization layers; all other
tensors are maintained in full precision.
A comparison between FP32 and BFLOAT16 is shown in Table 3 in terms of inception scores and
MS-SSIM. As evident from the table, the outputs obtained for FP32 and BFLOAT16 are comparable.
Table 3: Comparison between FP32 and BFLOAT16 for DC-GAN on face dataset
Datatype Inception Score MS-SSIM
Baseline (FP32) 1.97 ± 0.054 0.262
BFLOAT16 2.06 ± 0.055 0.217
6

4.3.2 SR-GAN
SR-GAN generates photo-realistic high-resolution images by super-resolving from a single shot of the
low-resolution image [26]. The low-resolution images are scaled 4× preserving the spatial features
while minimizing the noise. The quality of the output is measured using SSIM (Structural Similarity)
and MS-SSIM (multi-scale structural similarity) and PNSR (peak signal to noise ratio) metrics. The
topology consists of a “generator” network based on Resnet architecture, and the “discriminator”
consists of 8 convolution layers each followed by a batchnorm and LeakyReLu. The network uses a
“VGG loss” function using a pre-trained VGG19 network [36].
For the BFLOAT16 experiments, we converted all the inputs tensors (weights, activations) at convolu-
tion layers to BFLOAT16, while keeping the rest of the layers (Batchnorm, ReLU, LeakyReLu and
Eltwise) at full precision.
Table 4: SR-GAN model trained with BFLOAT16 on DIV2K (http://www.vision.ee.ethz.ch/ntire17/)
dataset.
DATATYPE PSNR SSIM MS-SSIM
BASELINE (FP32) 26.1749 0.73753 0.99999
BFLOAT16 26.1415 0.74079 0.99999
(a) Generator Network (b) Discriminator Network
Figure 4: Training loss for SR-GAN training using BFLOAT16
4.4 Industrial Scale Recommendation System
Recommendation system and personalization models are very important for many practical-scale
applications. Here we evaluate the Deep & Cross Network [38] on a small Kaggle Criteo Dataset4
and a typical DNN recommender system [43, 29] on a large Terabyte Criteo Dataset5
, which target
predicting the ads click-through rate [34]. The accuracy of the recommendation system models is
measured by the log loss [38, 43, 29], which predicts when the users will click on ads. Lower log
loss translates into higher prediction accuracy for the recommendation model. Note that an accuracy
loss of 0.001 in log loss is considered unacceptable in practice.
For our BFLOAT16 experiments, all input tensors (activations and weights) are converted to
BFLOAT16 for fully connected layers in both forward and backward propagation passes. Dur-
ing the weight update stages, we use a FP32 master copy [28] to reduce the additional accuracy loss.
We use either the round-to-nearest or direct truncation scheme when we do the conversion from
BFLOAT16 to FP32.
The accuracy evaluation results are shown in Table 5. As we can observe, BFLOAT16 with the
round-to-nearest scheme is almost the same as FP32 baseline accuracy, while BFLOAT16 with the
direct truncation scheme suffers from a tiny accuracy degradation (∼ 0.02%).
4
https://www.kaggle.com/c/criteo-display-ad-challenge/data
5
https://www.criteo.com/news/press-releases/2015/07/criteo-releases-industrys-largest-ever-dataset/
7

Table 5: The log loss for Deep & Cross Network [38] on a small Kaggle Criteo dataset and a
DNN recommender system [43] on a TeraByte Criteo dataset trained with BFLOAT16 (with either
round-to-nearest or direct truncation for the conversion from FP32 to BFLOAT16).
RECOMMENDATION SYSTEM BASELINE(FP32) BFLOAT16 (RND) BFLOAT16 (TRUNC)
DEEP & CROSS NETWORK 0.44372 0.44372 0.44393
DNN RECOMMENDER SYSTEM 0.12520 0.12520 0.12537
4.5 Beyond Emulation - Towards Bare Metal Execution
We close this section by highlighting that our presented emulation strategy is an excellent approx-
imation of future Intel Xeon CPUs. We therefore took the slim CNN training framework GxM,
which was presented in [14], and implemented all important operators (convolution, fully-connected,
batch-normalization and pooling layers) utilizing the AVX512BF16 instruction set extensions [2].
Therefore, all activation and weight data was only present as 16bit data in memory and the special
VNNI (vector neural network instructions) datalayout was employed to support the BFLOAT16
dot-product instruction with FP32 accumulation. The execution of these instructions was done by
bit-accurate emulation on current AVX512 silicon with only a very slight performance tax. When
training ResNet-50 on Imagenet using the AVX512BF16 instructions, we achieved a Top-1 accuracy
of 75.62%, which matches the current state-of-the-art performance. Additionally, the code is already
heavily optimized and ready for prime-time. Additionally we have implemented a full BFLOAT16
LSTM-cell which is currently being integrated into Tensorflow.
5 Conclusion
Our goal in this paper was to establish BFLOAT16 as an alternative half-precision format for Deep
Learning training, given that its dynamic range is the same as that of FP32 and conversion to/from
FP32 is straightforward. Our empirical study demonstrates that, unlike IEEE 754 half-precision
format and 16-bit Integer, BFLOAT16 based training eliminates the need for hyperparameter tuning or
complex software management for block quantization. Our study also demonstrates that BFLOAT16
is a robust datatype having the ability to cover the range of tensors across application domains
including vision, speech, language, generative networks, and recommendation systems. We expect
industry-wide adoption of BFLOAT16 across emerging domains.
References
[1] BFLOAT16 - hardware numerics definition. https://
software.intel.com/sites/default/files/managed/40/8b/
bf16-hardware-numerics-definition-white-paper.pdf. Accessed: 2019-03-22.
[2] Intel architecture instruction set extensions and future features programming refer-
ence. https://software.intel.com/sites/default/files/managed/c5/15/
architecture-instruction-set-extensions-programming-reference.pdf. Ac-
cessed: 2019-05-21.
[3] Using bfloat16 with tensorflow models. https://cloud.google.com/tpu/docs/
bfloat16. Accessed: 2019-16-04.
[4] Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro,
Greg S Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, et al. Tensorflow: Large-scale
machine learning on heterogeneous distributed systems. arXiv preprint arXiv:1603.04467,
2016.
[5] Dario Amodei, Sundaram Ananthanarayanan, Rishita Anubhai, Jingliang Bai, Eric Battenberg,
Carl Case, Jared Casper, Bryan Catanzaro, Qiang Cheng, Guoliang Chen, et al. Deep speech 2:
End-to-end speech recognition in english and mandarin. In ICML, pages 173–182, 2016.
[6] Jeff Bezanson, Alan Edelman, Stefan Karpinski, and Viral B. Shah. Julia: A fresh approach to
numerical computing. SIAM Review, 59(1):65–98, 2017.
8

[7] Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Training deep neural networks
with low precision multiplications. arXiv preprint arXiv:1412.7024, 2014.
[8] Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Binaryconnect: Training deep
neural networks with binary weights during propagations. In NIPS, pages 3123–3131, 2015.
[9] Dipankar Das, Naveen Mellempudi, Dheevatsa Mudigere, Dhiraj D. Kalamkar, Sasikanth
Avancha, Kunal Banerjee, Srinivas Sridharan, Karthik Vaidyanathan, Bharat Kaul, Evange-
los Georganas, Alexander Heinecke, Pradeep Dubey, Jesús Corbal, Nikita Shustrov, Roman
Dubtsov, Evarist Fomenko, and Vadim O. Pirogov. Mixed precision training of convolutional
neural networks using integer operations. In ICLR, 2018.
[10] Jeffrey Dean, Greg Corrado, Rajat Monga, Kai Chen, Matthieu Devin, Mark Mao, Andrew
Senior, Paul Tucker, Ke Yang, Quoc V Le, et al. Large scale distributed deep networks. In
Advances in neural information processing systems, pages 1223–1231, 2012.
[11] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale
hierarchical image database. In CVPR, pages 248–255, 2009.
[12] Tim Dettmers. 8-bit approximations for parallelism in deep learning. arXiv preprint
arXiv:1511.04561, 2015.
[13] Keno Fischer and Elliot Saba. Automatic full compilation of julia programs and ML models to
cloud TPUs. CoRR, abs/1810.09868, 2018.
[14] Evangelos Georganas, Sasikanth Avancha, Kunal Banerjee, Dhiraj Kalamkar, Greg Henry, Hans
Pabst, and Alexander Heinecke. Anatomy of high-performance deep learning convolutions
on simd architectures. In Proceedings of the International Conference for High Performance
Computing, Networking, Storage, and Analysis, SC ’18, pages 66:1–66:12, Piscataway, NJ,
USA, 2018. IEEE Press.
[15] Boris Ginsburg, Sergei Nikolaev, and Paulius Micikevicius. Training of deep networks with
half-precision float. NVidia GPU Technology Conference, 2017.
[16] Alex Graves, Santiago Fernández, Faustino Gomez, and Jürgen Schmidhuber. Connectionist
temporal classification: labelling unsegmented sequence data with recurrent neural networks. In
Proceedings of the 23rd international conference on Machine learning, pages 369–376. ACM,
2006.
[17] Scott Gray, Alec Radford, and Diederik P. Kingma. Gpu kernels for block-sparse
weights. https://s3-us-west-2.amazonaws.com/openai-assets/blocksparse/
blocksparsepaper.pdf. Accessed: 2019-16-04.
[18] Suyog Gupta, Ankur Agrawal, Kailash Gopalakrishnan, and Pritish Narayanan. Deep learning
with limited numerical precision. In ICML, pages 1737–1746, 2015.
[19] Song Han, Huizi Mao, and William J. Dally. Deep compression: Compressing deep neural
network with pruning, trained quantization and huffman coding. In ICLR, 2016.
[20] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image
recognition. In CVPR, pages 770–778, 2016.
[21] Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Binarized
neural networks. In NIPS, pages 4107–4115, 2016.
[22] Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Quan-
tized neural networks: Training neural networks with low precision weights and activations.
arXiv preprint arXiv:1609.07061, 2016.
[23] Urs Köster, Tristan Webb, Xin Wang, Marcel Nassar, Arjun K. Bansal, William Constable,
Oguz Elibol, Stewart Hall, Luke Hornof, Amir Khosrowshahi, Carey Kloss, Ruby J. Pai, and
Naveen Rao. Flexpoint: An adaptive numerical format for efficient training of deep neural
networks. CoRR, abs/1711.02213, 2017.
[24] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep
convolutional neural networks. In NIPS, pages 1097–1105, 2012.
[25] Abhisek Kundu, Kunal Banerjee, Naveen Mellempudi, Dheevatsa Mudigere, Dipankar Das,
Bharat Kaul, and Pradeep Dubey. Ternary residual networks. CoRR, abs/1707.04679, 2017.
9

[26] Christian Ledig, Lucas Theis, Ferenc Huszár, Jose Caballero, Andrew Cunningham, Alejandro
Acosta, Andrew P Aitken, Alykhan Tejani, Johannes Totz, Zehan Wang, et al. Photo-realistic
single image super-resolution using a generative adversarial network. In CVPR, volume 2,
page 4, 2017.
[27] Naveen Mellempudi, Abhisek Kundu, Dheevatsa Mudigere, Dipankar Das, Bharat Kaul, and
Pradeep Dubey. Ternary neural networks with fine-grained quantization. arXiv preprint
arXiv:1705.01462, 2017.
[28] Paulius Micikevicius, Sharan Narang, Jonah Alben, Gregory Diamos, Erich Elsen, David Garcia,
Boris Ginsburg, Michael Houston, Oleksii Kuchaev, Ganesh Venkatesh, et al. Mixed precision
training. arXiv preprint arXiv:1710.03740, 2017.
[29] Maxim Naumov, Dheevatsa Mudigere, et al. Deep learning recommendation model for person-
alization and recommendation systems. arXiv preprint arXiv:1906.00091, 2019.
[30] NVIDIA. Automatic mixed precision for deep learning. https://developer.nvidia.com/
automatic-mixed-precision. Accessed: 2019-22-05.
[31] Vassil Panayotov, Guoguo Chen, Daniel Povey, and Sanjeev Khudanpur. Librispeech: an
asr corpus based on public domain audio books. In 2015 IEEE International Conference on
Acoustics, Speech and Signal Processing (ICASSP), pages 5206–5210. IEEE, 2015.
[32] Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with
deep convolutional generative adversarial networks. In ICLR, 2016.
[33] Mohammad Rastegari, Vicente Ordonez, Joseph Redmon, and Ali Farhadi. Xnor-net: Imagenet
classification using binary convolutional neural networks. In ECCV, 2016.
[34] Matthew Richardson, Ewa Dominowska, and Robert Ragno. Predicting clicks: Estimating the
click-through rate for new ads. In Proceedings of the 16th International Conference on World
Wide Web, WWW ’07, pages 521–530, New York, NY, USA, 2007. ACM.
[35] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng
Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual
recognition challenge. International Journal of Computer Vision, 115(3):211–252, 2015.
[36] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale
image recognition. arXiv preprint arXiv:1409.1556, 2014.
[37] Vincent Vanhoucke, Andrew Senior, and Mark Z Mao. Improving the speed of neural networks
on CPUs. In Proc. Deep Learning and Unsupervised Feature Learning NIPS Workshop,
volume 1, 2011.
[38] Ruoxi Wang, Bin Fu, Gang Fu, and Mingliang Wang. Deep & cross network for ad click
predictions. In Proceedings of the ADKDD’17, ADKDD’17, pages 12:1–12:7, New York, NY,
USA, 2017. ACM.
[39] Darrell Williamson. Dynamically scaled fixed point arithmetic. In PacRim, pages 315–318,
1991.
[40] Yonghui Wu, Mike Schuster, Zhifeng Chen, Quoc V Le, Mohammad Norouzi, Wolfgang
Macherey, Maxim Krikun, Yuan Cao, Qin Gao, Klaus Macherey, et al. Google’s neural machine
translation system: Bridging the gap between human and machine translation. arXiv preprint
arXiv:1609.08144, 2016.
[41] Kun Yang, Yi-Fan Chen, George Roumpos, Chris Colby, and John R. Anderson. High per-
formance monte carlo simulation of ising model on TPU clusters. CoRR, abs/1903.11714,
2019.
[42] Chris Ying, Sameer Kumar, Dehao Chen, Tao Wang, and Youlong Cheng. Image classification
at supercomputer scale. CoRR, abs/1811.06992, 2018.
[43] Jian Zhang, Jiyan Yang, and Hector Yuen. Training with low-precision embedding tables. In
Systems for Machine Learning Workshop at NeurIPS 2018. 2018.
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