original_content.txt

Published as a conference paper at ICLR 2021
ANIMAGE IS WORTH 16X16 W ORDS :
TRANSFORMERS FOR IMAGE RECOGNITION AT SCALE
Alexey Dosovitskiy;y, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn,
Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer,
Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, Neil Houlsby;y
equal technical contribution,yequal advising
Google Research, Brain Team
fadosovitskiy, neilhoulsby g@google.com
ABSTRACT
While the Transformer architecture has become the de-facto standard for natural
language processing tasks, its applications to computer vision remain limited. In
vision, attention is either applied in conjunction with convolutional networks, or
used to replace certain components of convolutional networks while keeping their
overall structure in place. We show that this reliance on CNNs is not necessary
and a pure transformer applied directly to sequences of image patches can perform
very well on image classification tasks. When pre-trained on large amounts of
data and transferred to multiple mid-sized or small image recognition benchmarks
(ImageNet, CIFAR-100, VTAB, etc.), Vision Transformer (ViT) attains excellent
results compared to state-of-the-art convolutional networks while requiring sub-
stantially fewer computational resources to train.1
1 I NTRODUCTION
Self-attention-based architectures, in particular Transformers (Vaswani et al., 2017), have become
the model of choice in natural language processing (NLP). The dominant approach is to pre-train on
a large text corpus and then fine-tune on a smaller task-specific dataset (Devlin et al., 2019). Thanks
to Transformers’ computational efficiency and scalability, it has become possible to train models of
unprecedented size, with over 100B parameters (Brown et al., 2020; Lepikhin et al., 2020). With the
models and datasets growing, there is still no sign of saturating performance.
In computer vision, however, convolutional architectures remain dominant (LeCun et al., 1989;
Krizhevsky et al., 2012; He et al., 2016). Inspired by NLP successes, multiple works try combining
CNN-like architectures with self-attention (Wang et al., 2018; Carion et al., 2020), some replacing
the convolutions entirely (Ramachandran et al., 2019; Wang et al., 2020a). The latter models, while
theoretically efficient, have not yet been scaled effectively on modern hardware accelerators due to
the use of specialized attention patterns. Therefore, in large-scale image recognition, classic ResNet-
like architectures are still state of the art (Mahajan et al., 2018; Xie et al., 2020; Kolesnikov et al.,
2020).
Inspired by the Transformer scaling successes in NLP, we experiment with applying a standard
Transformer directly to images, with the fewest possible modifications. To do so, we split an image
into patches and provide the sequence of linear embeddings of these patches as an input to a Trans-
former. Image patches are treated the same way as tokens (words) in an NLP application. We train
the model on image classification in supervised fashion.
When trained on mid-sized datasets such as ImageNet without strong regularization, these mod-
els yield modest accuracies of a few percentage points below ResNets of comparable size. This
seemingly discouraging outcome may be expected: Transformers lack some of the inductive biases
1Fine-tuning code and pre-trained models are available at https://github.com/
google-research/vision_transformer
1arXiv:2010.11929v2  [cs.CV]  3 Jun 2021
Published as a conference paper at ICLR 2021
inherent to CNNs, such as translation equivariance and locality, and therefore do not generalize well
when trained on insufficient amounts of data.
However, the picture changes if the models are trained on larger datasets (14M-300M images). We
find that large scale training trumps inductive bias. Our Vision Transformer (ViT) attains excellent
results when pre-trained at sufficient scale and transferred to tasks with fewer datapoints. When
pre-trained on the public ImageNet-21k dataset or the in-house JFT-300M dataset, ViT approaches
or beats state of the art on multiple image recognition benchmarks. In particular, the best model
reaches the accuracy of 88:55% on ImageNet, 90:72% on ImageNet-ReaL, 94:55% on CIFAR-100,
and77:63% on the VTAB suite of 19 tasks.
2 R ELATED WORK
Transformers were proposed by Vaswani et al. (2017) for machine translation, and have since be-
come the state of the art method in many NLP tasks. Large Transformer-based models are often
pre-trained on large corpora and then fine-tuned for the task at hand: BERT (Devlin et al., 2019)
uses a denoising self-supervised pre-training task, while the GPT line of work uses language mod-
eling as its pre-training task (Radford et al., 2018; 2019; Brown et al., 2020).
Naive application of self-attention to images would require that each pixel attends to every other
pixel. With quadratic cost in the number of pixels, this does not scale to realistic input sizes. Thus,
to apply Transformers in the context of image processing, several approximations have been tried in
the past. Parmar et al. (2018) applied the self-attention only in local neighborhoods for each query
pixel instead of globally. Such local multi-head dot-product self attention blocks can completely
replace convolutions (Hu et al., 2019; Ramachandran et al., 2019; Zhao et al., 2020). In a different
line of work, Sparse Transformers (Child et al., 2019) employ scalable approximations to global self-
attention in order to be applicable to images. An alternative way to scale attention is to apply it in
blocks of varying sizes (Weissenborn et al., 2019), in the extreme case only along individual axes (Ho
et al., 2019; Wang et al., 2020a). Many of these specialized attention architectures demonstrate
promising results on computer vision tasks, but require complex engineering to be implemented
efficiently on hardware accelerators.
Most related to ours is the model of Cordonnier et al. (2020), which extracts patches of size 22
from the input image and applies full self-attention on top. This model is very similar to ViT,
but our work goes further to demonstrate that large scale pre-training makes vanilla transformers
competitive with (or even better than) state-of-the-art CNNs. Moreover, Cordonnier et al. (2020)
use a small patch size of 22pixels, which makes the model applicable only to small-resolution
images, while we handle medium-resolution images as well.
There has also been a lot of interest in combining convolutional neural networks (CNNs) with forms
of self-attention, e.g. by augmenting feature maps for image classification (Bello et al., 2019) or by
further processing the output of a CNN using self-attention, e.g. for object detection (Hu et al., 2018;
Carion et al., 2020), video processing (Wang et al., 2018; Sun et al., 2019), image classification (Wu
et al., 2020), unsupervised object discovery (Locatello et al., 2020), or unified text-vision tasks (Chen
et al., 2020c; Lu et al., 2019; Li et al., 2019).
Another recent related model is image GPT (iGPT) (Chen et al., 2020a), which applies Transformers
to image pixels after reducing image resolution and color space. The model is trained in an unsu-
pervised fashion as a generative model, and the resulting representation can then be fine-tuned or
probed linearly for classification performance, achieving a maximal accuracy of 72% on ImageNet.
Our work adds to the increasing collection of papers that explore image recognition at larger scales
than the standard ImageNet dataset. The use of additional data sources allows to achieve state-of-
the-art results on standard benchmarks (Mahajan et al., 2018; Touvron et al., 2019; Xie et al., 2020).
Moreover, Sun et al. (2017) study how CNN performance scales with dataset size, and Kolesnikov
et al. (2020); Djolonga et al. (2020) perform an empirical exploration of CNN transfer learning from
large scale datasets such as ImageNet-21k and JFT-300M. We focus on these two latter datasets as
well, but train Transformers instead of ResNet-based models used in prior works.
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Transformer 
Encoder
MLP 
Head
Vision 
Transformer 
(ViT)*
Linear 
Projection 
of 
Flattened 
Patches
*
 
Extra 
learnable
     
[class]
 
embedding
1
2
3
4
5
6
7
8
90Patch 
+ 
Position 
Embedding
Class
Bird
Ball
Car
...
Embedded 
Patches
Multi-Head 
Attention
Norm
MLP
Norm
+
L
 
x
+Transformer 
Encoder
Figure 1: Model overview. We split an image into fixed-size patches, linearly embed each of them,
add position embeddings, and feed the resulting sequence of vectors to a standard Transformer
encoder. In order to perform classification, we use the standard approach of adding an extra learnable
“classification token” to the sequence. The illustration of the Transformer encoder was inspired by
Vaswani et al. (2017).
3 M ETHOD
In model design we follow the original Transformer (Vaswani et al., 2017) as closely as possible.
An advantage of this intentionally simple setup is that scalable NLP Transformer architectures – and
their efficient implementations – can be used almost out of the box.
3.1 V ISION TRANSFORMER (VIT)
An overview of the model is depicted in Figure 1. The standard Transformer receives as input a 1D
sequence of token embeddings. To handle 2D images, we reshape the image x2RHWCinto a
sequence of flattened 2D patches xp2RN(P2
C), where (H;W )is the resolution of the original
image,Cis the number of channels, (P;P)is the resolution of each image patch, and N=HW=P2
is the resulting number of patches, which also serves as the effective input sequence length for the
Transformer. The Transformer uses constant latent vector size Dthrough all of its layers, so we
flatten the patches and map to Ddimensions with a trainable linear projection (Eq. 1). We refer to
the output of this projection as the patch embeddings.
Similar to BERT’s [class] token, we prepend a learnable embedding to the sequence of embed-
ded patches ( z0
0=xclass), whose state at the output of the Transformer encoder ( z0
L) serves as the
image representation y(Eq. 4). Both during pre-training and fine-tuning, a classification head is at-
tached to z0
L. The classification head is implemented by a MLP with one hidden layer at pre-training
time and by a single linear layer at fine-tuning time.
Position embeddings are added to the patch embeddings to retain positional information. We use
standard learnable 1D position embeddings, since we have not observed significant performance
gains from using more advanced 2D-aware position embeddings (Appendix D.4). The resulting
sequence of embedding vectors serves as input to the encoder.
The Transformer encoder (Vaswani et al., 2017) consists of alternating layers of multiheaded self-
attention (MSA, see Appendix A) and MLP blocks (Eq. 2, 3). Layernorm (LN) is applied before
every block, and residual connections after every block (Wang et al., 2019; Baevski & Auli, 2019).
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The MLP contains two layers with a GELU non-linearity.
z0= [xclass;x1
pE;x2
pE;


;xN
pE] +Epos;E2R(P2
C)D;Epos2R(N+1)D(1)
z0
`= MSA(LN( z`1)) +z`1; ` = 1:::L (2)
z`= MLP(LN( z0
`)) +z0
`; ` = 1:::L (3)
y= LN( z0
L) (4)
Inductive bias. We note that Vision Transformer has much less image-specific inductive bias than
CNNs. In CNNs, locality, two-dimensional neighborhood structure, and translation equivariance are
baked into each layer throughout the whole model. In ViT, only MLP layers are local and transla-
tionally equivariant, while the self-attention layers are global. The two-dimensional neighborhood
structure is used very sparingly: in the beginning of the model by cutting the image into patches and
at fine-tuning time for adjusting the position embeddings for images of different resolution (as de-
scribed below). Other than that, the position embeddings at initialization time carry no information
about the 2D positions of the patches and all spatial relations between the patches have to be learned
from scratch.
Hybrid Architecture. As an alternative to raw image patches, the input sequence can be formed
from feature maps of a CNN (LeCun et al., 1989). In this hybrid model, the patch embedding
projection E(Eq. 1) is applied to patches extracted from a CNN feature map. As a special case,
the patches can have spatial size 1x1, which means that the input sequence is obtained by simply
flattening the spatial dimensions of the feature map and projecting to the Transformer dimension.
The classification input embedding and position embeddings are added as described above.
3.2 F INE-TUNING AND HIGHER RESOLUTION
Typically, we pre-train ViT on large datasets, and fine-tune to (smaller) downstream tasks. For
this, we remove the pre-trained prediction head and attach a zero-initialized DKfeedforward
layer, where Kis the number of downstream classes. It is often beneficial to fine-tune at higher
resolution than pre-training (Touvron et al., 2019; Kolesnikov et al., 2020). When feeding images
of higher resolution, we keep the patch size the same, which results in a larger effective sequence
length. The Vision Transformer can handle arbitrary sequence lengths (up to memory constraints),
however, the pre-trained position embeddings may no longer be meaningful. We therefore perform
2D interpolation of the pre-trained position embeddings, according to their location in the original
image. Note that this resolution adjustment and patch extraction are the only points at which an
inductive bias about the 2D structure of the images is manually injected into the Vision Transformer.
4 E XPERIMENTS
We evaluate the representation learning capabilities of ResNet, Vision Transformer (ViT), and the
hybrid. To understand the data requirements of each model, we pre-train on datasets of varying size
and evaluate many benchmark tasks. When considering the computational cost of pre-training the
model, ViT performs very favourably, attaining state of the art on most recognition benchmarks at
a lower pre-training cost. Lastly, we perform a small experiment using self-supervision, and show
that self-supervised ViT holds promise for the future.
4.1 S ETUP
Datasets. To explore model scalability, we use the ILSVRC-2012 ImageNet dataset with 1k classes
and 1.3M images (we refer to it as ImageNet in what follows), its superset ImageNet-21k with
21k classes and 14M images (Deng et al., 2009), and JFT (Sun et al., 2017) with 18k classes and
303M high-resolution images. We de-duplicate the pre-training datasets w.r.t. the test sets of the
downstream tasks following Kolesnikov et al. (2020). We transfer the models trained on these
dataset to several benchmark tasks: ImageNet on the original validation labels and the cleaned-up
ReaL labels (Beyer et al., 2020), CIFAR-10/100 (Krizhevsky, 2009), Oxford-IIIT Pets (Parkhi et al.,
2012), and Oxford Flowers-102 (Nilsback & Zisserman, 2008). For these datasets, pre-processing
follows Kolesnikov et al. (2020).
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Model Layers Hidden size D MLP size Heads Params
ViT-Base 12 768 3072 12 86M
ViT-Large 24 1024 4096 16 307M
ViT-Huge 32 1280 5120 16 632M
Table 1: Details of Vision Transformer model variants.
We also evaluate on the 19-task VTAB classification suite (Zhai et al., 2019b). VTAB evaluates
low-data transfer to diverse tasks, using 1 000 training examples per task. The tasks are divided into
three groups: Natural – tasks like the above, Pets, CIFAR, etc. Specialized – medical and satellite
imagery, and Structured – tasks that require geometric understanding like localization.
Model Variants. We base ViT configurations on those used for BERT (Devlin et al., 2019), as
summarized in Table 1. The “Base” and “Large” models are directly adopted from BERT and we
add the larger “Huge” model. In what follows we use brief notation to indicate the model size and
the input patch size: for instance, ViT-L/16 means the “Large” variant with 1616input patch size.
Note that the Transformer’s sequence length is inversely proportional to the square of the patch size,
thus models with smaller patch size are computationally more expensive.
For the baseline CNNs, we use ResNet (He et al., 2016), but replace the Batch Normalization lay-
ers (Ioffe & Szegedy, 2015) with Group Normalization (Wu & He, 2018), and used standardized
convolutions (Qiao et al., 2019). These modifications improve transfer (Kolesnikov et al., 2020),
and we denote the modified model “ResNet (BiT)”. For the hybrids, we feed the intermediate fea-
ture maps into ViT with patch size of one “pixel”. To experiment with different sequence lengths,
we either (i) take the output of stage 4 of a regular ResNet50 or (ii) remove stage 4, place the same
number of layers in stage 3 (keeping the total number of layers), and take the output of this extended
stage 3. Option (ii) results in a 4x longer sequence length, and a more expensive ViT model.
Training & Fine-tuning. We train all models, including ResNets, using Adam (Kingma & Ba,
2015) with1= 0:9,2= 0:999, a batch size of 4096 and apply a high weight decay of 0:1, which
we found to be useful for transfer of all models (Appendix D.1 shows that, in contrast to common
practices, Adam works slightly better than SGD for ResNets in our setting). We use a linear learning
rate warmup and decay, see Appendix B.1 for details. For fine-tuning we use SGD with momentum,
batch size 512, for all models, see Appendix B.1.1. For ImageNet results in Table 2, we fine-tuned at
higher resolution: 512for ViT-L/16 and 518for ViT-H/14, and also used Polyak & Juditsky (1992)
averaging with a factor of 0:9999 (Ramachandran et al., 2019; Wang et al., 2020b).
Metrics. We report results on downstream datasets either through few-shot or fine-tuning accuracy.
Fine-tuning accuracies capture the performance of each model after fine-tuning it on the respective
dataset. Few-shot accuracies are obtained by solving a regularized least-squares regression problem
that maps the (frozen) representation of a subset of training images to f1;1gKtarget vectors. This
formulation allows us to recover the exact solution in closed form. Though we mainly focus on
fine-tuning performance, we sometimes use linear few-shot accuracies for fast on-the-fly evaluation
where fine-tuning would be too costly.
4.2 C OMPARISON TO STATE OF THE ART
We first compare our largest models – ViT-H/14 and ViT-L/16 – to state-of-the-art CNNs from
the literature. The first comparison point is Big Transfer (BiT) (Kolesnikov et al., 2020), which
performs supervised transfer learning with large ResNets. The second is Noisy Student (Xie et al.,
2020), which is a large EfficientNet trained using semi-supervised learning on ImageNet and JFT-
300M with the labels removed. Currently, Noisy Student is the state of the art on ImageNet and
BiT-L on the other datasets reported here. All models were trained on TPUv3 hardware, and we
report the number of TPUv3-core-days taken to pre-train each of them, that is, the number of TPU
v3 cores (2 per chip) used for training multiplied by the training time in days.
Table 2 shows the results. The smaller ViT-L/16 model pre-trained on JFT-300M outperforms BiT-L
(which is pre-trained on the same dataset) on all tasks, while requiring substantially less computa-
tional resources to train. The larger model, ViT-H/14, further improves the performance, especially
on the more challenging datasets – ImageNet, CIFAR-100, and the VTAB suite. Interestingly, this
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Ours-JFT Ours-JFT Ours-I21k BiT-L Noisy Student
(ViT-H/14) (ViT-L/16) (ViT-L/16) (ResNet152x4) (EfficientNet-L2)
ImageNet 88:550:04 87:760:03 85:300:02 87:540:02 88:4=88:5
ImageNet ReaL 90:720:05 90:540:03 88:620:05 90:54 90 :55
CIFAR-10 99:500:06 99:420:03 99:150:03 99:370:06
CIFAR-100 94:550:04 93:900:05 93:250:05 93:510:08
Oxford-IIIT Pets 97:560:03 97:320:11 94:670:15 96:620:23
Oxford Flowers-102 99:680:0299:740:0099:610:02 99:630:03
VTAB (19 tasks) 77:630:23 76:280:46 72:720:21 76:291:70
TPUv3-core-days 2:5k 0:68k 0:23k 9:9k 12:3k
Table 2: Comparison with state of the art on popular image classification benchmarks. We re-
port mean and standard deviation of the accuracies, averaged over three fine-tuning runs. Vision
Transformer models pre-trained on the JFT-300M dataset outperform ResNet-based baselines on all
datasets, while taking substantially less computational resources to pre-train. ViT pre-trained on the
smaller public ImageNet-21k dataset performs well too.Slightly improved 88:5%result reported
in Touvron et al. (2020).
VTAB (19 tasks)65707580Accuracy [%]
Natural (7 tasks)708090
Specialized (4 tasks)8082858890
Structured (8 tasks)506070ViT-H/14 BiT-L (R152x4) VIVI-Ex-100% (R50x3) S4L (R50x1)
Figure 2: Breakdown of VTAB performance in Natural ,Specialized , and Structured task groups.
model still took substantially less compute to pre-train than prior state of the art. However, we note
that pre-training efficiency may be affected not only by the architecture choice, but also other pa-
rameters, such as training schedule, optimizer, weight decay, etc. We provide a controlled study of
performance vs. compute for different architectures in Section 4.4. Finally, the ViT-L/16 model
pre-trained on the public ImageNet-21k dataset performs well on most datasets too, while taking
fewer resources to pre-train: it could be trained using a standard cloud TPUv3 with 8 cores in ap-
proximately 30 days.
Figure 2 decomposes the VTAB tasks into their respective groups, and compares to previous SOTA
methods on this benchmark: BiT, VIVI – a ResNet co-trained on ImageNet and Youtube (Tschannen
et al., 2020), and S4L – supervised plus semi-supervised learning on ImageNet (Zhai et al., 2019a).
ViT-H/14 outperforms BiT-R152x4, and other methods, on the Natural andStructured tasks. On the
Specialized the performance of the top two models is similar.
4.3 P RE-TRAINING DATA REQUIREMENTS
The Vision Transformer performs well when pre-trained on a large JFT-300M dataset. With fewer
inductive biases for vision than ResNets, how crucial is the dataset size? We perform two series of
experiments.
First, we pre-train ViT models on datasets of increasing size: ImageNet, ImageNet-21k, and JFT-
300M. To boost the performance on the smaller datasets, we optimize three basic regularization
parameters – weight decay, dropout, and label smoothing. Figure 3 shows the results after fine-
tuning to ImageNet (results on other datasets are shown in Table 5)2. When pre-trained on the
smallest dataset, ImageNet, ViT-Large models underperform compared to ViT-Base models, despite
(moderate) regularization. With ImageNet-21k pre-training, their performances are similar. Only
with JFT-300M, do we see the full benefit of larger models. Figure 3 also shows the performance
2Note that the ImageNet pre-trained models are also fine-tuned, but again on ImageNet. This is because the
resolution increase during fine-tuning improves the performance.
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ImageNet ImageNet-21k JFT-300M
Pre-training dataset7075808590ImageNet Top1 Accuracy [%]
BiT
ViT-B/32
ViT-B/16ViT-L/32
ViT-L/16
ViT-H/14
Figure 3: Transfer to ImageNet. While
large ViT models perform worse than BiT
ResNets (shaded area) when pre-trained on
small datasets, they shine when pre-trained on
larger datasets. Similarly, larger ViT variants
overtake smaller ones as the dataset grows.
10 M 30 M 100 M 300 M
Number of JFT pre-training samples3040506070Linear 5-shot ImageNet Top1 [%]
ViT-L/16
ViT-L/32ViT-B/32
ViT-b/32ResNet50x1 (BiT)
ResNet152x2 (BiT)Figure 4: Linear few-shot evaluation on Ima-
geNet versus pre-training size. ResNets per-
form better with smaller pre-training datasets
but plateau sooner than ViT, which performs
better with larger pre-training. ViT-b is ViT-B
with all hidden dimensions halved.
1021039095Transfer accuracy [%]Average-5
Transformer (ViT)
ResNet (BiT)
Hybrid
10210375808590ImageNet
Transformer (ViT)
ResNet (BiT)
Hybrid
Total pre-training compute [exaFLOPs]
Figure 5: Performance versus pre-training compute for different architectures: Vision Transformers,
ResNets, and hybrids. Vision Transformers generally outperform ResNets with the same compu-
tational budget. Hybrids improve upon pure Transformers for smaller model sizes, but the gap
vanishes for larger models.
region spanned by BiT models of different sizes. The BiT CNNs outperform ViT on ImageNet, but
with the larger datasets, ViT overtakes.
Second, we train our models on random subsets of 9M, 30M, and 90M as well as the full JFT-
300M dataset. We do not perform additional regularization on the smaller subsets and use the same
hyper-parameters for all settings. This way, we assess the intrinsic model properties, and not the
effect of regularization. We do, however, use early-stopping, and report the best validation accuracy
achieved during training. To save compute, we report few-shot linear accuracy instead of full fine-
tuning accuracy. Figure 4 contains the results. Vision Transformers overfit more than ResNets with
comparable computational cost on smaller datasets. For example, ViT-B/32 is slightly faster than
ResNet50; it performs much worse on the 9M subset, but better on 90M+ subsets. The same is true
for ResNet152x2 and ViT-L/16. This result reinforces the intuition that the convolutional inductive
bias is useful for smaller datasets, but for larger ones, learning the relevant patterns directly from
data is sufficient, even beneficial.
Overall, the few-shot results on ImageNet (Figure 4), as well as the low-data results on VTAB
(Table 2) seem promising for very low-data transfer. Further analysis of few-shot properties of ViT
is an exciting direction of future work.
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4.4 S CALING STUDY
We perform a controlled scaling study of different models by evaluating transfer performance from
JFT-300M. In this setting data size does not bottleneck the models’ performances, and we assess
performance versus pre-training cost of each model. The model set includes: 7 ResNets, R50x1,
R50x2 R101x1, R152x1, R152x2, pre-trained for 7 epochs, plus R152x2 and R200x3 pre-trained
for 14 epochs; 6 Vision Transformers, ViT-B/32, B/16, L/32, L/16, pre-trained for 7 epochs, plus
L/16 and H/14 pre-trained for 14 epochs; and 5 hybrids, R50+ViT-B/32, B/16, L/32, L/16 pre-
trained for 7 epochs, plus R50+ViT-L/16 pre-trained for 14 epochs (for hybrids, the number at the
end of the model name stands not for the patch size, but for the total dowsampling ratio in the ResNet
backbone).
Figure 5 contains the transfer performance versus total pre-training compute (see Appendix D.5
for details on computational costs). Detailed results per model are provided in Table 6 in the Ap-
pendix. A few patterns can be observed. First, Vision Transformers dominate ResNets on the
performance/compute trade-off. ViT uses approximately 24less compute to attain the same
performance (average over 5 datasets). Second, hybrids slightly outperform ViT at small compu-
tational budgets, but the difference vanishes for larger models. This result is somewhat surprising,
since one might expect convolutional local feature processing to assist ViT at any size. Third, Vision
Transformers appear not to saturate within the range tried, motivating future scaling efforts.
4.5 I NSPECTING VISION TRANSFORMER
Input
 Attention
Figure 6: Representative ex-
amples of attention from the
output token to the input
space. See Appendix D.7 for
details.To begin to understand how the Vision Transformer processes im-
age data, we analyze its internal representations. The first layer of
the Vision Transformer linearly projects the flattened patches into a
lower-dimensional space (Eq. 1). Figure 7 (left) shows the top prin-
cipal components of the the learned embedding filters. The com-
ponents resemble plausible basis functions for a low-dimensional
representation of the fine structure within each patch.
After the projection, a learned position embedding is added to the
patch representations. Figure 7 (center) shows that the model learns
to encode distance within the image in the similarity of position em-
beddings, i.e. closer patches tend to have more similar position em-
beddings. Further, the row-column structure appears; patches in the
same row/column have similar embeddings. Finally, a sinusoidal
structure is sometimes apparent for larger grids (Appendix D). That
the position embeddings learn to represent 2D image topology ex-
plains why hand-crafted 2D-aware embedding variants do not yield
improvements (Appendix D.4).
Self-attention allows ViT to integrate information across the entire
image even in the lowest layers. We investigate to what degree
the network makes use of this capability. Specifically, we compute
the average distance in image space across which information is
integrated, based on the attention weights (Figure 7, right). This
“attention distance” is analogous to receptive field size in CNNs.
We find that some heads attend to most of the image already in the lowest layers, showing that
the ability to integrate information globally is indeed used by the model. Other attention heads
have consistently small attention distances in the low layers. This highly localized attention is
less pronounced in hybrid models that apply a ResNet before the Transformer (Figure 7, right),
suggesting that it may serve a similar function as early convolutional layers in CNNs. Further, the
attention distance increases with network depth. Globally, we find that the model attends to image
regions that are semantically relevant for classification (Figure 6).
4.6 S ELF-SUPERVISION
Transformers show impressive performance on NLP tasks. However, much of their success stems
not only from their excellent scalability but also from large scale self-supervised pre-training (Devlin
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Published as a conference paper at ICLR 2021
RGB embedding filters
(first 28 principal components)
1 2 3 4 5 6 7
Input patch column1
2
3
4
5
6
7Input patch rowPosition embedding similarity
1
1
Cosine similarity
0 5 10 15 20
Network depth (layer)020406080100120Mean attention distance (pixels)
ViT-L/16
Head 1
Head 2
Head 3
...
Figure 7: Left: Filters of the initial linear embedding of RGB values of ViT-L/32. Center: Sim-
ilarity of position embeddings of ViT-L/32. Tiles show the cosine similarity between the position
embedding of the patch with the indicated row and column and the position embeddings of all other
patches. Right: Size of attended area by head and network depth. Each dot shows the mean attention
distance across images for one of 16 heads at one layer. See Appendix D.7 for details.
et al., 2019; Radford et al., 2018). We also perform a preliminary exploration on masked patch
prediction for self-supervision, mimicking the masked language modeling task used in BERT. With
self-supervised pre-training, our smaller ViT-B/16 model achieves 79.9% accuracy on ImageNet, a
significant improvement of 2% to training from scratch, but still 4% behind supervised pre-training.
Appendix B.1.2 contains further details. We leave exploration of contrastive pre-training (Chen
et al., 2020b; He et al., 2020; Bachman et al., 2019; H ´enaff et al., 2020) to future work.
5 C ONCLUSION
We have explored the direct application of Transformers to image recognition. Unlike prior works
using self-attention in computer vision, we do not introduce image-specific inductive biases into
the architecture apart from the initial patch extraction step. Instead, we interpret an image as a
sequence of patches and process it by a standard Transformer encoder as used in NLP. This simple,
yet scalable, strategy works surprisingly well when coupled with pre-training on large datasets.
Thus, Vision Transformer matches or exceeds the state of the art on many image classification
datasets, whilst being relatively cheap to pre-train.
While these initial results are encouraging, many challenges remain. One is to apply ViT to other
computer vision tasks, such as detection and segmentation. Our results, coupled with those in Carion
et al. (2020), indicate the promise of this approach. Another challenge is to continue exploring self-
supervised pre-training methods. Our initial experiments show improvement from self-supervised
pre-training, but there is still large gap between self-supervised and large-scale supervised pre-
training. Finally, further scaling of ViT would likely lead to improved performance.
ACKNOWLEDGEMENTS
The work was performed in Berlin, Z ¨urich, and Amsterdam. We thank many colleagues at Google
for their help, in particular Andreas Steiner for crucial help with the infrastructure and the open-
source release of the code; Joan Puigcerver and Maxim Neumann for help with the large-scale
training infrastructure; Dmitry Lepikhin, Aravindh Mahendran, Daniel Keysers, Mario Lu ˇci´c, Noam
Shazeer, Ashish Vaswani, and Colin Raffel for useful discussions.
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Models Dataset Epochs Base LR LR decay Weight decay Dropout
ViT-B/f16,32g JFT-300M 7 8
104linear 0.1 0.0
ViT-L/32 JFT-300M 7 6
104linear 0.1 0.0
ViT-L/16 JFT-300M 7/14 4
104linear 0.1 0.0
ViT-H/14 JFT-300M 14 3
104linear 0.1 0.0
R50xf1,2g JFT-300M 7 103linear 0.1 0.0
R101x1 JFT-300M 7 8
104linear 0.1 0.0
R152xf1,2g JFT-300M 7 6
104linear 0.1 0.0
R50+ViT-B/f16,32gJFT-300M 7 8
104linear 0.1 0.0
R50+ViT-L/32 JFT-300M 7 2
104linear 0.1 0.0
R50+ViT-L/16 JFT-300M 7/14 4
104linear 0.1 0.0
ViT-B/f16,32g ImageNet-21k 90 103linear 0.03 0.1
ViT-L/f16,32g ImageNet-21k 30/90 103linear 0.03 0.1
ViT- ImageNet 300 3
103cosine 0.3 0.1
Table 3: Hyperparameters for training. All models are trained with a batch size of 4096 and learn-
ing rate warmup of 10k steps. For ImageNet we found it beneficial to additionally apply gradient
clipping at global norm 1. Training resolution is 224.
APPENDIX
A M ULTIHEAD SELF-ATTENTION
Standard qkv self-attention (SA, Vaswani et al. (2017)) is a popular building block for neural archi-
tectures. For each element in an input sequence z2RND, we compute a weighted sum over all
values vin the sequence. The attention weights Aijare based on the pairwise similarity between
two elements of the sequence and their respective query qiand key kjrepresentations.
[q;k;v] =zUqkv Uqkv2RD3Dh; (5)
A= softmax
qk>=p
Dh
A2RNN; (6)
SA(z) =Av: (7)
Multihead self-attention (MSA) is an extension of SA in which we run kself-attention operations,
called “heads”, in parallel, and project their concatenated outputs. To keep compute and number of
parameters constant when changing k,Dh(Eq. 5) is typically set to D=k .
MSA( z) = [SA 1(z); SA 2(z);


; SAk(z)]Umsa Umsa2Rk
DhD(8)
B E XPERIMENT DETAILS
B.1 T RAINING
Table 3 summarizes our training setups for our different models. We found strong regularization
to be key when training models from scratch on ImageNet. Dropout, when used, is applied after
every dense layer except for the the qkv-projections and directly after adding positional- to patch
embeddings. Hybrid models are trained with the exact setup as their ViT counterparts. Finally, all
training is done on resolution 224.
B.1.1 F INE-TUNING
We fine-tune all ViT models using SGD with a momentum of 0.9. We run a small grid search over
learning rates, see learning rate ranges in Table 4. To do so, we use small sub-splits from the training
set (10% for Pets and Flowers, 2% for CIFAR, 1% ImageNet) as development set and train on the
remaining data. For final results we train on the entire training set and evaluate on the respective
test data. For fine-tuning ResNets and hybrid models we use the exact same setup, with the only
exception of ImageNet where we add another value 0:06to the learning rate sweep. Additionally,
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Dataset Steps Base LR
ImageNet 20 000 f0.003, 0.01, 0.03, 0.06 g
CIFAR100 10 000 f0.001, 0.003, 0.01, 0.03 g
CIFAR10 10 000 f0.001, 0.003, 0.01, 0.03 g
Oxford-IIIT Pets 500 f0.001, 0.003, 0.01, 0.03 g
Oxford Flowers-102 500 f0.001, 0.003, 0.01, 0.03 g
VTAB (19 tasks) 2 500 0.01
Table 4: Hyperparameters for fine-tuning. All models are fine-tuned with cosine learning rate decay,
a batch size of 512, no weight decay, and grad clipping at global norm 1. If not mentioned otherwise,
fine-tuning resolution is 384.
for ResNets we also run the setup of Kolesnikov et al. (2020) and select the best results across
this run and our sweep. Finally, if not mentioned otherwise, all fine-tuning experiments run at 384
resolution (running fine-tuning at different resolution than training is common practice (Kolesnikov
et al., 2020)).
When transferring ViT models to another dataset, we remove the whole head (two linear layers) and
replace it by a single, zero-initialized linear layer outputting the number of classes required by the
target dataset. We found this to be a little more robust than simply re-initializing the very last layer.
For VTAB we follow the protocol in Kolesnikov et al. (2020), and use the same hyperparameter
setting for all tasks. We use a learning rate of 0:01and train for 2500 steps (Tab. 4). We chose this
setting by running a small sweep over two learning rates and two schedules, and selecting the setting
with the highest VTAB score on the 200-example validation sets. We follow the pre-processing used
in Kolesnikov et al. (2020), except that we do not use task-specific input resolutions. Instead we find
that Vision Transformer benefits most from a high resolution ( 384384) for all tasks.
B.1.2 S ELF-SUPERVISION
We employ the masked patch prediction objective for preliminary self-supervision experiments. To
do so we corrupt 50% of patch embeddings by either replacing their embeddings with a learnable
[mask] embedding (80%), a random other patch embedding (10%) or just keeping them as is
(10%). This setup is very similar to the one used for language by Devlin et al. (2019). Finally, we
predict the 3-bit, mean color (i.e., 512 colors in total) of every corrupted patch using their respective
patch representations.
We trained our self-supervised model for 1M steps (ca. 14 epochs) with batch size 4096 on JFT. We
use Adam, with a base learning rate of 2
104, warmup of 10k steps and cosine learning rate decay.
As prediction targets for pretraining we tried the following settings: 1) predicting only the mean,
3bit color (i.e., 1 prediction of 512 colors), 2) predicting a 44downsized version of the 1616
patch with 3bit colors in parallel (i.e., 16 predictions of 512 colors), 3) regression on the full patch
using L2 (i.e., 256 regressions on the 3 RGB channels). Surprisingly, we found that all worked quite
well, though L2 was slightly worse. We report final results only for option 1) because it has shown
best few-shot performance. We also experimented with 15% corruption rate as used by Devlin et al.
(2019) but results were also slightly worse on our few-shot metrics.
Lastly, we would like to remark that our instantiation of masked patch prediction doesn’t require
such an enormous amount of pretraining nor a large dataset such as JFT in order to lead to sim-
ilar performance gains on ImageNet classification. That is, we observed diminishing returns on
downstream performance after 100k pretraining steps, and see similar gains when pretraining on
ImageNet.
C A DDITIONAL RESULTS
We report detailed results corresponding to the figures presented in the paper. Table 5 corresponds
to Figure 3 from the paper and shows transfer performance of different ViT models pre-trained
on datasets of increasing size: ImageNet, ImageNet-21k, and JFT-300M. Table 6 corresponds to
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ViT-B/16 ViT-B/32 ViT-L/16 ViT-L/32 ViT-H/14
ImageNet CIFAR-10 98.13 97.77 97.86 97.94 -
CIFAR-100 87.13 86.31 86.35 87.07 -
ImageNet 77.91 73.38 76.53 71.16 -
ImageNet ReaL 83.57 79.56 82.19 77.83 -
Oxford Flowers-102 89.49 85.43 89.66 86.36 -
Oxford-IIIT-Pets 93.81 92.04 93.64 91.35 -
ImageNet-21k CIFAR-10 98.95 98.79 99.16 99.13 99.27
CIFAR-100 91.67 91.97 93.44 93.04 93.82
ImageNet 83.97 81.28 85.15 80.99 85.13
ImageNet ReaL 88.35 86.63 88.40 85.65 88.70
Oxford Flowers-102 99.38 99.11 99.61 99.19 99.51
Oxford-IIIT-Pets 94.43 93.02 94.73 93.09 94.82
JFT-300M CIFAR-10 99.00 98.61 99.38 99.19 99.50
CIFAR-100 91.87 90.49 94.04 92.52 94.55
ImageNet 84.15 80.73 87.12 84.37 88.04
ImageNet ReaL 88.85 86.27 89.99 88.28 90.33
Oxford Flowers-102 99.56 99.27 99.56 99.45 99.68
Oxford-IIIT-Pets 95.80 93.40 97.11 95.83 97.56
Table 5: Top1 accuracy (in %) of Vision Transformer on various datasets when pre-trained on Im-
ageNet, ImageNet-21k or JFT300M. These values correspond to Figure 3 in the main text. Models
are fine-tuned at 384 resolution. Note that the ImageNet results are computed without additional
techniques (Polyak averaging and 512 resolution images) used to achieve results in Table 2.
Epochs ImageNet ImageNet ReaL CIFAR-10 CIFAR-100 Pets Flowers exaFLOPs
name
ViT-B/32 7 80.73 86.27 98.61 90.49 93.40 99.27 55
ViT-B/16 7 84.15 88.85 99.00 91.87 95.80 99.56 224
ViT-L/32 7 84.37 88.28 99.19 92.52 95.83 99.45 196
ViT-L/16 7 86.30 89.43 99.38 93.46 96.81 99.66 783
ViT-L/16 14 87.12 89.99 99.38 94.04 97.11 99.56 1567
ViT-H/14 14 88.08 90.36 99.50 94.71 97.11 99.71 4262
ResNet50x1 7 77.54 84.56 97.67 86.07 91.11 94.26 50
ResNet50x2 7 82.12 87.94 98.29 89.20 93.43 97.02 199
ResNet101x1 7 80.67 87.07 98.48 89.17 94.08 95.95 96
ResNet152x1 7 81.88 87.96 98.82 90.22 94.17 96.94 141
ResNet152x2 7 84.97 89.69 99.06 92.05 95.37 98.62 563
ResNet152x2 14 85.56 89.89 99.24 91.92 95.75 98.75 1126
ResNet200x3 14 87.22 90.15 99.34 93.53 96.32 99.04 3306
R50x1+ViT-B/32 7 84.90 89.15 99.01 92.24 95.75 99.46 106
R50x1+ViT-B/16 7 85.58 89.65 99.14 92.63 96.65 99.40 274
R50x1+ViT-L/32 7 85.68 89.04 99.24 92.93 96.97 99.43 246
R50x1+ViT-L/16 7 86.60 89.72 99.18 93.64 97.03 99.40 859
R50x1+ViT-L/16 14 87.12 89.76 99.31 93.89 97.36 99.11 1668
Table 6: Detailed results of model scaling experiments. These correspond to Figure 5 in the main
paper. We show transfer accuracy on several datasets, as well as the pre-training compute (in ex-
aFLOPs).
Figure 5 from the paper and shows the transfer performance of ViT, ResNet, and hybrid models of
varying size, as well as the estimated computational cost of their pre-training.
D A DDITIONAL ANALYSES
D.1 SGD VS. ADAM FOR RESNETS
ResNets are typically trained with SGD and our use of Adam as optimizer is quite unconventional.
Here we show the experiments that motivated this choice. Namely, we compare the fine-tuning
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ResNet50 ResNet152x2
Dataset Adam SGD Adam SGD
ImageNet 77:54 78 :24 84 :97 84 :37
CIFAR10 97:67 97 :46 99 :06 99 :07
CIFAR100 86:07 85 :17 92 :05 91 :06
Oxford-IIIT Pets 91:11 91 :00 95 :37 94 :79
Oxford Flowers-102 94:26 92 :06 98 :62 99 :32
Average 89:33 88 :79 94 :01 93 :72
Table 7: Fine-tuning ResNet models pre-trained with Adam and SGD.
100101
Relative Compute0.20.30.40.50.6ImageNet 5shot
Models
All
Depth
Patch size
Width MLP
Width
100101
Relative Compute0.40.50.60.70.8Average 5shot
Models
All
Depth
Patch size
Width MLP
Width
Figure 8: Scaling different model dimensions of the Vision Transformer.
performance of two ResNets – 50x1 and 152x2 – pre-trained on JFT with SGD and Adam. For
SGD, we use the hyperparameters recommended by Kolesnikov et al. (2020). Results are presented
in Table 7. Adam pre-training outperforms SGD pre-training on most datasets and on average.
This justifies the choice of Adam as the optimizer used to pre-train ResNets on JFT. Note that the
absolute numbers are lower than those reported by Kolesnikov et al. (2020), since we pre-train only
for7epochs, not 30.
D.2 T RANSFORMER SHAPE
We ran ablations on scaling different dimensions of the Transformer architecture to find out which
are best suited for scaling to very large models. Figure 8 shows 5-shot performance on ImageNet
for different configurations. All configurations are based on a ViT model with 8layers,D= 1024 ,
DMLP = 2048 and a patch size of 32, the intersection of all lines. We can see that scaling the
depth results in the biggest improvements which are clearly visible up until 64 layers. However,
diminishing returns are already visible after 16 layers. Interestingly, scaling the width of the net-
work seems to result in the smallest changes. Decreasing the patch size and thus increasing the
effective sequence length shows surprisingly robust improvements without introducing parameters.
These findings suggest that compute might be a better predictor of performance than the number of
parameters, and that scaling should emphasize depth over width if any. Overall, we find that scaling
all dimensions proportionally results in robust improvements.
D.3 H EAD TYPE AND C L A S S TOKEN
In order to stay as close as possible to the original Transformer model, we made use of an additional
[class] token, which is taken as image representation. The output of this token is then trans-
formed into a class prediction via a small multi-layer perceptron (MLP) with tanh as non-linearity
in the single hidden layer.
This design is inherited from the Transformer model for text, and we use it throughout the main
paper. An initial attempt at using only image-patch embeddings, globally average-pooling (GAP)
them, followed by a linear classifier—just like ResNet’s final feature map—performed very poorly.
However, we found that this is neither due to the extra token, nor to the GAP operation. Instead,
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0 1 2 3 4 5 6 7
Epochs of training2530354045505560ImageNet linear 5-shot accuracy [%]CLS-Token, lr=8e-4
GAP, lr=8e-4
GAP, lr=3e-4
Figure 9: Comparison of class-token and global average pooling classifiers. Both work similarly
well, but require different learning-rates.
Pos. Emb. Default/Stem Every Layer Every Layer-Shared
No Pos. Emb. 0.61382 N/A N/A
1-D Pos. Emb. 0.64206 0.63964 0.64292
2-D Pos. Emb. 0.64001 0.64046 0.64022
Rel. Pos. Emb. 0.64032 N/A N/A
Table 8: Results of the ablation study on positional embeddings with ViT-B/16 model evaluated on
ImageNet 5-shot linear.
the difference in performance is fully explained by the requirement for a different learning-rate, see
Figure 9.
D.4 P OSITIONAL EMBEDDING
We ran ablations on different ways of encoding spatial information using positional embedding. We
tried the following cases:
• Providing no positional information: Considering the inputs as a bag of patches .
• 1-dimensional positional embedding: Considering the inputs as a sequence of patches in
the raster order (default across all other experiments in this paper).
• 2-dimensional positional embedding: Considering the inputs as a grid of patches in two
dimensions. In this case, two sets of embeddings are learned, each for one of the axes,
X-embedding, and Y-embedding, each with size D=2. Then, based on the coordinate on
the path in the input, we concatenate the XandYembedding to get the final positional
embedding for that patch.
• Relative positional embeddings: Considering the relative distance between patches to en-
code the spatial information as instead of their absolute position. To do so, we use 1-
dimensional Relative Attention, in which we define the relative distance all possible pairs
of patches. Thus, for every given pair (one as query, and the other as key/value in the at-
tention mechanism), we have an offset pqpk, where each offset is associated with an
embedding. Then, we simply run extra attention, where we use the original query (the
content of query), but use relative positional embeddings as keys. We then use the log-
its from the relative attention as a bias term and add it to the logits of the main attention
(content-based attention) before applying the softmax.
In addition to different ways of encoding spatial information, we also tried different ways of in-
corporating this information in our model. For the 1-dimensional and 2-dimensional positional
embeddings, we tried three different cases: (1) add positional embeddings to the inputs right after
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Figure 10: Position embeddings of models trained with different hyperparameters.
the stem of them model and before feeding the inputs to the Transformer encoder (default across
all other experiments in this paper); (2) learn and add positional embeddings to the inputs at the
beginning of each layer; (3) add a learned positional embeddings to the inputs at the beginning of
each layer (shared between layers).
Table 8 summarizes the results from this ablation study on a ViT-B/16 model. As we can see, while
there is a large gap between the performances of the model with no positional embedding and mod-
els with positional embedding, there is little to no difference between different ways of encoding
positional information. We speculate that since our Transformer encoder operates on patch-level
inputs, as opposed to pixel-level, the differences in how to encode spatial information is less impor-
tant. More precisely, in patch-level inputs, the spatial dimensions are much smaller than the original
pixel-level inputs, e.g., 1414as opposed to 224224, and learning to represent the spatial re-
lations in this resolution is equally easy for these different positional encoding strategies. Even so,
the specific pattern of position embedding similarity learned by the network depends on the training
hyperparameters (Figure 10).
0 5 10 15 20
Network depth (layer)020406080100120Mean attention distance (pixels)
ViT-L/16
Head 1
Head 2
Head 3
...
0 5 10 15 20
Network depth (layer)020406080100120
R50x1 + ViT-L/16
Head 1
Head 2
Head 3
...
Figure 11: Size of attended area by head and network depth. Attention distance was computed for
128 example images by averaging the distance between the query pixel and all other pixels, weighted
by the attention weight. Each dot shows the mean attention distance across images for one of 16
heads at one layer. Image width is 224 pixels.
D.5 E MPIRICAL COMPUTATIONAL COSTS
We are also interested in real-world speed of the architectures on our hardware, which is not always
well predicted by theoretical FLOPs due to details like lane widths and cache sizes. For this purpose,
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we perform timing of inference speed for the main models of interest, on a TPUv3 accelerator; the
difference between inference and backprop speed is a constant model-independent factor.
Figure 12 (left) shows how many images one core can handle per second, across various input sizes.
Every single point refers to the peak performance measured across a wide range of batch-sizes. As
can be seen, the theoretical bi-quadratic scaling of ViT with image size only barely starts happening
for the largest models at the largest resolutions.
Another quantity of interest is the largest batch-size each model can fit onto a core, larger being
better for scaling to large datasets. Figure 12 (right) shows this quantity for the same set of models.
This shows that large ViT models have a clear advantage in terms of memory-efficiency over ResNet
models.
64 128 224 384 512
Input size [px]102103104Peak inference speed [img/sec/core]64 128 224 384 512
Input size [px]102103Largest per-core batch-sizeR50x1
R50x2ViT-B/32
ViT-L/32ViT-B/16
ViT-L/16ViT-H/14
R152x4
Figure 12: Left: Real wall-clock timings of various architectures across input sizes. ViT models
have speed comparable to similar ResNets. Right : Largest per-core batch-size fitting on device with
various architectures across input sizes. ViT models are clearly more memory-efficient.
D.6 A XIAL ATTENTION
Axial Attention (Huang et al., 2020; Ho et al., 2019) is a simple, yet effective technique to run self-
attention on large inputs that are organized as multidimensional tensors. The general idea of axial
attention is to perform multiple attention operations, each along a single axis of the input tensor,
instead of applying 1-dimensional attention to the flattened version of the input. In axial attention,
each attention mixes information along a particular axis, while keeping information along the other
axes independent. Along this line, Wang et al. (2020b) proposed the AxialResNet model in which
all the convolutions with kernel size 33in a ResNet50 are replaced by axial self-attention, i.e.
a row and column attention, augmented by relative positional encoding. We have implemented
AxialResNet as a baseline model.3.
Moreover, we have modified ViT to process inputs in the 2-dimensional shape, instead of a 1-
dimensional sequence of patches, and incorporate Axial Transformer blocks, in which instead of
a self-attention followed by an MLP, we have a a row-self-attention plus an MLP followed by a
column-self-attention plus an MLP.
Figure 13, present the performance of Axial ResNet, Axial-ViT-B/32 and Axial-ViT-B/16 on Ima-
geNet 5shot linear, when pretrained on JFT dataset, verses the pretraining compute, both in terms of
number of FLOPs and inference time (example per seconds). As we can see, both Axial-ViT-B/32
and Axial-ViT-B/16 do better than their ViT-B counterpart in terms of performance, but it comes at
3Our implementation is based on the open-sourced PyTorch implementation in https://github.com/
csrhddlam/axial-deeplab . In our experiments, we reproduced the scores reported in (Wang et al.,
2020b) in terms of accuracy, however, our implementation, similar to the open-source implementation, is very
slow on TPUs. Therefore, we were not able to use it for extensive large-scale experiments. These may be
unlocked by a carefully optimized implementation.
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102
Total compute [exaFLOPs]0.5000.5250.5500.5750.6000.6250.650ImageNet 5-shot linear top-1 accuracyAxialViT-B/16
AxialViT-B/32ViT-B/16
ViT-B/32
ResNet50AxialResNet50
102103
Peak inference speed [img/sec/core]0.5000.5250.5500.5750.6000.6250.650ImageNet 5-shot linear top-1 accuracyAxialViT-B/16
AxialViT-B/32ViT-B/16
ViT-B/32
ResNet50AxialResNet50
Figure 13: Performance of Axial-Attention based models, in terms of top-1 accuracy on ImageNet
5-shot linear, versus their speed in terms of number of FLOPs ( left) and inference time ( left).
the cost of more compute. This is because in Axial-ViT models, each Transformer block with global
self-attention is replaced by two Axial Transformer blocks, one with row and one with column self-
attention and although the sequence length that self-attention operates on is smaller in axial case,
there is a extra MLP per Axial-ViT block. For the AxialResNet, although it looks reasonable in
terms of accuracy/compute trade-off (Figure 13, left), the naive implementation is extremely slow
on TPUs (Figure 13, right).
D.7 A TTENTION DISTANCE
To understand how ViT uses self-attention to integrate information across the image, we analyzed
the average distance spanned by attention weights at different layers (Figure 11). This “attention
distance” is analogous to receptive field size in CNNs. Average attention distance is highly variable
across heads in lower layers, with some heads attending to much of the image, while others attend
to small regions at or near the query location. As depth increases, attention distance increases for all
heads. In the second half of the network, most heads attend widely across tokens.
D.8 A TTENTION MAPS
To compute maps of the attention from the output token to the input space (Figures 6 and 14), we
used Attention Rollout (Abnar & Zuidema, 2020). Briefly, we averaged attention weights of ViT-
L/16 across all heads and then recursively multiplied the weight matrices of all layers. This accounts
for the mixing of attention across tokens through all layers.
D.9 O BJECT NETRESULTS
We also evaluate our flagship ViT-H/14 model on the ObjectNet benchmark following the evaluation
setup in Kolesnikov et al. (2020), resulting in 82.1% top-5 accuracy and 61.7% top-1 accuracy.
D.10 VTAB B REAKDOWN
Table 9 shows the scores attained on each of the VTAB-1k tasks.
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Figure 14: Further example attention maps as in Figure 6 (random selection).
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Table 9: Breakdown of VTAB-1k performance across tasks.Caltech101
CIFAR-100
DTD
Flowers102
Pets
Sun397
SVHN
Camelyon
EuroSAT
Resisc45
Retinopathy
Clevr-Count
Clevr-Dist
DMLab
dSpr-Loc
dSpr-Ori
KITTI-Dist
sNORB-Azim
sNORB-Elev
Mean
ViT-H/14 (JFT) 95.3 85.5 75.2 99.7 97.2 65.0 88.9 83.3 96.7 91.4 76.6 91.7 63.8 53.1 79.4 63.3 84.5 33.2 51.2 77.6
ViT-L/16 (JFT) 95.4 81.9 74.3 99.7 96.7 63.5 87.4 83.6 96.5 89.7 77.1 86.4 63.1 49.7 74.5 60.5 82.2 36.2 51.1 76.3
ViT-L/16 (I21k) 90.8 84.1 74.1 99.3 92.7 61.0 80.9 82.5 95.6 85.2 75.3 70.3 56.1 41.9 74.7 64.9 79.9 30.5 41.7 72.7
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