We will walk step by step through the Vision Transformer, and implement all parts by ourselves. First, let’s implement the image preprocessing: an image of size \(N\times N\) has to be split into \((N/M)^2\) patches of size \(M\times M\). These represent the input words to the Transformer.

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Human eyesfocal length

A linear projection layer that maps the input patches to a feature vector of larger size. It is implemented by a simple linear layer that takes each \(M\times M\) patch independently as input.

Finally, we can put everything into a PyTorch Lightning Module as usual. We use torch.optim.AdamW as the optimizer, which is Adam with a corrected weight decay implementation. Since we use the Pre-LN Transformer version, we do not need to use a learning rate warmup stage anymore. Instead, we use the same learning rate scheduler as the CNNs in our previous tutorial on image classification.

Let’s take a look at how that works for our CIFAR examples above. For our images of size \(32\times 32\), we choose a patch size of 4. Hence, we obtain sequences of 64 patches of size \(4\times 4\). We visualize them below:

Focal length

Finally, the learning rate for Transformers is usually relatively small, and in papers, a common value to use is 3e-5. However, since we work with a smaller dataset and have a potentially easier task, we found that we are able to increase the learning rate to 3e-4 without any problems. To reduce overfitting, we use a dropout value of 0.2. Remember that we also use small image augmentations as regularization during training.

Learnable positional encodings that are added to the tokens before being processed by the Transformer. Those are needed to learn position-dependent information, and convert the set to a sequence. Since we usually work with a fixed resolution, we can learn the positional encodings instead of having the pattern of sine and cosine functions.

Focal lengthcamera

Compared to the original images, it is much harder to recognize the objects from those patch lists now. Still, this is the input we provide to the Transformer for classifying the images. The model has to learn itself how it has to combine the patches to recognize the objects. The inductive bias in CNNs that an image is a grid of pixels, is lost in this input format.

Chen, Xiangning, et al. “When Vision Transformers Outperform ResNets without Pretraining or Strong Data Augmentations.” arXiv preprint arXiv:2106.01548 (2021). link

All those observed phenomenons can be explained with a concept that we have visited before: inductive biases. Convolutional Neural Networks have been designed with the assumption that images are translation invariant. Hence, we apply convolutions with shared filters across the image. Furthermore, a CNN architecture integrates the concept of distance in an image: two pixels that are close to each other are more related than two distant pixels. Local patterns are combined into larger patterns until we perform our classification prediction. All those aspects are inductive biases of a CNN. In contrast, a Vision Transformer does not know which two pixels are close to each other, and which are far apart. It has to learn this information solely from the sparse learning signal of the classification task. This is a huge disadvantage when we have a small dataset since such information is crucial for generalizing to an unseen test dataset. With large enough datasets and/or good pre-training, a Transformer can learn this information without the need for inductive biases, and instead is more flexible than a CNN. Especially long-distance relations between local patterns can be difficult to process in CNNs, while in Transformers, all patches have the distance of one. This is why Vision Transformers are so strong on large-scale datasets such as ImageNet but underperform a lot when being applied to a small dataset such as CIFAR10.

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The Vision Transformer achieves a validation and test performance of about 75%. In comparison, almost all CNN architectures that we have tested in Tutorial 5 obtained a classification performance of around 90%. This is a considerable gap and shows that although Vision Transformers perform strongly on ImageNet with potential pretraining, they cannot come close to simple CNNs on CIFAR10 when being trained from scratch. The differences between a CNN and Transformer can be well observed in the training curves. Let’s look at them in a tensorboard below:

Focal lengthformula

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First, let’s consider the patch size. The smaller we make the patches, the longer the input sequences to the Transformer become. While in general, this allows the Transformer to model more complex functions, it requires a longer computation time due to its quadratic memory usage in the attention layer. Furthermore, small patches can make the task more difficult since the Transformer has to learn which patches are close-by, and which are far away. We experimented with patch sizes of 2, 4, and 8 which gives us the input sequence lengths of 256, 64, and 16 respectively. We found 4 to result in the best performance and hence pick it below.

In optics, the distance from the middle of the lens to its focal point. Light rays run in parallel to one another, while lenses distort light rays: a convex lens (the type that is thicker in the centre than at the edges) brings them closer together and a concave lens (the type that is thinner in the centre) forces them apart. Cameras use convex lenses to bring the light rays together to a point where they converge and the image is in focus: this is where the film or light sensitive diode goes. The more convex (or thicker) the lens, the more severely the light rays are bent and the shorter the focal length (conversely, the thinner the lens the longer the focal length). Different focal lengths create different kinds of image effects. Lenses with very short focal lengths (or wide angle lenses) allow more of the picture to be seen and emphasize foreground elements, whereas lenses with very long focal lengths (or telephoto lenses) allow less of the picture to be seen and emphasize background elements which appear to be magnified. These different effects are dramatically illustrated by a technique used in feature films called a Hitchcock zoom, where the camera tracks out at the same time as it zooms in (or vice versa), an effect used in the film Vertigo (1958).

focallength是什么

If you are not familiar with Transformers yet, take a look at Tutorial 6 where we discuss the fundamentals of Multi-Head Attention and Transformers. As in many previous tutorials, we will use PyTorch Lightning again (introduced in Tutorial 5). Let’s start with importing our standard set of libraries.

Commonly, Vision Transformers are applied to large-scale image classification benchmarks such as ImageNet to leverage their full potential. However, here we take a step back and ask: can Vision Transformer also succeed on classical, small benchmarks such as CIFAR10? To find this out, we train a Vision Transformer from scratch on the CIFAR10 dataset. Let’s first create a training function for our PyTorch Lightning module which also loads the pre-trained model if you have downloaded it above.

Next, the embedding and hidden dimensionality have a similar impact on a Transformer as to an MLP. The larger the sizes, the more complex the model becomes, and the longer it takes to train. In Transformers, however, we have one more aspect to consider: the query-key sizes in the Multi-Head Attention layers. Each key has the feature dimensionality of embed_dim/num_heads. Considering that we have an input sequence length of 64, a minimum reasonable size for the key vectors is 16 or 32. Lower dimensionalities can restrain the possible attention maps too much. We observed that more than 8 heads are not necessary for the Transformer, and therefore pick an embedding dimensionality of 256. The hidden dimensionality in the feed-forward networks is usually 2-4x larger than the embedding dimensionality, and thus we pick 512.

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In this tutorial, we will take a closer look at a recent new trend: Transformers for Computer Vision. Since Alexey Dosovitskiy et al. successfully applied a Transformer on a variety of image recognition benchmarks, there have been an incredible amount of follow-up works showing that CNNs might not be optimal architecture for Computer Vision anymore. But how do Vision Transformers work exactly, and what benefits and drawbacks do they offer in contrast to CNNs? We will answer these questions by implementing a Vision Transformer ourselves and train it on the popular, small dataset CIFAR10. We will compare these results to the convolutional architectures of Tutorial 5.

An MLP head that takes the output feature vector of the CLS token, and maps it to a classification prediction. This is usually implemented by a small feed-forward network or even a single linear layer.

A classification token that is added to the input sequence. We will use the output feature vector of the classification token (CLS token in short) for determining the classification prediction.

Transformers have been originally proposed to process sets since it is a permutation-equivariant architecture, i.e., producing the same output permuted if the input is permuted. To apply Transformers to sequences, we have simply added a positional encoding to the input feature vectors, and the model learned by itself what to do with it. So, why not do the same thing on images? This is exactly what Alexey Dosovitskiy et al. proposed in their paper “An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale”. Specifically, the Vision Transformer is a model for image classification that views images as sequences of smaller patches. As a preprocessing step, we split an image of, for example, \(48\times 48\) pixels into 9 \(16\times 16\) patches. Each of those patches is considered to be a “word”/“token” and projected to a feature space. With adding positional encodings and a token for classification on top, we can apply a Transformer as usual to this sequence and start training it for our task. A nice GIF visualization of the architecture is shown below (figure credit - Phil Wang):

focallength中文

In this tutorial, we have implemented our own Vision Transformer from scratch and applied it to the task of image classification. Vision Transformers work by splitting an image into a sequence of smaller patches, use those as input to a standard Transformer encoder. While Vision Transformers achieved outstanding results on large-scale image recognition benchmarks such as ImageNet, they considerably underperform when being trained from scratch on small-scale datasets like CIFAR10. The reason is that in contrast to CNNs, Transformers do not have the inductive biases of translation invariance and the feature hierarchy (i.e. larger patterns consist of many smaller patterns). However, these aspects can be learned when enough data is provided, or the model has been pre-trained on other large-scale tasks. Considering that Vision Transformers have just been proposed end of 2020, there is likely a lot more to come on Transformers for Computer Vision.

Focaldistance vsfocal length

We load the CIFAR10 dataset below. We use the same setup of the datasets and data augmentations as for the CNNs in Tutorial 5 to keep a fair comparison. The constants in the transforms.Normalize correspond to the values that scale and shift the data to a zero mean and standard deviation of one.

After we have looked at the preprocessing, we can now start building the Transformer model. Since we have discussed the fundamentals of Multi-Head Attention in Tutorial 6, we will use the PyTorch module nn.MultiheadAttention (docs) here. Further, we use the Pre-Layer Normalization version of the Transformer blocks proposed by Ruibin Xiong et al. in 2020. The idea is to apply Layer Normalization not in between residual blocks, but instead as a first layer in the residual blocks. This reorganization of the layers supports better gradient flow and removes the necessity of a warm-up stage. A visualization of the difference between the standard Post-LN and the Pre-LN version is shown below.

FOV tofocal length

Xiong, Ruibin, et al. “On layer normalization in the transformer architecture.” International Conference on Machine Learning. PMLR, 2020. link

Now, we can already start training our model. As seen in our implementation, we have a couple of hyperparameters that we have to set. When creating this notebook, we have performed a small grid search over hyperparameters and listed the best hyperparameters in the cell below. Nevertheless, it is worth discussing the influence that each hyperparameter has, and what intuition we have for choosing its value.

Feel free to explore the hyperparameters yourself by changing the values below. In general, the Vision Transformer did not show to be too sensitive to the hyperparameter choices on the CIFAR10 dataset.

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Now we have all modules ready to build our own Vision Transformer. Besides the Transformer encoder, we need the following modules:

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Dosovitskiy, Alexey, et al. “An image is worth 16x16 words: Transformers for image recognition at scale.” International Conference on Learning Representations (2021). link

We provide a pre-trained Vision Transformer which we download in the next cell. However, Vision Transformers can be relatively quickly trained on CIFAR10 with an overall training time of less than an hour on an NVIDIA TitanRTX. Feel free to experiment with training your own Transformer once you went through the whole notebook.

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The tensorboard compares the Vision Transformer to a ResNet trained on CIFAR10. When looking at the training losses, we see that the ResNet learns much more quickly in the first iterations. While the learning rate might have an influence on the initial learning speed, we see the same trend in the validation accuracy. The ResNet achieves the best performance of the Vision Transformer after just 5 epochs (2000 iterations). Further, while the ResNet training loss and validation accuracy have a similar trend, the validation performance of the Vision Transformers only marginally changes after 10k iterations while the training loss has almost just started going down. Yet, the Vision Transformer is also able to achieve close to 100% accuracy on the training set.

Mastering depth of field requires a basic understanding of f-stop, focal length, focus range, and camera lenses. We will quickly cover these first.