๐ What is a Vision Transformer (ViT)?
A Vision Transformer (ViT) is a deep learning model that applies the Transformer architecture (originally designed for natural language processing) to image recognition tasks. Instead of processing images pixel by pixel, ViTs split an image into smaller patches and treat these patches as individual tokens, similar to how words are treated in a sentence. This allows the model to capture global relationships between different parts of the image, leading to improved performance in many computer vision applications.
๐ History and Background
The Transformer architecture was introduced in the groundbreaking paper "Attention is All You Need" in 2017. Its success in natural language processing prompted researchers to explore its applicability to computer vision. The Vision Transformer (ViT), introduced in 2020 by Google researchers, demonstrated that a pure Transformer model could achieve state-of-the-art results on image classification tasks without relying on convolutional neural networks (CNNs).
๐ Key Principles of ViT
- ๐ผ๏ธ Image Patching: An input image is divided into fixed-size patches. For example, a 224x224 image might be divided into 16x16 patches, resulting in 196 patches.
- ๐ข Linear Embedding of Patches: Each patch is then flattened into a vector and linearly transformed into an embedding. This embedding represents the patch in a higher-dimensional space.
- โ Positional Encoding: To retain spatial information, positional embeddings are added to the patch embeddings. These embeddings indicate the position of each patch in the original image.
- โจ Transformer Encoder: The sequence of embedded patches is then fed into a standard Transformer encoder. This encoder consists of multiple layers of multi-head self-attention and feed-forward neural networks.
- ๐ง Self-Attention Mechanism: The self-attention mechanism allows the model to weigh the importance of different patches when processing each patch. This enables the model to capture global relationships between different parts of the image.
- ๐งฎ Classification Head: Finally, the output of the Transformer encoder is passed through a classification head (typically a multi-layer perceptron) to predict the class label of the image.
โ The Math Behind ViT
Here are a few key formulas that explain the math:
- ๐ Patch Creation: Suppose we have an image $X \in \mathbb{R}^{H \times W \times C}$, where $H$ is the height, $W$ is the width, and $C$ is the number of channels. The image is divided into $N$ patches, where each patch $x_i \in \mathbb{R}^{P \times P \times C}$, and $N = \frac{H}{P} \times \frac{W}{P}$.
- ๐ Linear Projection: Each patch $x_i$ is flattened and projected to a $D$-dimensional embedding space using a linear transformation $E \in \mathbb{R}^{(P^2 \cdot C) \times D}$: $z_0 = [x_1E; x_2E; ... ; x_NE] + E_{pos}$, where $E_{pos}$ is the positional encoding.
- ๐ฏ Self-Attention: The self-attention mechanism is defined as $\text{Attention}(Q, K, V) = \text{softmax}(\frac{QK^T}{\sqrt{d_k}})V$, where $Q$, $K$, and $V$ are the query, key, and value matrices, respectively, and $d_k$ is the dimension of the key.
๐ Real-world Examples
- โ๏ธ Medical Imaging: ViTs are used to analyze medical images such as X-rays and MRIs to detect diseases and abnormalities.
- ๐ Autonomous Driving: They help self-driving cars recognize objects, pedestrians, and traffic signs.
- ๐ฑ Agriculture: ViTs can analyze satellite images to monitor crop health and identify areas that need attention.
- ๐๏ธ Retail: They can be used for image-based product recognition and visual search.
๐ Conclusion
Vision Transformers have revolutionized computer vision by leveraging the power of the Transformer architecture. By treating images as sequences of patches, ViTs can capture global relationships and achieve state-of-the-art performance in various applications. As research continues, we can expect to see even more innovative uses of ViTs in the future.
