Possible blog post:
Can Tensor Cores on Graphics Cards Enable Powerful Machine Learning Applications?
If you are interested in artificial intelligence, you have probably heard about deep learning, a type of machine learning that uses artificial neural networks with many layers to learn from large datasets and perform tasks such as image recognition, speech synthesis, and game playing. Deep learning has achieved remarkable results in various domains, from medicine to finance, and has been enabled by advances in hardware, software, and data. In particular, the use of graphical processing units (GPUs) has accelerated the training and inference of deep neural networks, thanks to their parallel computing power and memory bandwidth. However, for some types of neural networks, GPUs are still not fast enough, and can consume a lot of energy and space, which limits their deployment on mobile devices or in real-time applications. To overcome these challenges, the latest GPUs from Nvidia, called Turing and Ampere, include dedicated hardware units called Tensor Cores that can perform matrix multiplication, a key operation in deep learning, more efficiently than traditional GPUs. In this blog post, we will explore what Tensor Cores are, how they work, and what benefits they can bring to machine learning.
What are Tensor Cores?
Before we dive into Tensor Cores, let’s review some basics of linear algebra and neural networks. A tensor is a multi-dimensional array of numbers that represents a computation in a neural network. For instance, a vector is a one-dimensional tensor, a matrix is a two-dimensional tensor, and a cube is a three-dimensional tensor. Tensors can be multiplied together using the dot product or matrix multiplication, which involves multiplying elements from one tensor with corresponding elements from another tensor, and summing up the products along certain axes of the resulting tensor. Matrix multiplication is used in various steps of a neural network, such as computing the activations of a layer or the gradients of the loss with respect to the parameters. However, matrix multiplication can be slow and memory-intensive, especially for large or sparse tensors. To speed up this operation and reduce the memory footprint, Nvidia introduced Tensor Cores in its Volta architecture, which has been further improved in the Turing and Ampere architectures.
A Tensor Core is a computational unit that can perform mixed-precision matrix multiplication on 4×4 matrices of half-precision floating-point numbers (FP16). Mixed-precision means that the inputs are down-casted from single-precision (FP32) to half-precision, which reduces the storage and bandwidth requirements, and the outputs are up-casted to single-precision for accuracy. A 4×4 matrix is a square matrix with four rows and four columns, and can represent an operation that involves processing four elements in parallel. By using Tensor Cores, a GPU can perform one matrix multiplication per clock cycle, which can speed up the training and inference of deep neural networks by several times. Moreover, the Tensor Cores can accumulate the products and sum them up with other products in a single instruction, called a fused multiply-add (FMA), which further improves the computational efficiency. By combining Tensor Cores with other features of the Turing and Ampere GPUs, such as real-time ray tracing, denoising, and shading, one can create advanced AI applications that can generate realistic images, interpret natural language, or predict complex behaviors.
How do Tensor Cores work?
Now let’s see how Tensor Cores actually perform matrix multiplication. Suppose we have two 4×4 matrices A and B, and we want to compute their product C = AB. If we multiply A and B element-wise and sum up the resulting products, we get the elements of C as follows:
Cij = Σk=1^4 Aik * Bkj
where i and j are indices representing the rows and columns of C, and k is an index representing the common dimension (columns of A, rows of B). By expanding this formula, we can see that each element of C involves four multiplications and three additions:
C11 = A11 * B11 + A12 * B21 + A13 * B31 + A14 * B41
C12 = A11 * B12 + A12 * B22 + A13 * B32 + A14 * B42
C13 = A11 * B13 + A12 * B23 + A13 * B33 + A14 * B43
C14 = A11 * B14 + A12 * B24 + A13 * B34 + A14 * B44
and so on for the other elements of C. This means that we need to perform 16 multiplications and 12 additions for each element of C, which can be time-consuming and energy-consuming, especially for large matrices. Moreover, for some tensor operations, such as convolutional layers in a convolutional neural network, matrix multiplication can involve overlapping and striding, which requires additional padding and computation. For instance, to compute one output feature map from one input feature map using a kernel of size 3×3 and stride 1×1, we need to extract a 3×3 patch from the input feature map, flatten it into a 1×9 vector, multiply it with a 9×1 vector of weights, and add a bias term, resulting in a scalar output. To compute all the output feature maps from all the input feature maps using multiple kernels, we need to perform many such convolutions, which can be a bottleneck in deep learning applications.
Tensor Cores can accelerate matrix multiplication by exploiting the hardware features of the Volta, Turing, and Ampere architectures. Specifically, Tensor Cores can perform four matrix multiplications at once and accumulate the products in mixed-precision registers, which can store 64 half-precision numbers at a time. This is achieved by packing eight 4×4 half-precision matrices into one 4×4 matrix of single-precision numbers, called a tensor core matrix, which is loaded into the Tensor Core along with the other operands. Each Tensor Core has 64 KB of on-chip memory, called the Tensor Core memory, which is used to store the intermediate results and avoid accessing the slower main memory. A Tensor Core can fetch four 4×4 matrix blocks from the Tensor Core memory in parallel, and reuse them to compute four 4×4 output blocks, which are accumulated with the products of the other blocks in the same FMA instruction. This reduces the number of memory accesses, and increases the throughput and efficiency of the matrix multiplication. Moreover, since Tensor Cores operate on half-precision numbers, which have fewer bits than single-precision numbers, they consume less power and generate less heat than traditional GPUs.
What benefits can Tensor Cores bring to machine learning?
By using Tensor Cores, one can accelerate the training and inference of deep neural networks by several times, and improve their accuracy and stability. The main benefits of Tensor Cores are:
1. Speed: Tensor Cores can perform one matrix multiplication per clock cycle, which can speed up the training and inference of deep neural networks by several times. For instance, Tensor Core-accelerated matrix multiplication can be up to 6 times faster than traditional GPU matrix multiplication, according to Nvidia. This means that one can train a larger model, with more layers and more parameters, in the same time or even less time as a smaller model, which can lead to better performance.
2. Efficiency: Tensor Cores can perform matrix multiplication more efficiently than traditional GPUs, by reducing the memory footprint and the power consumption of the operation. This allows one to train and infer deep neural networks on smaller devices or in real-time applications, such as autonomous driving, robotics, or gaming. For instance, Tensor Core-accelerated convolutional layers can be up to 3 times more energy-efficient than traditional GPU convolutional layers, according to Nvidia. This means that one can run a model on a battery-powered device for longer or do more computations with the same energy budget, which can lead to more versatile and accessible AI applications.
3. Flexibility: Tensor Cores can perform various types of matrix multiplication, beyond the simple case of 4×4 half-precision matrices. For example, Tensor Cores can handle mixed-precision matrices with larger or smaller dimensions, or sparse matrices with non-zero elements in few positions. This allows one to customize the precision and sparsity of the computation according to the specific needs of the application, and to avoid unnecessary overhead or memory usage.
4. Quality: Tensor Cores can improve the quality of the computation by reducing the numerical errors and the sensitivity to noise in the inputs or gradients. This is achieved by using the half-precision format for the inputs and the outputs, which can preserve the general trends and patterns in the data, while filtering out some of the noise or outliers. Moreover, Tensor Cores can use a technique called automatic mixed-precision (AMP), which can dynamically switch between different precisions and optimize the accuracy and efficiency of the computation, depending on the magnitude and variability of the values.
Overall, Tensor Cores can enable powerful machine learning applications by providing a faster, more efficient, more flexible, and more accurate way to perform matrix multiplication, a fundamental operation in deep learning. Tensor Cores can help researchers and engineers to explore new frontiers of AI, and to solve more complex and impactful problems, from climate modeling to drug discovery, from virtual assistants to art generators. By leveraging the full potential of Tensor Cores, one can create AI systems that can learn from more data, generalize better to unseen data, interact more naturally with humans, and enhance our understanding and creativity.
Conclusion:
This blog post has explained what Tensor Cores are, how they work, and what benefits they can bring to machine learning. We hope that by reading this post, you have gained a better appreciation of the role of Tensor Cores in accelerating and enhancing deep learning, and that you have found some inspiration for exploring and creating new AI applications. If you want to learn more about Tensor Cores, you can check out the Nvidia website, where you can find resources such as whitepapers, code samples, and benchmarks. If you want to use Tensor Cores in your own projects, you can use programming frameworks such as TensorFlow, PyTorch, or MXNet, which have built-in support for Tensor Cores and other GPU features. If you want to share your own experience or insights about Tensor Cores, you can leave a comment below, or post on social media using the hashtag #TensorCores. We wish you happy and fruitful deep learning!
Image Credit: Pexels