# What is Neural Tangent Kernel

##### The Power of Neural Tangent Kernel in Machine Learning

In recent years, the field of machine learning has experienced a massive explosion, which has led to the development of various techniques, methodologies, and algorithms used in the field. One of the most prominent developments in machine learning is the introduction of the neural tangent kernel. Neural Tangent Kernel (NTK), also known as Neural Tangent Activation Function (NTAF), is an algorithm that addresses the problem of scalability and efficiency in the training of neural networks.

The Neural Tangent Kernel is a function that computes the similarity between the outputs of two neural networks. Its efficacy lies in its ability to compute derivative of its output with respect to the network's parameters, allowing for efficient computation of gradients in the training process. This function computes the similarity between two models by comparing the outputs of the two models, hence enabling a faster and more efficient training process.

In this article, we will explore the concept of Neural Tangent Kernel in more detail, and explain how it is utilized in a machine learning context.

##### The Basics of Neural Tangent Kernel

Before we delve deeper into the concept of Neural Tangent Kernel, it is important to understand the basics of neural networks. A neural network is an algorithm that can learn a complex, non-linear function from input data. It consists of layers of neurons, where each neuron performs a simple computation on its input and produces an output.

The training of a neural network involves adjusting the weights and biases of the neurons such that the network produces output that matches the desired output. This is typically done using a technique called backpropagation. Backpropagation is an optimization algorithm that calculates the error between the actual output and the desired output, and then adjusts the weights and biases of the neurons to minimize the error.

However, one of the major challenges of training a neural network is scalability and efficiency. As the network becomes larger, the computation required in the backpropagation process becomes increasingly expensive, which ultimately slows down the training process. This is where the Neural Tangent Kernel comes in.

Neural Tangent Kernel represents the similarity between the outputs of two neural networks, and as such can be used to optimize the training process. It is based on the concept of Gaussian Process, which is a mathematical framework that uses a probability distribution over a set of functions. Gaussian Process allows us to quantify the uncertainty in the prediction of the function and can be used to make predictive inferences.

The Neural Tangent Kernel can be thought of as a way to compute the derivative of the output of a neural network with respect to its parameters. This allows for a faster and more efficient training process, making it highly suitable for large-scale machine learning problems.

##### How Neural Tangent Kernel Works

Neural Tangent Kernel is based on the concept of tangent space, which is a mathematical concept that describes the set of all possible directions in which a function can change. The tangent space of a function refers to the set of all possible directions in which the function can change. In other words, it refers to the set of all possible directions in which the function can change while keeping the point of origin intact.

The Neural Tangent Kernel represents the similarity between two neural networks by computing the dot product of their outputs in the tangent space of the network's parameters. The similarity between the two networks is determined by the similarity between their outputs when changing the parameters of the network within the tangent space.

• The first step in the process involves computing the tangent vectors of the two neural networks at a given point in the parameter space. These tangent vectors represent the changes in the network's output that occur when the parameters are changed slightly.
• The next step is to compute the dot product of the two tangent vectors, which is equivalent to the cosine of the angle between the tangent vectors. This dot product measures the similarity between the two networks at that particular point in the parameter space.
• The final step is to compute the Neural Tangent Kernel by averaging the dot products of the tangent vectors across all possible point in the parameter space. This gives us a measure of the overall similarity between the two networks.

The Neural Tangent Kernel can be used to compute the gradients of the output of a neural network with respect to its parameters. This makes it possible to optimize the training process and speed up the convergence of the network.

##### Applications of Neural Tangent Kernel

The Neural Tangent Kernel has been applied in various areas of machine learning, including supervised learning, unsupervised learning, and reinforcement learning. One of the most significant applications of Neural Tangent Kernel is in deep learning, where it has been used to speed up the training of large-scale neural networks.

Neural Tangent Kernel has also been used in the development of new machine learning algorithms. For instance, it has been used in the design of new kernel methods that can handle large-scale datasets. It has also been used in the development of new reinforcement learning algorithms that can improve the speed and efficiency of the learning process.

One of the significant advantages of Neural Tangent Kernel is its scalability. The algorithm can be used to train large-scale neural networks with millions of parameters without encountering scalability issues. This is a significant development in machine learning, as it allows for the development of more complex and accurate models that can handle large datasets and real-world problems.

##### Conclusion

The Neural Tangent Kernel is a significant development in the field of machine learning. It addresses the problem of scalability and efficiency in the training of neural networks, enabling the development of larger and more accurate models that can handle real-world problems. The algorithm can be used in various areas of machine learning, including supervised learning, unsupervised learning, and reinforcement learning. Its scalability and efficiency make it highly suitable for large-scale machine learning problems, enabling faster and more accurate training of complex neural networks. As such, Neural Tangent Kernel represents a significant advancement in the field of machine learning, and its applications will only continue to grow in the future.