Automatic Differentiation with Autograd in JAX
JAX provides an automatic differentiation system known as Autograd. This powerful feature allows for the efficient computation of gradients, which are crucial in machine learning for optimization tasks like training neural networks. In this post, we'll delve into the principles of automatic differentiation and demonstrate how to implement gradient descent from scratch using JAX.
Principles of Automatic Differentiation
Automatic differentiation (AD) is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.). JAX's Autograd is capable of automatically and efficiently computing the gradient of functions with respect to their inputs.
Implementing Gradient Descent from Scratch
Gradient descent is an optimization algorithm used to minimize some function by iteratively moving in the direction of steepest descent, as defined by the negative of the gradient. In JAX, you can use Autograd to compute gradients with ease. Here's a simple example of implementing gradient descent to find the minimum of a quadratic function:
import jax
import jax.numpy as jnp
def quadratic_function(x):
return x ** 2
# Gradient of the function
grad_func = jax.grad(quadratic_function)
# Initial guess
x = 2.0
# Learning rate
alpha = 0.1
# Gradient descent loop
for i in range(100):
gradient = grad_func(x)
x -= alpha * gradient
print("Minimum x:", x)
print("Minimum value:", quadratic_function(x))
In this example, the jax.grad function automatically computes the gradient of quadratic_function. We then use this gradient in a simple loop to update our variable x iteratively, moving it towards the function's minimum.
Tags:
- #GoogleJAX
- #NumericalComputing
- #MachineLearning
- #ScientificComputing
- #PythonProgramming
- #GPUPerformance
- #TPUAcceleration
- #Autograd
- #JAXLibrary
- #DeepLearning
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