Posted on: April 20, 2024
Author: Mehrdad Zakershahrak
Categories: PyTorch, Deep Learning, Automatic Differentiation, Backpropagation
<aside> 💡 This in-depth guide explores PyTorch's autograd system, the powerful automatic differentiation engine that makes training neural networks possible. Dive into the mathematics, implementation details, and practical usage of autograd to gain a deeper understanding of how PyTorch computes gradients.
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At the core of PyTorch's ability to train complex neural networks lies its autograd system. Autograd, short for automatic differentiation, is the engine that computes gradients automatically, enabling the backpropagation algorithm that powers neural network training. In this post, we'll explore the intricacies of autograd, from its mathematical foundations to its practical implementation in PyTorch.
Before diving into PyTorch's implementation, let's understand the mathematical principles behind automatic differentiation.
The chain rule is the cornerstone of automatic differentiation. For composite functions, it states that:
$$ \frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x) $$
In the context of neural networks, where we have multiple layers of computations, the chain rule allows us to compute gradients through the entire network.
There are two primary modes of automatic differentiation:
PyTorch uses reverse mode differentiation, which is more efficient for functions with many inputs and few outputs - precisely the case for most neural networks.
PyTorch builds a dynamic computational graph as operations are performed. Each node in this graph represents an operation or a variable, and edges represent data flow.