How computational graphs turn complex calculus into a simple flow of information
In short: This lecture explains how the chain rule functions within computational graphs. By visualizing calculations as nodes and functions as edges, you can understand the fundamental mechanics behind automatic differentiation in machine learning.
In the context of MIT's 18.S096 course, instructors Alan Edelman and Steven G. Johnson demonstrate that differentiation is essentially a flow of values through a network. By treating intermediate values as nodes and the functions acting upon them as connecting edges, the chain rule becomes a structured process of propagation.
The lecture distinguishes between two primary modes of automatic differentiation. Forward-mode propagates derivatives from inputs toward outputs, while reverse-mode—which the course explores further in lecture 8—works from outputs back to inputs. This framework provides a general, systematic way to handle the complex calculus required for modern machine learning.
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Sources
- Summary by Intellect · source: Lecture 5 Part 3: Differentiation on Computational Graphs
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