🧮 Computation Graphs – Visualizing How Functions Work

🧠 What is a Computation Graph?

A computation graph is a visual way to break down complex math into smaller, easy-to-understand steps. Each step becomes a node in the graph. It helps us:

• See how data flows through a function
• Track dependencies between variables
• Prepare for backpropagation (learning!)

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🧩 Example Function

We are given the function:

J(a,b,c)=3(a+bc)J(a, b, c) = 3(a + bc)

J(a,b,c)=3(a+bc)

We break this down into intermediate steps:

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u = b × c
v = a + u
J = 3 × v

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🧮 Given Values

• a=5a = 5a=5
• b=3b = 3b=3
• c=2c = 2c=2

Step-by-Step Computation

Step	Formula	Result
1	u=bcu = bcu=bc	u=3×2=6u = 3 × 2 = 6u=3×2=6
2	v=a+uv = a + uv=a+u	v=5+6=11v = 5 + 6 = 11v=5+6=11
3	J=3vJ = 3vJ=3v	J=3×11=33J = 3 × 11 = 33J=3×11=33

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📊 Computation Graph

Here’s how it looks visually:

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   a = 5     b = 3      c = 2
     │         │         │
     │         └──┬──────┘
     │            ▼
     │         [ u = b × c ] → u = 6
     │                │
     └────────────┐   ▼
                  ▼ [ v = a + u ] → v = 11
                       │
                       ▼
                  [ J = 3 × v ] → J = 33

Each box is a small computation. Together, they form a chain of dependencies from input to output.

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💡 Why Use Computation Graphs?

• They simplify complex math
• They make it easy to trace and debug values
• They're essential for automatic differentiation in deep learning

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🧠 Summary

Concept	Explanation
Computation Graph	Visual map of how a function computes
Nodes	Each math operation (like u = bc)
Flow	Arrows show how values move from inputs to output
Used For	Forward pass, and later, backpropagation