Introduction and Prerequisites

• StatQuest episode on neural networks with multiple inputs/outputs
• Supported by Ital, inspired by Michael in Svalbard
• Assumes understanding of basic neural networks and ReLU activation function
• Previous networks: simple single input (drug dosage) → single output (effectiveness)

Single Input/Output Networks Review

• Previous examples: one input node, one output node
• Input data (dosages) fits on x-axis - one-dimensional
• Output on y-axis - creates two-dimensional graph
• Weights/biases slice, flip, stretch curved activation functions
• Functions added together to form 2D squiggle fitting data

Multiple Input Network Introduction

• New network: two input nodes → multiple output nodes
• Task: iris flower classification using petal width + sepal width
• Three species: setosa, versicolor, virginica
• Simplified start: two inputs → one output (setosa only)

Two Inputs, One Output Analysis

• Inputs: petal width, sepal width (scaled 0-1)
• Output: setosa prediction
• Requires 3D graph: two input axes + one output axis
• Mathematical walkthrough with specific weights:
  • Top hidden node: petal weight = -2.5, sepal weight = 0.6, bias = 1.6
  • Bottom hidden node: different weights
  • Output weights: top node = -0.1, bottom node = 1.5, final bias = 0

3D Surface Generation Process

• Starting point: petal width = 0, sepal width = 0
• Top node calculation: (-2.5 × 0) + (0.6 × 0) + 1.6 = 1.6
• ReLU activation: max(0, 1.6) = 1.6
• Systematic calculation across all input combinations
• Creates blue bent surface from top node
• Orange bent surface from bottom node
• Surfaces added together → green crinkled surface
• Final bias (0) added → final setosa prediction surface

Setosa Prediction Analysis

• Green crinkled surface shows setosa highest when petal width ≈ 0
• Setosa lowest when petal width ≈ 1
• Example prediction: petal width = 0.5, sepal width = 0.37 → output = 0.09
• Indicates iris probably not setosa (closer to 0 than 1)

Versicolor Output Surface

• Same hidden layer weights/biases as setosa
• Different output weights: top node = 2.4, bottom node = -5.2, bias = 0
• Y-axis range expanded to -6 to 6 for visualization
• Creates red crinkled surface
• Rescaled to -0.5 to 1 range shows peak at petal width ≈ 0.4

Virginica Output Surface

• Same hidden layer structure
• Output weights: top node = -2.2, bottom node = 3.7, bias = 1
• Creates purple crinkled surface
• Rescaled to 0-1 range shows peak at petal width ≈ 1

Final Classification Example

• Test iris: petal width = 0.5, sepal width = 0.37
• Outputs: setosa = 0.09, versicolor = 0.86, virginica = [not specified]
• Prediction: versicolor (highest output value = 0.86)
• Note: typically outputs sent to argmax or softmax for final decision

Next Steps Preview

• Future episode will cover argmax and softmax functions
• These functions used for final decision making with multiple outputs