Interactive Neural Network Laboratory (Phase 1)

Visualize the mathematical foundations of Unit 1: single-neuron perceptron boundaries, multi-layer banking credit decisions, and non-linear activation gradient dynamics.

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3-Input Perceptron & 2D Decision Boundary Studio

Textbook Sec 1.6

Simulate biological-to-artificial neuron summation, step activation, and linear separability.

Presets:

1. Binary Inputs (xᵢ ∈ {0, 1})Click to toggle

2. Synaptic Weights (wᵢ) & Bias (b) Free Preset Mode

w₁ (Weight for x₁):3.0

w₂ (Weight for x₂):2.0

w₃ (Weight for x₃):1.0

Bias (b) or -θ:-4.0

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Unlock dynamic weight adjustment to design custom logic gates and see continuous decision boundary transformations. Free preview lets you run default textbook examples. Unlock to explore all parameters and custom experiments.

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3. Artificial Neuron Signal Architecture

z = ∑ wᵢxᵢ + b = (3 × 1) + (2 × 1) + (1 × 0) + (-4) = 1.0

Inputs × Weights

x₁: 1→ w₁=3

x₂: 1→ w₂=2

x₃: 0→ w₃=1

∑1.0

Summation

Step(z)z ≥ 0 ? 1 : 0

Activation

Walk (YES)

4. 2D Decision Boundary ($w_1 x_1 + w_2 x_2 + b = 0$)x₁ vs x₂ Plane

Green Circle:Target Class 1

Red Circle:Target Class 0

Dotted Line:Hyperplane boundary

Linearly Separable:
The boundary line cleanly divides all Class 1 points from Class 0. A single perceptron easily converges here.

Python Laboratory ScriptCopy standard Numpy Perceptron snippet with active parameters

Section 1.6 Curriculum Focus

Single Perceptron & XOR Limitations

Illustrates how a single artificial neuron separates binary spaces linearly. Use the XOR preset to visually prove Minsky & Papert's 1969 theorem to students.

Page 12 Banking Case Study

6 → 10 → 5 → 1 Feedforward MLP

Simulates real-world credit risk scoring with ReLU hidden layer activations and Sigmoid approval probability. Features SHAP explainability charts.

Section 1.9 & 1.9.4 Lab

Activation Curves & Housing Prices

Demonstrates why ReLU outperforms Sigmoid in deep networks by preventing vanishing gradients ($f'(z) < 0.05$), accompanied by California housing regression.