# Interactive Explorations

Hands-on applets for Classical Foundations of Artificial Neural Networks

← Back to course notes · Presentation slides →

Part I — Origins (Chapters 1–3)

### McCulloch-Pitts Gate Explorer

Toggle inputs, change thresholds, and watch logic gates compute in real time. See how AND, OR, NOT, NAND, and NOR emerge from a single neuron model.

Chapter 1

### XOR Network Simulator

Watch signals propagate through a multi-layer network that solves XOR. Animated pulse flow shows how the hidden layer transforms the problem.

Chapter 2

### McCulloch-Pitts Network Builder

Drag-and-drop neurons, wire them together, and simulate step-by-step. Build logic gates, latches, counters, and finite automata from scratch.

Chapters 1–3

Part II — The Perceptron (Chapters 4–7)

### Decision Boundary Lab

Drag sliders to adjust weights and bias. See the decision boundary rotate and shift in real time. Understand the geometric meaning of the perceptron.

Chapter 4

### Perceptron Learning Simulator

Draw data points, then train the perceptron step-by-step or in animated mode. Watch the decision boundary converge — or fail on XOR.

Chapter 5

### Convergence Bound Explorer

Adjust data spread R and margin γ to see how the convergence bound k ≤ R²/γ² changes. Visualize the squeeze proof in action.

Chapter 6

### Boolean Functions & Shattering

Explore all 16 two-input Boolean functions. Then drag 3 points to test shattering and understand VC dimension interactively.

Chapter 7

Part V — Backpropagation (Chapters 15–19)

### Backprop Gradient Explorer

Click any weight in a feedforward network to see its gradient derived step-by-step via BP1–BP3. 12 topologies from simple perceptrons to deep funnels.

Chapter 16

### Backprop Worked Example

Full numerical walkthrough of ∂L/∂w in a [3,2,2,1] network. Every forward & backward step shown with color-coded BP1–BP4 derivations.

Chapters 16–18 · PDF version

Interactive Papers — Monico (2024): An Elementary UAT Proof

### Squashing Function Lab

Adjust points x⊂0, x⊂1 and tolerance ϵ to see how σ(s+tx) separates them. Watch the 2×2 linear system solution update in real time.

Lemma 3.1 · Course notes

### Point-Set Separator

Drag a point x⊂0 around a compact set B and watch the N⊂2 separator build itself: open covers, finite subcovers, and summed sigmoids.

Lemma 3.2 · Course notes

### Set-Set Separator

Choose disjoint compact sets A and B, then visualize the N⊂3 separator as a heatmap. Toggle between raw h and squashed H to see double-squashing in action.

Lemma 3.3 · Course notes

### UAT Contradiction Machine

Step through the proof of Theorem 3.4: pick a target, build an approximation, identify U⁺ and U⁻, apply Lemma 3.3, and watch the contradiction emerge.

Theorem 3.4 · Course notes

### Constructive UAT Training

Watch a network build itself neuron-by-neuron to approximate any function. Weights shown with color; hover to see activations flow through the architecture.

Theorem 3.4 · Course notes