Neural Network Visualizer

🔮 Interactive Network

🎯 What is a Neural Network?

A neural network is an "absurdly complicated" mathematical function that transforms raw input (like an image) into meaningful output (a prediction). It processes information through successive levels of abstraction.

🔢 The Numbers

784

Input Neurons

~13,000

Parameters

10

Output Classes

4

Layers Total

💡 Learning = Adjusting

When we say a network is "learning," we simply mean it's automatically adjusting thousands of parameters until they're set correctly to solve the problem.

📊 The Structure of Abstraction

📥

Input Layer

784 neurons • Raw pixel data

✨

Hidden Layers

Where the magic happens

〰️

Edges

→

⭕

Loops

→

🔢

Digits

📤

Output Layer

10 neurons • Final prediction

How Layers Work

Layers provide the architecture for information processing. The network operates by passing information from one layer to the next, where the activations in one layer determine the activations in the subsequent layer.

1️⃣

Input Layer

784 neurons represent grayscale values (0-1) of a 28×28 pixel grid

2️⃣

Hidden Layers

Break down complex problems into subcomponents—edges → loops → complete digits

3️⃣

Output Layer

10 neurons (0-9), activation = confidence that image is that digit

⚖️ Pattern Recognition

Adjust weights to see how they affect pattern detection:

Center Weight: +1.0

Edge Weight: -0.5

Weighted Sum Calculation

Σ (input × weight) = 0.00

+ bias → activation function → output

How Weights Work

✅ Positive Weights

Amplify matching patterns. If a neuron wants to detect a specific feature, it assigns positive weights to relevant pixels.

❌ Negative Weights

Suppress non-matching areas. Surrounding pixels that shouldn't be active get negative weights.

📊 Weighted Sum

Each neuron multiplies all inputs by their weights and adds them together. A high sum = strong pattern match!

🔍

Weights act as pattern filters, looking for specific features in the data

🎚️ Activation Thresholds

0

INACTIVE

+10 0 -10

Weighted Sum: 5.0

Bias: -3.0

5.0 + (-3.0) = 2.0

weighted sum + bias = input to activation function

How Biases Work

🚫 Inducing Inactivity

You may not want a neuron to fire just because the weighted sum is slightly greater than zero. Bias shifts the threshold!

➕ Mathematical Shift

The bias is added to the weighted sum before passing through the activation function.

📝 Example

Adding a bias of -10 ensures the neuron remains inactive unless the weighted input exceeds 10.

🎯

Biases determine how sensitive each neuron is to its detected pattern

⚡ The "Squashing" Function

Input (x): 0.0

Output: 0.50

Why "Squash"?

To ensure the network behaves like biological neurons (which are either active or inactive), we compress outputs into a range between 0 and 1.

📈 Sigmoid

The classic "S-curve" that smoothly squishes values:

• Very negative → approaches 0
• Very positive → approaches 1
• Used in older networks

⚡ ReLU (Rectified Linear Unit)

Modern, simpler alternative:

• Negative → outputs 0
• Positive → keeps the value
• Easier to train!

🎛️ The Sound Mixing Board Analogy

Understanding neural networks through audio production

📊

Layers = Processing Stages

🎤

Recording

Raw input capture

↓

🎚️

Processing

EQ, compression, effects

↓

🔊

Mastering

Final polished output

⚖️

Weights = Faders

CH1

+0.8

CH2

-0.3

CH3

+0.5

Each fader controls how much of each sound contributes to the mix—just like weights control input importance!

🎚️

Biases = Noise Gates

Signal Level Threshold: -10dB

✓ Pass ✗ Block ✓ Pass ✗ Block

A noise gate only lets signals through if they're loud enough—biases work the same way for neuron activation!

🎤 Input

→

🎛️ Mix (Weights)

→

🚪 Gate (Bias)

→

📊 Compress (Activation)

→

🔊 Output