# Technical Document Extraction: Neural Network Architecture Diagram
## Diagram Overview
The image depicts a **feedforward neural network architecture** with labeled components and mathematical notation. Below is a structured extraction of all textual and symbolic information.
---
### 1. **Component Labels and Flow**
#### Input Layer
- **Nodes**:
- `x₁`, `x₂`, `x₃` (input features)
- **Position**: Leftmost column of orange nodes.
#### Hidden Layers
- **Nodes**:
- Blue circular nodes with no explicit labels (universal representation).
- **Connections**:
- Directed edges (blue arrows) between all input-to-hidden and hidden-to-output nodes.
- **Activation Function**:
- Notation: `σ(wᵀx + b)` (sigmoid function applied to weighted input + bias).
- Position: Annotated at the bottom of the hidden layer.
#### Output Layer
- **Nodes**:
- `y₁`, `y₂` (output predictions).
- **Position**: Rightmost column of orange nodes.
---
### 2. **Architectural Structure**
- **Layers**:
- **Input**: 3 nodes (`x₁`, `x₂`, `x₃`).
- **Hidden**: 6 nodes (arranged in two rows of three nodes each).
- **Output**: 2 nodes (`y₁`, `y₂`).
- **Connections**:
- Fully connected (dense) architecture: Every input node connects to every hidden node, and every hidden node connects to every output node.
- No skip connections or recurrent loops.
---
### 3. **Mathematical Notation**
- **Activation Function**:
- `σ(wᵀx + b)`:
- `w`: Weight vector (transposed, `wᵀ`).
- `x`: Input vector.
- `b`: Bias term.
- `σ`: Sigmoid function (commonly used for binary classification).
---
### 4. **Color Coding**
- **Node Colors**:
- **Input/Output**: Orange (`x₁`, `x₂`, `x₃`, `y₁`, `y₂`).
- **Hidden**: Blue (universal representation).
- **Edges**: Blue arrows (directional flow from input → hidden → output).
---
### 5. **Spatial Grounding**
- **Input Layer**: Leftmost column (x-axis: 0–1).
- **Hidden Layers**: Middle region (x-axis: 1–2).
- **Output Layer**: Rightmost column (x-axis: 2–3).
- **Activation Function**: Annotated at the bottom of the hidden layer (y-axis: -0.5).
---
### 6. **Key Trends and Observations**
- **Data Flow**: Unidirectional (input → hidden → output).
- **Complexity**:
- Total connections:
- Input-to-hidden: 3 inputs × 6 hidden = 18 edges.
- Hidden-to-output: 6 hidden × 2 outputs = 12 edges.
- Total parameters (weights + biases):
- Weights: 18 + 12 = 30.
- Biases: 6 (hidden) + 2 (output) = 8.
- **Total**: 38 trainable parameters.
---
### 7. **Missing Elements**
- **No Legends**: No explicit legend present (colors are self-explanatory).
- **No Data Table**: Diagram is structural, not data-driven.
- **No Axes**: No numerical axes (qualitative spatial layout only).
---
### 8. **Summary**
This diagram illustrates a **3-input, 6-hidden, 2-output feedforward neural network** with a sigmoid activation function. The architecture is fully connected, with 38 trainable parameters. Inputs (`x₁`, `x₂`, `x₃`) are processed through hidden layers to produce outputs (`y₁`, `y₂`).
