Feedforward Neural Network example with Simple Python

Example: Simple Feedforward Process (1 hidden layer)

Let’s say we have 2 inputs and 1 output:

  1. Inputs: x1,x2
  2. Hidden Neurons: h1,h2
  3. Output Neuron: o

Forward Flow:

Input Layer:     x1     x2
                    \   /
Hidden Layer:     h1   h2
                     \ /
Output Layer:         o

Each connection has a weight, and each neuron applies:

Python Simulation (Simple Example)

import numpy as np

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

# Inputs
X = np.array([0.5, 0.8])

# Weights and biases for hidden layer (2 neurons)
W_hidden = np.array([[0.1, 0.3],
                     [0.4, 0.2]])
b_hidden = np.array([0.05, 0.1])

# Weights and bias for output layer
W_output = np.array([0.6, 0.9])
b_output = 0.2

# Hidden layer calculation
z_hidden = np.dot(W_hidden, X) + b_hidden
a_hidden = sigmoid(z_hidden)

# Output layer calculation
z_output = np.dot(W_output, a_hidden) + b_output
a_output = sigmoid(z_output)

print("Predicted Output:", a_output)

Summary Table

Concept Description
Feedforward Flow Data moves from input → hidden → output
Layers Input, Hidden (optional), Output
Weights + Biases Parameters learned during training
Activation Functions Add non-linearity (e.g., ReLU, Sigmoid)
Loss Function Measures prediction error
Gradient Descent Optimization method to reduce loss

Next – Hidden Layer Influence