Generalized Forward Propagation Implementation

• Goal of video: show general implementation of forward propagation in Python

• “When you see it again in their practice lab, in the optional labs, you know how to interpret it”

• No need to take notes on every line - understanding is enough

• Dense Layer Function Implementation:

• Purpose: “Implement a dense layer” (single neural network layer)

• Function signature: dense(a_prev, W, b)

  • Inputs:
    • a_prev: activation from previous layer
    • W: weight parameters stacked in columns
    • b: bias parameters in 1D array
  • Output: activations for current layer

• Weight Matrix Organization:

  • Parameters stacked in columns
  • Example (for 3 neurons):
    • W matrix = [w_1,1, w_1,2, w_1,3] (2×3 matrix)
    • b array = [-1, 1, 2]

• Dense Function Implementation Details:

• Get number of units: units = W.shape[1]

• Initialize output array: a = np.zeros(units)

• Loop through each unit/neuron:

  for j in range(units):
      w = W[:, j]        # Extract jth column of W
      z = np.dot(w, a_prev) + b[j]
      a[j] = g(z)        # Apply sigmoid activation

• Return array of activations

• Complete Forward Propagation for Neural Network:

• String multiple dense layers together:

  a_1 = dense(x, W_1, b_1)
  a_2 = dense(a_1, W_2, b_2)
  a_3 = dense(a_2, W_3, b_3)
  a_4 = dense(a_3, W_4, b_4)
  f_x = a_4
  return f_x

Note: Capital W is used for matrices, lowercase for vectors/scalars (linear algebra convention)

• Benefits of Understanding Implementation:
• “Even when you’re using powerful libraries like TensorFlow, it’s helpful to know how it works under the hood”
• Aids debugging when:
  • Code runs slowly
  • Strange results occur
  • Potential bugs appear
• “My ability to debug my code to be a TensorFlow code or something else, is really important to being an effective machine learning engineer”

This generalized implementation provides the core functionality of forward propagation without having to hard-code each neuron. Understanding this gives insight into how neural network frameworks work internally, which is valuable for debugging and optimizing models even when using high-level libraries.