Click4Ai

100.

Medium

Implement a **Dense (Fully Connected) Layer**, the most common layer type in neural networks.

Forward Pass:

output = inputs @ weights + bias

Where:

  • `inputs`: shape (batch_size, n_inputs)
  • `weights`: shape (n_inputs, n_neurons)
  • `bias`: shape (1, n_neurons)
  • `output`: shape (batch_size, n_neurons)

    • Example:

    layer = DenseLayer(n_inputs=3, n_neurons=2)

    inputs = [[1.0, 2.0, 3.0],

    [4.0, 5.0, 6.0]]

    output = layer.forward(inputs) # shape (2, 2)

    **Explanation:** Each neuron in the layer computes a weighted sum of ALL inputs plus a bias. The "dense" name comes from every input being connected to every neuron. This is the matrix multiplication form of multiple neurons working in parallel.

    Constraints:

  • Initialize weights with small random values (randn * 0.01)
  • Initialize biases to zeros
  • Support batch inputs (multiple samples at once)

    • Test Cases

    Test Case 1
    Input: inputs shape (1,3), layer DenseLayer(3,4)
    Expected: output shape (1,4)
    Test Case 2
    Input: inputs shape (5,3), layer DenseLayer(3,2)
    Expected: output shape (5,2)
    Test Case 3
    Input: bias=0, weights=identity, input=[1,2,3]
    Expected: [1,2,3]
    + 2 hidden test cases