Question

Consider a fully-connected feed-forward multi-layer perceptron. It has 30 neurons in the input layer, followed by two hidden layers and an output layer. The first hidden layer has 4 neurons and the second hidden layer has 3 neurons. The output layer has only one neuron. Assume that no bias parameters are used.

The number of learnable parameters in the multi-layer perceptron is _______ . (Answer in integer)

Hint:

With no bias terms, count only the weight connections between each pair of consecutive layers (input to output) and add them up: 30x4 + 4x3 + 3x1.

Answer 1

Correct Answer: 135

Step 1: Identify the layer sizes.
Input layer: 30 neurons.
Hidden layer 1: 4 neurons.
Hidden layer 2: 3 neurons.
Output layer: 1 neuron.
Since the network is fully connected, every neuron in one layer connects to every neuron in the next layer with a separate weight, and no bias terms are used, so the only learnable parameters are these connection weights.

Step 2: Count the weights between the input layer and hidden layer 1.
Each of the 30 input neurons connects to each of the 4 neurons in hidden layer 1:
\[ 30 \times 4 = 120 \]

Step 3: Count the weights between hidden layer 1 and hidden layer 2.
Each of the 4 neurons in hidden layer 1 connects to each of the 3 neurons in hidden layer 2:
\[ 4 \times 3 = 12 \]

Step 4: Count the weights between hidden layer 2 and the output layer.
Each of the 3 neurons in hidden layer 2 connects to the single output neuron:
\[ 3 \times 1 = 3 \]

Step 5: Add up all the weights.
\[ 120 + 12 + 3 = 135 \]
No bias parameters are added anywhere, since the problem states none are used.

Final Answer:
The multi-layer perceptron has 135 learnable parameters. \[ \boxed{135} \]