Dense (fully connected) layers in TensorFlow - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output shape of a Dense layer

Given the following TensorFlow code, what is the shape of the output tensor after the Dense layer?

TensorFlow

import tensorflow as tf

input_tensor = tf.random.uniform((5, 10))  # batch size 5, input features 10
layer = tf.keras.layers.Dense(8)
output = layer(input_tensor)
output_shape = output.shape
print(output_shape)

A (10, 8)

B (5, 8)

C (5, 10)

D (8, 5)

💡 Hint

Remember the Dense layer changes the last dimension to the number of units.

The Dense layer transforms each input vector of size 10 into a vector of size 8. Since the batch size is 5, the output shape is (5, 8).

❓ Model Choice

intermediate

Choosing the correct Dense layer for classification

You want to build a neural network to classify images into 10 categories. Which Dense layer configuration is most appropriate for the final layer?

A Dense(10, activation='softmax')

B Dense(1, activation='sigmoid')

C Dense(10, activation='relu')

D Dense(5, activation='softmax')

💡 Hint

For multi-class classification, the output layer should have one unit per class with softmax activation.

For 10 classes, the output layer should have 10 units with softmax activation to output probabilities for each class.

❓ Hyperparameter

advanced

Effect of changing units in Dense layer

What is the effect of increasing the number of units in a Dense layer from 32 to 128 in a neural network?

A Increases model capacity and may improve learning but risks overfitting

B Decreases model capacity and speeds up training

C Has no effect on model capacity or training time

D Always guarantees better accuracy on test data

💡 Hint

More units mean more parameters to learn.

Increasing units increases the number of parameters, allowing the model to learn more complex patterns but also increasing overfitting risk.

🔧 Debug

advanced

Identifying error in Dense layer usage

What error will this code raise when run?

TensorFlow

import tensorflow as tf

input_tensor = tf.random.uniform((5, 10))
layer = tf.keras.layers.Dense(-5)
output = layer(input_tensor)

A RuntimeError: layer not built

B TypeError: input_tensor shape invalid

C No error, runs successfully

D ValueError: units must be a positive integer

💡 Hint

Check the units argument for Dense layer.

Dense layer units must be a positive integer. Negative units cause a ValueError.

🧠 Conceptual

expert

Why use bias in Dense layers?

What is the main purpose of including a bias term in a Dense (fully connected) layer?

A To reduce the number of parameters in the model

B To normalize the input data automatically

C To allow the model to fit data that does not pass through the origin

D To prevent overfitting by adding regularization

💡 Hint

Think about shifting the activation function.

Bias allows the activation function to shift, enabling the model to fit data that does not pass through zero.