Loss functions (MSE, cross-entropy) in TensorFlow - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of MSE loss calculation

What is the output of the Mean Squared Error (MSE) loss calculation for the given predictions and true values?

TensorFlow

import tensorflow as tf

y_true = tf.constant([1.0, 2.0, 3.0])
y_pred = tf.constant([1.5, 2.5, 2.0])

mse = tf.keras.losses.MeanSquaredError()
loss_value = mse(y_true, y_pred).numpy()
print(loss_value)

A 0.41666666

B 0.33333334

C 0.5

D 0.25

💡 Hint

Recall MSE is the average of squared differences between true and predicted values.

MSE is calculated as the average of (y_true - y_pred)^2. Here, differences are [-0.5, -0.5, 1.0], squared are [0.25, 0.25, 1.0], average is (0.25+0.25+1.0)/3 = 0.5.

🧠 Conceptual

intermediate

Choosing loss function for binary classification

Which loss function is most appropriate for a binary classification problem with outputs as probabilities?

A Binary Cross-Entropy

B Categorical Cross-Entropy

C Hinge Loss

D Mean Squared Error (MSE)

💡 Hint

Binary classification outputs probabilities between 0 and 1 for two classes.

Binary Cross-Entropy is designed for two-class problems with probability outputs. Categorical Cross-Entropy is for multi-class problems. MSE is less suitable for probabilities.

❓ Metrics

advanced

Interpreting cross-entropy loss value

Given a binary classification model outputting probabilities, what does a cross-entropy loss value close to 0 indicate?

A The model predictions are very close to the true labels

B The model predictions are random guesses

C The model predictions are completely wrong

D The model is overfitting

💡 Hint

Cross-entropy loss measures the difference between predicted probabilities and true labels.

A loss close to 0 means predicted probabilities match true labels well, indicating good model performance.

🔧 Debug

advanced

Error in cross-entropy loss with logits

What error will occur when using tf.keras.losses.BinaryCrossentropy(from_logits=False) on raw logits instead of probabilities?

TensorFlow

import tensorflow as tf

loss_fn = tf.keras.losses.BinaryCrossentropy(from_logits=False)
logits = tf.constant([0.0, 2.0, -1.0])
labels = tf.constant([0, 1, 0], dtype=tf.float32)
loss = loss_fn(labels, logits).numpy()
print(loss)

A TypeError because labels and logits have different types

B ValueError due to logits not being probabilities

C No error, loss computed correctly

D RuntimeWarning about invalid values in loss

💡 Hint

Check the from_logits parameter and input values expected.

Setting from_logits=False expects probabilities between 0 and 1. Passing raw logits causes ValueError because inputs are out of range.

❓ Model Choice

expert

Selecting loss function for multi-class classification with logits

You have a multi-class classification problem with 5 classes. Your model outputs raw logits (not probabilities). Which loss function and parameter setting is correct to use in TensorFlow?

A tf.keras.losses.CategoricalCrossentropy(from_logits=False)

B tf.keras.losses.BinaryCrossentropy(from_logits=True)

C tf.keras.losses.SparseCategoricalCrossentropy(from_logits=False)

D tf.keras.losses.CategoricalCrossentropy(from_logits=True)

💡 Hint

Multi-class with logits requires categorical cross-entropy with from_logits=True.

CategoricalCrossentropy with from_logits=True correctly applies softmax internally to logits. from_logits=False expects probabilities. SparseCategoricalCrossentropy is for integer labels, not one-hot. BinaryCrossentropy is for binary tasks.