Loss functions (MSELoss, CrossEntropyLoss) in PyTorch - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of MSELoss with simple tensors

What is the output of the following PyTorch code that calculates Mean Squared Error loss?

PyTorch

import torch
import torch.nn as nn

loss_fn = nn.MSELoss()
pred = torch.tensor([2.0, 3.0, 4.0])
target = torch.tensor([1.0, 3.0, 5.0])
loss = loss_fn(pred, target)
print(loss.item())

A 0.6666667

B 1.0

C 2.0

D 0.5

💡 Hint

Recall that MSELoss computes the average of squared differences.

MSELoss calculates the average of (pred - target)^2. Here, differences are [1, 0, -1], squares are [1, 0, 1], average is (1+0+1)/3 = 0.6666667.

❓ Predict Output

intermediate

Output of CrossEntropyLoss with logits

What is the output of this PyTorch code using CrossEntropyLoss with logits for a 3-class classification?

PyTorch

import torch
import torch.nn as nn

loss_fn = nn.CrossEntropyLoss()
logits = torch.tensor([[1.0, 2.0, 0.5]])  # batch size 1, 3 classes
labels = torch.tensor([1])  # correct class index
loss = loss_fn(logits, labels)
print(round(loss.item(), 4))

A 0.4649

B 0.4170

C 1.0986

D 0.6931

💡 Hint

CrossEntropyLoss applies softmax internally and computes negative log likelihood.

Softmax probabilities are approx [0.2311, 0.6284, 0.1404]. Negative log of probability for class 1 is -log(0.6284) ≈ 0.4649.

❓ Model Choice

advanced

Choosing loss function for regression vs classification

You want to train a model to predict house prices (a continuous value) and another model to classify images into 5 categories. Which loss functions should you choose respectively?

A MSELoss for both tasks

B CrossEntropyLoss for house prices, MSELoss for image classification

C MSELoss for house prices, CrossEntropyLoss for image classification

D CrossEntropyLoss for both tasks

💡 Hint

Think about the type of output each task produces.

Regression tasks predict continuous values, so MSELoss fits best. Classification tasks predict class probabilities, so CrossEntropyLoss is appropriate.

❓ Hyperparameter

advanced

Effect of reduction parameter in MSELoss

What is the effect of setting the 'reduction' parameter to 'sum' in PyTorch's MSELoss compared to the default 'mean'?

A Loss values are averaged over batch dimension only

B Loss values are squared twice

C Loss values are normalized by the number of classes

D Loss values are summed over all elements instead of averaged

💡 Hint

Check how reduction changes aggregation of individual losses.

'sum' adds all squared errors together, while 'mean' averages them. This changes the scale of the loss.

❓ Metrics

expert

Interpreting CrossEntropyLoss output for multi-class classification

Given a batch of 2 samples with logits and true labels, what is the CrossEntropyLoss output? Code: import torch import torch.nn as nn loss_fn = nn.CrossEntropyLoss() logits = torch.tensor([[2.0, 1.0, 0.1], [0.5, 2.5, 0.3]]) labels = torch.tensor([0, 1]) loss = loss_fn(logits, labels) print(round(loss.item(), 4))

A 0.5514

B 0.3190

C 0.4170

D 1.0986

💡 Hint

Calculate softmax probabilities for each sample and average negative log likelihood.

For sample 1: softmax probs ≈ [0.659, 0.242, 0.099], loss = -log(0.659) ≈ 0.4170. For sample 2: softmax probs ≈ [0.109, 0.803, 0.089], loss = -log(0.803) ≈ 0.2200. Average loss = (0.4170 + 0.2200)/2 = 0.3185 (rounded to 0.3190).

Practice

1. Which loss function in PyTorch is best suited for predicting continuous values like house prices?

easy

A. torch.nn.MSELoss

B. torch.nn.CrossEntropyLoss

C. torch.nn.BCELoss

D. torch.nn.NLLLoss

Solution

1. Step 1: Understand the type of prediction

   Predicting house prices is a regression problem where output is continuous.

2. Step 2: Match loss function to problem type

   MSELoss calculates mean squared error, ideal for continuous outputs. CrossEntropyLoss is for classification, not regression.

3. Final Answer:

   torch.nn.MSELoss -> Option A

4. Quick Check:

   Regression uses MSELoss = C [OK]

Hint: Use MSELoss for continuous outputs, CrossEntropyLoss for classes [OK]

Common Mistakes:

• Choosing CrossEntropyLoss for regression tasks
• Confusing BCELoss with MSELoss
• Using NLLLoss without log probabilities

2. Which of the following is the correct way to create a CrossEntropyLoss object in PyTorch?

easy

A. loss = torch.nn.CrossEntropy()

B. loss = torch.nn.MSELoss()

C. loss = torch.nn.CrossEntropyLoss()

D. loss = torch.CrossEntropyLoss()

Solution

1. Step 1: Recall PyTorch loss function syntax

   Loss functions are in torch.nn and instantiated with parentheses.

2. Step 2: Identify correct class name and module

   CrossEntropyLoss is the correct class name under torch.nn. Options A misses 'Loss' and C misses 'nn'.

3. Final Answer:

   loss = torch.nn.CrossEntropyLoss() -> Option C

4. Quick Check:

   Correct class and module = D [OK]

Hint: Use torch.nn.CrossEntropyLoss() exactly for classification loss [OK]

Common Mistakes:

• Missing parentheses when creating loss object
• Using torch.CrossEntropyLoss() instead of torch.nn.CrossEntropyLoss()
• Confusing MSELoss with CrossEntropyLoss

3. What will be the output loss value when using torch.nn.MSELoss on predictions tensor([2.0, 3.0]) and targets tensor([1.0, 5.0])?

medium

A. 2.5

B. 3.0

C. 1.5

D. 4.0

Solution

1. Step 1: Calculate squared differences

   Differences: (2.0-1.0)=1.0, (3.0-5.0)=-2.0; squared: 1.0, 4.0

2. Step 2: Compute mean of squared differences

   Mean = (1.0 + 4.0) / 2 = 2.5

3. Final Answer:

   2.5 -> Option A

4. Quick Check:

   MSE = mean squared error = 2.5 [OK]

Hint: Square errors, then average for MSELoss output [OK]

Common Mistakes:

• Forgetting to square the differences
• Summing without averaging
• Mixing up prediction and target order

4. Given this code snippet, what is the error?

import torch
loss_fn = torch.nn.CrossEntropyLoss()
pred = torch.tensor([[0.2, 0.8], [0.6, 0.4]])
target = torch.tensor([1, 0])
loss = loss_fn(pred, target)
print(loss.item())

medium

A. Loss function should be MSELoss for this target

B. Target tensor should be one-hot encoded

C. No error, code runs correctly

D. Predictions should be raw scores (logits), not probabilities

Solution

1. Step 1: Check input requirements for CrossEntropyLoss

   CrossEntropyLoss expects raw scores (logits), not probabilities.

2. Step 2: Analyze given predictions

   Predictions are probabilities (sum to 1), so applying CrossEntropyLoss directly causes incorrect loss calculation.

3. Final Answer:

   Predictions should be raw scores (logits), not probabilities -> Option D

4. Quick Check:

   CrossEntropyLoss needs logits = A [OK]

Hint: Use logits, not probabilities, with CrossEntropyLoss [OK]

Common Mistakes:

• Passing probabilities instead of logits to CrossEntropyLoss
• Using one-hot targets instead of class indices
• Confusing MSELoss with CrossEntropyLoss for classification

5. You have a multi-class classification problem with 4 classes. Your model outputs raw scores (logits) of shape (batch_size, 4). Which loss function and target format should you use in PyTorch?

hard

A. Use torch.nn.MSELoss with target as one-hot vectors

B. Use torch.nn.CrossEntropyLoss with target as class indices (0 to 3)

C. Use torch.nn.BCELoss with target as class indices

D. Use torch.nn.CrossEntropyLoss with target as one-hot vectors

Solution

1. Step 1: Identify loss function for multi-class classification

   CrossEntropyLoss is designed for multi-class classification with logits.

2. Step 2: Determine correct target format

   CrossEntropyLoss expects target as class indices (integers), not one-hot vectors.

3. Final Answer:

   Use torch.nn.CrossEntropyLoss with target as class indices (0 to 3) -> Option B

4. Quick Check:

   CrossEntropyLoss + class indices = B [OK]

Hint: CrossEntropyLoss needs logits and integer class labels [OK]

Common Mistakes:

• Passing one-hot vectors as targets to CrossEntropyLoss
• Using MSELoss for classification
• Using BCELoss for multi-class without sigmoid