Semantic similarity with embeddings in NLP - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the cosine similarity output between two embeddings?

Given two 3-dimensional embeddings:

embedding1 = [1, 0, 1]
embedding2 = [0, 1, 1]

Calculate the cosine similarity using the formula:

cosine_similarity = (A · B) / (||A|| * ||B||)

NLP

import numpy as np
embedding1 = np.array([1, 0, 1])
embedding2 = np.array([0, 1, 1])
cosine_similarity = np.dot(embedding1, embedding2) / (np.linalg.norm(embedding1) * np.linalg.norm(embedding2))
print(round(cosine_similarity, 3))

A 0.5

B 0.707

C 0.0

D 1.0

💡 Hint

Recall cosine similarity measures the angle between vectors, dot product divided by product of magnitudes.

The dot product is 1*0 + 0*1 + 1*1 = 1. The norms are sqrt(1+0+1)=sqrt(2) each. So cosine similarity = 1 / (sqrt(2)*sqrt(2)) = 1/2 = 0.5.

❓ Model Choice

intermediate

Which embedding model is best for capturing sentence-level semantic similarity?

You want to compare the meaning of full sentences, not just words. Which model is most suitable?

A Word2Vec trained on individual words

B One-hot encoding of words

C Sentence-BERT (SBERT) embeddings

D GloVe embeddings for words

💡 Hint

Consider models designed to produce embeddings for entire sentences.

Word2Vec and GloVe produce word embeddings, not sentence embeddings. One-hot encoding is sparse and does not capture semantics. Sentence-BERT is designed for sentence-level semantic similarity.

❓ Hyperparameter

advanced

Which hyperparameter affects the quality of semantic similarity in embedding training?

When training a Word2Vec model, which hyperparameter most directly influences the semantic quality of embeddings?

A Number of training epochs

B Window size (context window)

C Learning rate decay schedule

D Batch size

💡 Hint

Think about how much context the model sees around each word.

Window size controls how many neighboring words are considered context, directly affecting semantic relationships captured. Other parameters affect training speed or convergence but less directly semantic quality.

❓ Metrics

advanced

Which metric is best to evaluate semantic similarity between embeddings?

You have two sentence embeddings and want to measure how similar their meanings are. Which metric is most appropriate?

A Euclidean distance

B Jaccard similarity

C Mean squared error

D Cosine similarity

💡 Hint

Consider a metric that measures angle between vectors regardless of length.

Cosine similarity measures the angle between vectors, capturing semantic similarity well. Euclidean distance is sensitive to vector length. MSE is for regression errors. Jaccard similarity is for sets, not vectors.

🔧 Debug

expert

Why does this semantic similarity code produce a runtime error?

Code snippet:

import numpy as np
embedding1 = [0.1, 0.3, 0.5]
embedding2 = [0.2, 0.4]
cos_sim = np.dot(embedding1, embedding2) / (np.linalg.norm(embedding1) * np.linalg.norm(embedding2))
print(cos_sim)

What causes the error?

NLP

import numpy as np
embedding1 = [0.1, 0.3, 0.5]
embedding2 = [0.2, 0.4]
cos_sim = np.dot(embedding1, embedding2) / (np.linalg.norm(embedding1) * np.linalg.norm(embedding2))
print(cos_sim)

A Vectors have different lengths causing dot product error

B np.linalg.norm cannot compute norm of lists

C Division by zero due to zero norm

D np.dot requires integer inputs

💡 Hint

Check if both vectors have the same number of elements.

The dot product requires vectors of the same length. embedding1 has 3 elements, embedding2 has 2, causing a ValueError.

Practice

1. What does semantic similarity with embeddings help us do in natural language processing?

easy

A. Translate text from one language to another

B. Count the number of words in a sentence

C. Measure how similar the meanings of two texts are

D. Generate random sentences

Solution

1. Step 1: Understand semantic similarity

   Semantic similarity means checking how close the meanings of two texts are, not just the words.

2. Step 2: Role of embeddings

   Embeddings convert text into numbers that capture meaning, allowing comparison of texts by meaning.

3. Final Answer:

   Measure how similar the meanings of two texts are -> Option C

4. Quick Check:

   Semantic similarity = meaning comparison [OK]

Hint: Semantic similarity compares meanings, not word counts [OK]

Common Mistakes:

• Confusing similarity with word count
• Thinking embeddings translate text
• Assuming semantic similarity generates text

2. Which Python library is commonly used to compute cosine similarity between embeddings?

easy

A. matplotlib

B. scikit-learn

C. pandas

D. flask

Solution

1. Step 1: Identify cosine similarity function

   Cosine similarity is often computed using scikit-learn's metrics module.

2. Step 2: Check other libraries

   matplotlib is for plotting, pandas for data frames, flask for web apps, so they don't compute cosine similarity.

3. Final Answer:

   scikit-learn -> Option B

4. Quick Check:

   Cosine similarity = scikit-learn [OK]

Hint: Use scikit-learn for cosine similarity calculations [OK]

Common Mistakes:

• Using matplotlib for similarity
• Confusing pandas with similarity tools
• Thinking flask handles embeddings

3. What is the output of this Python code snippet?

from sklearn.metrics.pairwise import cosine_similarity
import numpy as np

emb1 = np.array([[1, 0, 0]])
emb2 = np.array([[0, 1, 0]])
sim = cosine_similarity(emb1, emb2)
print(sim[0][0])

medium

A. Error

B. 1.0

C. -1.0

D. 0.0

Solution

1. Step 1: Understand cosine similarity formula

   Cosine similarity measures the cosine of the angle between two vectors. Orthogonal vectors have similarity 0.

2. Step 2: Analyze given vectors

   emb1 is [1,0,0], emb2 is [0,1,0]. They are perpendicular, so similarity is 0.

3. Final Answer:

   0.0 -> Option D

4. Quick Check:

   Orthogonal vectors similarity = 0.0 [OK]

Hint: Orthogonal vectors have cosine similarity zero [OK]

Common Mistakes:

• Assuming similarity is 1 for any vectors
• Confusing dot product with cosine similarity
• Expecting error due to shape

4. Identify the error in this code that tries to compute semantic similarity:

from sklearn.metrics.pairwise import cosine_similarity

emb1 = [0.1, 0.2, 0.3]
emb2 = [0.1, 0.2, 0.3]
sim = cosine_similarity(emb1, emb2)
print(sim)

medium

A. emb1 and emb2 should be 2D arrays, not 1D lists

B. cosine_similarity function does not exist in sklearn

C. embeddings must be strings, not numbers

D. print statement syntax is incorrect

Solution

1. Step 1: Check input format for cosine_similarity

   cosine_similarity expects 2D arrays (like [[...]]), but emb1 and emb2 are 1D lists.

2. Step 2: Confirm other options

   cosine_similarity exists, embeddings are numeric vectors, and print syntax is correct in Python 3.

3. Final Answer:

   emb1 and emb2 should be 2D arrays, not 1D lists -> Option A

4. Quick Check:

   Input shape must be 2D arrays [OK]

Hint: cosine_similarity needs 2D arrays, not 1D lists [OK]

Common Mistakes:

• Passing 1D lists instead of 2D arrays
• Thinking embeddings must be text
• Misunderstanding print syntax

5. You have two sentences: "I love apples" and "I adore oranges". Using a pre-trained embedding model, you get vectors for both. Which approach best helps you find if these sentences have similar meaning?

hard

A. Calculate cosine similarity between their embeddings

B. Count common words between the sentences

C. Check if sentence lengths are equal

D. Compare the first letters of each word

Solution

1. Step 1: Understand semantic similarity goal

   We want to compare meanings, not just words or sentence length.

2. Step 2: Use embeddings and cosine similarity

   Pre-trained embeddings capture meaning; cosine similarity measures closeness of meanings numerically.

3. Final Answer:

   Calculate cosine similarity between their embeddings -> Option A

4. Quick Check:

   Meaning comparison = cosine similarity on embeddings [OK]

Hint: Use cosine similarity on embeddings for meaning comparison [OK]

Common Mistakes:

• Relying on word overlap only
• Using sentence length as similarity
• Comparing letters instead of meaning