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.