Similarity search and retrieval in Prompt Engineering / GenAI - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

What is the main purpose of similarity search in AI?

Imagine you have a large photo album and want to find pictures that look like a specific photo. What does similarity search do in this context?

A It finds photos that are exactly the same as the given photo.

B It finds photos that share similar features or patterns with the given photo.

C It sorts all photos by their file size.

D It deletes photos that are not similar to the given photo.

💡 Hint

Think about how you find things that look alike, not exactly the same.

Similarity search helps find items that share common features or patterns, not just exact copies.

❓ Predict Output

intermediate

Output of cosine similarity calculation

What is the output of this cosine similarity calculation between vectors A and B?

Prompt Engineering / GenAI

import numpy as np
A = np.array([1, 2, 3])
B = np.array([4, 5, 6])
cos_sim = np.dot(A, B) / (np.linalg.norm(A) * np.linalg.norm(B))
print(round(cos_sim, 2))

A 0.97

B 1.00

C 0.87

D 0.75

💡 Hint

Recall cosine similarity formula and calculate dot product and norms carefully.

Cosine similarity measures the angle between two vectors; here it is approximately 0.87.

❓ Model Choice

advanced

Best model type for similarity search on text data

You want to build a system that finds similar sentences in a large document collection. Which model type is best suited for this task?

A K-means clustering on raw text tokens

B Recurrent Neural Network (RNN) trained for language modeling

C Convolutional Neural Network (CNN) trained for image classification

D Transformer-based model producing sentence embeddings

💡 Hint

Think about models that create meaningful vector representations of sentences.

Transformer models like BERT create embeddings that capture sentence meaning, ideal for similarity search.

❓ Metrics

advanced

Choosing the right metric for nearest neighbor search

Which distance metric is most appropriate for measuring similarity between high-dimensional dense vectors from a neural network embedding?

A Cosine similarity

B Manhattan distance

C Euclidean distance

D Hamming distance

💡 Hint

Consider which metric focuses on the angle between vectors rather than magnitude.

Cosine similarity measures the angle between vectors, which is effective for high-dimensional embeddings.

🔧 Debug

expert

Debugging a similarity search code snippet

What error does this code raise when trying to compute similarity between two lists of different lengths?

Prompt Engineering / GenAI

def jaccard_similarity(list1, list2):
    intersection = len(set(list1) & set(list2))
    union = len(set(list1) | set(list2))
    return intersection / union

result = jaccard_similarity([1, 2, 3], [1, 2])
print(result)

A No error, output is 0.67

B TypeError

C ZeroDivisionError

D IndexError

💡 Hint

Check how sets handle different length lists and the division operation.

The code correctly computes Jaccard similarity without error even if lists differ in length.

Practice

1.

What is the main goal of similarity search in machine learning?

easy

A. To count the number of items in a dataset

B. To sort items alphabetically

C. To find items that are close or alike in a collection

D. To remove duplicate items from a list

Solution

1. Step 1: Understand the purpose of similarity search

   Similarity search is used to find items that are similar or close to each other in a dataset.

2. Step 2: Compare options with the definition

   Only To find items that are close or alike in a collection describes finding similar or close items, which matches the goal of similarity search.

3. Final Answer:

   To find items that are close or alike in a collection -> Option C

4. Quick Check:

   Similarity search = find similar items [OK]

Hint: Similarity search finds close or alike items [OK]

Common Mistakes:

• Confusing similarity search with sorting
• Thinking similarity search counts items
• Assuming it removes duplicates

2.

Which of the following is the correct way to compute cosine similarity between two vectors A and B in Python using numpy?

import numpy as np
A = np.array([1, 2, 3])
B = np.array([4, 5, 6])
# What code computes cosine similarity?

easy

A. np.dot(A, B) * (np.linalg.norm(A) + np.linalg.norm(B))

B. np.dot(A, B) / (np.linalg.norm(A) - np.linalg.norm(B))

C. np.sum(A * B) / (np.linalg.norm(A) - np.linalg.norm(B))

D. np.dot(A, B) / (np.linalg.norm(A) * np.linalg.norm(B))

Solution

1. Step 1: Recall cosine similarity formula

   Cosine similarity = dot product of A and B divided by product of their norms.

2. Step 2: Match formula to code options

   np.dot(A, B) / (np.linalg.norm(A) * np.linalg.norm(B)) matches the formula exactly: np.dot(A, B) / (np.linalg.norm(A) * np.linalg.norm(B)).

3. Final Answer:

   np.dot(A, B) / (np.linalg.norm(A) * np.linalg.norm(B)) -> Option D

4. Quick Check:

   Cosine similarity = dot / (norm A * norm B) [OK]

Hint: Cosine similarity = dot product divided by norms product [OK]

Common Mistakes:

• Adding norms instead of multiplying
• Subtracting norms in denominator
• Multiplying dot product by sum of norms

3.

Given the following vectors, what is the cosine similarity between vec1 and vec2?

import numpy as np
vec1 = np.array([1, 0, 0])
vec2 = np.array([0, 1, 0])
cos_sim = np.dot(vec1, vec2) / (np.linalg.norm(vec1) * np.linalg.norm(vec2))
print("{:.2f}".format(cos_sim))

medium

A. 0.00

B. 0.50

C. -1.00

D. 1.00

Solution

1. Step 1: Calculate dot product of vec1 and vec2

   Dot product = 1*0 + 0*1 + 0*0 = 0.

2. Step 2: Calculate norms and cosine similarity

   Norm of vec1 = 1, norm of vec2 = 1, so cosine similarity = 0 / (1*1) = 0.

3. Final Answer:

   0.00 -> Option A

4. Quick Check:

   Orthogonal vectors have cosine similarity 0 [OK]

Hint: Orthogonal vectors have cosine similarity zero [OK]

Common Mistakes:

• Confusing dot product with cosine similarity
• Forgetting to divide by norms
• Rounding errors causing wrong answer

4.

Consider this code snippet for similarity search. What is the error?

import numpy as np
vectors = [np.array([1, 2]), np.array([3, 4])]
query = np.array([1, 0])
scores = []
for v in vectors:
    score = np.dot(query, v) / np.linalg.norm(query) * np.linalg.norm(v)
    scores.append(score)
print(scores)

medium

A. Missing parentheses causing wrong order of operations

B. Using np.dot instead of np.cross

C. Vectors have different lengths

D. Query vector is not normalized

Solution

1. Step 1: Analyze the cosine similarity formula in code

   The formula should divide dot product by product of norms: dot(query, v) / (norm(query) * norm(v)).

2. Step 2: Identify missing parentheses

   Code does np.dot(query, v) / np.linalg.norm(query) * np.linalg.norm(v), which computes division then multiplication separately, causing wrong result.

3. Final Answer:

   Missing parentheses causing wrong order of operations -> Option A

4. Quick Check:

   Use parentheses to group denominator multiplication [OK]

Hint: Use parentheses to group denominator in cosine similarity [OK]

Common Mistakes:

• Forgetting parentheses around denominator
• Using cross product instead of dot product
• Ignoring vector length mismatch

5.

You have a collection of text documents converted into vectors. You want to find the top 2 most similar documents to a new query vector using cosine similarity. Which approach is best?

1. Compute cosine similarity between query and each document vector.
2. Sort documents by similarity score descending.
3. Return top 2 documents.

Which code snippet correctly implements this?

import numpy as np

docs = [np.array([1, 0]), np.array([0, 1]), np.array([1, 1])]
query = np.array([1, 0])

# Choose the correct code:

hard

A. scores = [np.dot(query, d) * np.linalg.norm(query) * np.linalg.norm(d) for d in docs]
top2 = sorted(scores)[:2]
print(top2)

B. scores = [np.dot(query, d) / (np.linalg.norm(query) * np.linalg.norm(d)) for d in docs]
top2 = sorted(range(len(scores)), key=lambda i: scores[i], reverse=True)[:2]
print(top2)

C. scores = [np.dot(query, d) / (np.linalg.norm(query) - np.linalg.norm(d)) for d in docs]
top2 = sorted(range(len(scores)), key=lambda i: scores[i])[:2]
print(top2)

D. scores = [np.cross(query, d) / (np.linalg.norm(query) * np.linalg.norm(d)) for d in docs]
top2 = sorted(range(len(scores)), key=lambda i: scores[i], reverse=True)[:2]
print(top2)

Solution

1. Step 1: Compute cosine similarity correctly

   scores = [np.dot(query, d) / (np.linalg.norm(query) * np.linalg.norm(d)) for d in docs] top2 = sorted(range(len(scores)), key=lambda i: scores[i], reverse=True)[:2] print(top2) computes cosine similarity as dot product divided by product of norms, which is correct.

2. Step 2: Sort indices by similarity descending and select top 2

   scores = [np.dot(query, d) / (np.linalg.norm(query) * np.linalg.norm(d)) for d in docs] top2 = sorted(range(len(scores)), key=lambda i: scores[i], reverse=True)[:2] print(top2) sorts indices by scores descending and selects top 2, matching the requirement.

3. Final Answer:

   scores = [np.dot(query, d) / (np.linalg.norm(query) * np.linalg.norm(d)) for d in docs] top2 = sorted(range(len(scores)), key=lambda i: scores[i], reverse=True)[:2] print(top2) -> Option B

4. Quick Check:

   Cosine similarity + sort descending + top 2 = scores = [np.dot(query, d) / (np.linalg.norm(query) * np.linalg.norm(d)) for d in docs] top2 = sorted(range(len(scores)), key=lambda i: scores[i], reverse=True)[:2] print(top2) [OK]

Hint: Compute cosine similarity, sort descending, pick top results [OK]

Common Mistakes:

• Multiplying norms instead of dividing
• Using cross product instead of dot product
• Sorting ascending instead of descending