Why Similarity search and retrieval in Prompt Engineering / GenAI? - Purpose & Use Cases

The Big Idea

What if your computer could instantly find anything that looks or feels like your favorite thing, saving you hours of searching?

The Scenario

Imagine you have thousands of photos on your phone and want to find all pictures that look like your favorite sunset photo. Trying to look through each photo one by one is tiring and takes forever.

The Problem

Manually checking each photo is slow and easy to make mistakes. You might miss some similar photos or spend hours scrolling. It's like finding a needle in a haystack without any help.

The Solution

Similarity search and retrieval lets computers quickly find items that look or feel alike by comparing their features. Instead of checking every photo, the computer uses smart math to find the closest matches fast and accurately.

Before vs After

✗ Before

for photo in all_photos:
    if looks_similar(photo, favorite_photo):
        print(photo)

✓ After

similar_photos = search_similar(favorite_photo, all_photos)
print(similar_photos)

What It Enables

This concept makes it easy to find related items instantly, unlocking powerful tools like personalized recommendations, fast image search, and smart document retrieval.

Real Life Example

Online shopping sites use similarity search to show you products that look like the one you clicked on, helping you find styles you love without endless browsing.

Key Takeaways

Manually searching for similar items is slow and error-prone.

Similarity search uses smart comparisons to find close matches quickly.

This enables fast, accurate retrieval in images, text, and more.

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