Word similarity and analogies in NLP - Model Pipeline Trace

Model Pipeline - Word similarity and analogies

This pipeline learns word meanings by looking at many sentences. It then finds how similar words are or solves analogies like 'king is to queen as man is to ?'.

Data Flow - 4 Stages

1Raw Text Data

10000 sentences x variable length→Collect sentences from books and articles→10000 sentences x variable length

"The cat sat on the mat."

↓

2Tokenization

10000 sentences x variable length→Split sentences into words→10000 sentences x variable length (words)

["The", "cat", "sat", "on", "the", "mat"]

↓

3Build Vocabulary

Words from all sentences→Create list of unique words→5000 unique words

["the", "cat", "sat", "on", "mat", "dog", "king", "queen"]

↓

4Word Embedding Training

Sentences with words→Train model to learn word vectors (e.g., Word2Vec)→5000 words x 100 features

"king" vector: [0.25, -0.1, 0.4, ..., 0.05]

Training Trace - Epoch by Epoch

2.5 | *
2.0 |  *
1.5 |   *
1.0 |    *
0.5 |     *
    +------------
     1 2 3 4 5 Epochs

Epoch	Loss ↓	Accuracy ↑	Observation
1	2.3	N/A	Initial training with high loss as model starts learning word contexts
2	1.8	N/A	Loss decreases as word vectors improve
3	1.5	N/A	Model captures better word relationships
4	1.3	N/A	Loss continues to decrease steadily
5	1.2	N/A	Training converges with stable loss

Prediction Trace - 4 Layers

Layer 1: Input word pair vectors

Layer 2: Vector arithmetic for analogy

Layer 3: Find closest word vector

Layer 4: Compute similarity scores

Model Quiz - 3 Questions

What does the vector arithmetic 'queen - king + man' aim to find?

A The word 'king'

B A random word

C A word similar to 'woman'

D The word 'queen'

Key Insight

Word embeddings capture meanings by placing similar words close in space. Vector math on these embeddings can solve analogies, showing how machines learn language relationships.

Practice

1. What does word similarity measure in natural language processing?

easy

A. How close two words are in meaning using numbers

B. How often two words appear together in a sentence

C. The length difference between two words

D. The number of letters two words share

Solution

1. Step 1: Understand the concept of word similarity

   Word similarity measures how close two words are in meaning, often represented by a number like cosine similarity.

2. Step 2: Differentiate from other word properties

   Frequency or letter count does not capture meaning closeness, so those options are incorrect.

3. Final Answer:

   How close two words are in meaning using numbers -> Option A

4. Quick Check:

   Word similarity = meaning closeness [OK]

Hint: Similarity means meaning closeness, not letter or frequency count [OK]

Common Mistakes:

• Confusing similarity with word frequency
• Thinking similarity is about word length
• Assuming similarity counts shared letters

2. Which of the following is the correct way to find the cosine similarity between two word vectors vec1 and vec2 in Python using NumPy?

easy

A. np.dot(vec1, vec2) / (np.linalg.norm(vec1) * np.linalg.norm(vec2))

B. np.dot(vec1, vec2) * (np.linalg.norm(vec1) + np.linalg.norm(vec2))

C. np.dot(vec1, vec2) - (np.linalg.norm(vec1) * np.linalg.norm(vec2))

D. np.dot(vec1, vec2) / (np.linalg.norm(vec1) + np.linalg.norm(vec2))

Solution

1. Step 1: Recall cosine similarity formula

   Cosine similarity = dot product of vectors divided by product of their norms.

2. Step 2: Match formula to code

   np.dot(vec1, vec2) / (np.linalg.norm(vec1) * np.linalg.norm(vec2)) matches the formula exactly using np.dot and np.linalg.norm.

3. Final Answer:

   np.dot(vec1, vec2) / (np.linalg.norm(vec1) * np.linalg.norm(vec2)) -> Option A

4. Quick Check:

   Cosine similarity = dot / (norm1 * norm2) [OK]

Hint: Cosine similarity divides dot product by product of norms [OK]

Common Mistakes:

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

3. Given the following word vectors:

king = [0.5, 0.8, 0.3]
queen = [0.45, 0.75, 0.35]
man = [0.6, 0.7, 0.2]
woman = [0.55, 0.65, 0.25]

What is the closest word to the vector king - man + woman?

medium

A. king

B. man

C. queen

D. woman

Solution

1. Step 1: Calculate the vector for king - man + woman

   Subtract man from king: [0.5-0.6, 0.8-0.7, 0.3-0.2] = [-0.1, 0.1, 0.1]. Add woman: [-0.1+0.55, 0.1+0.65, 0.1+0.25] = [0.45, 0.75, 0.35].

2. Step 2: Compare result to known vectors

   The resulting vector matches queen exactly: [0.45, 0.75, 0.35].

3. Final Answer:

   queen -> Option C

4. Quick Check:

   king - man + woman = queen [OK]

Hint: king - man + woman equals queen vector [OK]

Common Mistakes:

• Not subtracting man vector before adding woman
• Mixing up vector addition order
• Choosing original words instead of analogy result

4. The following code tries to find the word most similar to king - man + woman but has a flaw:

import numpy as np
words = {'king': np.array([0.5, 0.8, 0.3]), 'queen': np.array([0.45, 0.75, 0.35]), 'man': np.array([0.6, 0.7, 0.2]), 'woman': np.array([0.55, 0.65, 0.25])}
result = words['king'] - words['man'] + words['woman']
max_word = None
max_sim = -1
for word, vec in words.items():
    sim = np.dot(result, vec) / (np.linalg.norm(result) * np.linalg.norm(vec))
    if sim > max_sim:
        max_word = word
print(max_word)

What is the main flaw?

medium

A. The variable max_sim is initialized incorrectly

B. Division by zero occurs due to zero vector norm

C. The dot product is computed without normalizing vectors

D. The code does not exclude the original words from similarity search

Solution

1. Step 1: Analyze the similarity search loop

   The loop compares the result vector to all words including 'king', 'man', and 'woman' which are part of the calculation.

2. Step 2: Understand why this is problematic

   Including original words can cause the highest similarity to be the input words themselves, which is usually unwanted and can cause misleading results.

3. Final Answer:

   The code does not exclude the original words from similarity search -> Option D

4. Quick Check:

   Exclude input words to avoid bias [OK]

Hint: Exclude input words from similarity search to avoid bias [OK]

Common Mistakes:

• Assuming zero division error without checking norms
• Thinking max_sim initialization causes error
• Ignoring normalization in dot product

5. You want to find the word that fits the analogy: Paris is to France as Tokyo is to ? Using pre-trained word vectors, which approach is best to find the answer?

hard

A. Calculate vector: France - Tokyo + Paris, then find closest word vector

B. Calculate vector: Tokyo - Paris + France, then find closest word vector

C. Calculate vector: Paris + France - Tokyo, then find closest word vector

D. Calculate vector: Tokyo + Paris - France, then find closest word vector

Solution

1. Step 1: Understand analogy vector arithmetic

   Analogies use the formula: word2 - word1 + word3 to find the missing word. Here, Paris is word1, France is word2, Tokyo is word3.

2. Step 2: Apply formula to this analogy

   Calculate Tokyo - Paris + France to get the vector representing the answer.

3. Final Answer:

   Calculate vector: Tokyo - Paris + France, then find closest word vector -> Option B

4. Quick Check:

   Analogy vector = word3 - word1 + word2 [OK]

Hint: Use analogy formula: word3 - word1 + word2 [OK]

Common Mistakes:

• Swapping order of subtraction and addition
• Adding all vectors without subtraction
• Using wrong words in formula