Word embeddings and where models go wrong

A word embedding is a list of numbers that stands for a word, set so that words with similar meanings sit close together. Language models are built on embeddings, and knowing how they work also shows where those models go wrong.

This lesson uses tiny invented vectors you can follow by hand. Real ones have hundreds of numbers.

A bag of words sees "essay" and "revision" as two unrelated words. Yet they are used in the same places: near "deadline", "library" and "lecture".

An embedding gives each word a vector, and training moves words used in the same context close together. Nearness is measured with the cosine you already know.

docker exec jupyter python3 -c "import math; print(round(73/(math.sqrt(83)*math.sqrt(65)),3))"

docker exec jupyter python3 -c "import math; print(round(12/(math.sqrt(83)*math.sqrt(90)),3))"

import math

words = {"lunch": [1, 1, 9], "sandwich": [0, 1, 8], "report": [9, 3, 0]}

def cosine(a, b):
    top = 0
    for n in range(len(a)):
        top = top + a[n] * b[n]
    return top / (math.sqrt(sum(x * x for x in a)) * math.sqrt(sum(x * x for x in b)))

for other in ["sandwich", "report"]:
    print("lunch and", other, round(cosine(words["lunch"], words[other]), 3))
# Add "coffee": [2, 0, 7] to the dictionary and to the loop.

One word can mean different things. "Bank" is a river edge in one sentence and a place for money in another.

Attention gives each word in the context a weight for the word being read. The model blends the vectors using those weights, so "bank" near "river" ends up near the river words.

A model learns from text that people wrote. If that text pairs one job with one group of people, the vectors for them end up close, and the model repeats the pairing.

This is bias. You find it by testing: swap the group in a sentence and see whether the answer changes. Ask who the training text left out.

A language model picks likely words. It has no step that checks the answer against the world. So it can write a made-up answer: a clear, confident sentence that is false, such as a reference to a report that does not exist.

Open the source yourself, redo any numbers, and keep private data out of tools your organisation has not approved.

Add four words of your own to the vector table, with three numbers each, and use the function to see which are near. Then check where your own choices of numbers were a judgement.

Write three checks you would run before using a model's answer in a report for work.