Large Language Models (LLMs) have transformed the world of artificial intelligence, enabling machines to generate human-like text, answer questions, and even write code. But how do they actually work? This article breaks down the key concepts behind LLMs in a way that is easy to understand, with just enough math to show how things come together.
1. How Do LLMs Understand Text?
At the heart of modern LLMs is a technology called the Transformer model, which allows the system to process words in a sentence efficiently. Unlike older models that read text word by word (like humans reading a book), Transformers analyze all words at once, figuring out relationships between them using a mechanism called self-attention.
What is Self-Attention?
Imagine you’re trying to understand the sentence:
The cat sat on the mat because it was soft.
To understand what “it” refers to, you need to connect it back to “the mat.” This is what self-attention does—it helps the model determine which words in a sentence relate to each other.
Mathematically, self-attention uses three key concepts: Queries (Q), Keys (K), and Values (V). Each word in a sentence is transformed into these three vectors using learned parameters. Then, we compute how much attention one word should pay to another.
The formula for attention is:
This means:
• We take the dot product of Query and Key vectors to get similarity scores.
• We scale them by the square root of the vector size ( 
).
• We apply the softmax function to get probability scores.
• Finally, we use these scores to weigh the Value vectors and get the final word representation.
This process allows LLMs to understand context better and focus on important words in a sentence.
2. How Do LLMs Learn Language?
Training an LLM involves showing it huge amounts of text and teaching it to predict the next word in a sentence. For example, if the model sees:
The sun is shining in the…
It should learn that the next word might be “sky” or “morning”, based on what it has seen before.
The Loss Function: How the Model Improves Itself
The model learns by comparing its predictions to real text and adjusting itself to improve accuracy. This is done using a mathematical function called cross-entropy loss, which measures how far the model’s predictions are from the actual words in the dataset.
The formula for cross-entropy loss is:
Here:
•
is the probability the model assigns to the correct word.
• The loss gets smaller as the model improves its predictions.
By repeating this process millions (or even billions) of times, the model learns to generate text that makes sense.
3. How Do LLMs Generate Text?
Once trained, an LLM can generate new sentences by predicting words one by one. This process is called autoregressive generation, meaning the model predicts a word, adds it to the sentence, and then predicts the next one.
For example, if you prompt an LLM with:
Once upon a time, a brave knight…
The model might generate:
Once upon a time, a brave knight rode through the dark forest on a quest to find the lost treasure.
Each word is chosen based on probabilities, ensuring fluent and coherent text.
4. Challenges in Training LLMs
Training large-scale models like GPT-4 or ChatGPT requires huge computing power and lots of data. Researchers have discovered important rules, known as scaling laws, that describe the best way to allocate computing resources.
A key discovery is the Chinchilla scaling law, which suggests that to get the best performance, the number of model parameters ( N ) and the dataset size ( D ) should grow proportionally to the total compute budget ( C ):
This insight has helped build more efficient models without simply making them bigger.
6. Conclusion
LLMs have transformed AI by making it possible for machines to understand and generate human-like text. The key ideas behind them include:
- Self-attention, which helps the model understand word relationships.
- Training with massive datasets, using mathematical loss functions.
- Generating text one word at a time, based on probabilities.
- Scaling laws, which guide efficient model design.
These models continue to improve and evolve, leading to exciting developments in artificial intelligence.
References
1. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Å., & Polosukhin, I. (2017). Attention Is All You Need. Advances in Neural Information Processing Systems, 30.
2. Hoffmann, J., Borgeaud, S., Mensch, A., Buchatskaya, E., Cai, T., Rutherford, E., … & Irving, G. (2022). Training Compute-Optimal Large Language Models.
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