The Hidden World of Number Tokenization in Large Language Models

Large Language Models (LLMs) like BERT, GPT, and their variants, have achieved amazing feats in understanding and generating human language. However, they operate on tokens – discrete units of text – and not directly on the raw characters we humans see. This brings up an interesting challenge: how do these models handle numbers? The process, called number tokenization, is more nuanced than you might think and has significant impacts on how well LLMs can perform in numerical tasks.

Why is Number Tokenization Important?

Numbers are crucial in everyday language and many specialized domains. Consider scenarios like:

Mathematical Reasoning: Solving arithmetic or algebraic problems.
Data Analysis: Processing statistical information or financial data.
Time and Dates: Managing schedules, calendars, and historical records.
Measurements: Interpreting scientific data or engineering specifications.

If numbers aren’t tokenized effectively, models can struggle with these kinds of tasks. A model might see “123” and “12345” as having no specific relationship with each other, which is not the same as a human would. This limits the ability to reason and perform mathematical operations.

How Do LLMs Tokenize Numbers?

LLMs use subword tokenization techniques (like Byte-Pair Encoding or WordPiece). These techniques don’t simply treat a whole number as a single token. Here’s a breakdown:

Digit Splitting: Multi-digit numbers are often split into individual digits. For example, “1234” might be broken down into “1”, “2”, “3”, and “4”. Each digit becomes an independent token.
Subword Combinations: Sometimes, common sequences of digits could be combined into tokens if they are frequent in the training data. E.g., if “20” is common in a dataset “20” might be tokenized together as a singular token.
Special Tokens: The models may have special tokens for handling decimal points, commas, or other numeric related characters.
Context Matters: How a number is tokenized might also depend on the surrounding text, as LLMs consider the whole context.

The Implications

This approach of tokenizing numbers as individual digits or digit groupings has several consequences:

Increased Sequence Length: Long numbers require multiple tokens, which can increase sequence length and computation cost.
Lack of Semantic Meaning: The model may not fully understand the overall value of the number. 1, 2, 3 can be seen as independent from 123.
Difficulty in Arithmetic Operations: Processing numerical computations becomes complex because the model must learn relationships between individual digit tokens.

Common Tokenization Strategies & Examples

Let’s examine some practical examples of how tokenizers handle numbers with some Python code snippets.

from transformers import AutoTokenizer

def tokenize_and_show(text, tokenizer_name="bert-base-uncased"):
    tokenizer = AutoTokenizer.from_pretrained(tokenizer_name)
        tokens = tokenizer.tokenize(text)
            print(f"Text: '{text}'")
                print(f"Tokens: {tokens}")
                    token_ids = tokenizer.convert_tokens_to_ids(tokens)
                        print(f"Token IDs: {token_ids}")

                        print("BERT Tokenizer Examples:")
                        tokenize_and_show("The price is $123.45", "bert-base-uncased")
                        tokenize_and_show("The year is 2024.", "bert-base-uncased")
                        tokenize_and_show("Pi is approximately 3.14159", "bert-base-uncased")

                        print("\nGPT-2 Tokenizer Examples:")
                        tokenize_and_show("The price is $123.45", "gpt2")
                        tokenize_and_show("The year is 2024.", "gpt2")
                        tokenize_and_show("Pi is approximately 3.14159", "gpt2")

                        print("\nBART Tokenizer Examples:")
                        tokenize_and_show("The price is $123.45", "facebook/bart-base")
                        tokenize_and_show("The year is 2024.", "facebook/bart-base")
                        tokenize_and_show("Pi is approximately 3.14159", "facebook/bart-base")

Note: The code above requires the transformers library. You can install it using pip install transformers.

Results

BERT Tokenizer Examples:
Text: 'The price is $123.45'
Tokens: ['the', 'price', 'is', '$', '123', '.', '45']
Token IDs: [1996, 3923, 2003, 1002, 14887, 1012, 2345]
Text: 'The year is 2024.'
Tokens: ['the', 'year', 'is', '2024', '.']
Token IDs: [1996, 2095, 2003, 26590, 1012]
Text: 'Pi is approximately 3.14159'
Tokens: ['pi', 'is', 'approximately', '3', '.', '14159']
Token IDs: [12379, 2003, 10486, 1020, 1012, 22325]

GPT-2 Tokenizer Examples:
Text: 'The price is $123.45'
Tokens: ['The', 'Ġprice', 'Ġis', 'Ġ$', '123', '.', '45']
Token IDs: [464, 3518, 318, 502, 1251, 13, 1048]
Text: 'The year is 2024.'
Tokens: ['The', 'Ġyear', 'Ġis', 'Ġ2024', '.']
Token IDs: [464, 1380, 318, 14527, 13]
Text: 'Pi is approximately 3.14159'
Tokens: ['Pi', 'Ġis', 'Ġapproximately', 'Ġ3', '.', '14159']
Token IDs: [35301, 318, 11405, 383, 13, 47311]

BART Tokenizer Examples:
Text: 'The price is $123.45'
Tokens: ['The', 'Ġprice', 'Ġis', 'Ġ$', '123', '.', '45']
Token IDs: [464, 728, 16, 754, 1503, 4, 568]
Text: 'The year is 2024.'
Tokens: ['The', 'Ġyear', 'Ġis', 'Ġ2024', '.']
Token IDs: [464, 1030, 16, 14201, 4]
Text: 'Pi is approximately 3.14159'
Tokens: ['Pi', 'Ġis', 'Ġapproximately', 'Ġ3', '.', '14159']
Token IDs: [19693, 16, 3673, 69, 4, 31710]

You can observe that different tokenizers produce varying tokenizations. BERT’s tokenizer handles dollar amounts by keeping them together. The other tokenizers break it down into components. Similarly, each tokenizer breaks down the decimal number differently, sometimes having the digits together, and others seperating them.

Challenges and Future Directions

Effective number tokenization is still an area of active research. Some challenges and potential areas for improvement are:

Robust Handling of Different Number Formats: LLMs need to understand different notations and formats (e.g., scientific notation, currency symbols).
Arithmetic Reasoning: Models should be better at reasoning and performing calculations with numbers in text.
Domain Specific Considerations: Different domains might need unique methods for handling specialized numbers (e.g., gene sequences, addresses, and phone numbers).

Solutions include exploring better tokenization algorithms that can more effectively represent numbers, training strategies tailored for numerical data, and incorporating specialized arithmetic reasoning modules.

Conclusion

Number tokenization is a critical but often overlooked part of how Large Language Models understand and process text. How numbers are broken down into tokens significantly impacts the performance of LLMs, especially in tasks that require reasoning with numbers. While existing models have done well at natural language processing, continuing research in tokenization methods will only make their ability to understand and work with numbers more powerful.

By being aware of these underlying processes, both developers and users of LLMs can better understand the capabilities and limitations of these powerful tools when dealing with numbers.