▾Why can't ChatGPT calculate? The secret of mathematical errors revealed
Artificial intelligence writes poems but struggles with math. Why can't ChatGPT and other chatbots handle even basic arithmetic? We reveal the causes of AI's mathematical mistakes, from tokenization which breaks numbers into unintelligible fragments, to the statistical learning approach that fails in mathematics.
Artificial intelligence, including ChatGPT, can write poems, compose music, and translate texts. Yet, it often stumbles on simple mathematical tasks. Why can't a chatbot, that handles complex language tasks, deal with math at an elementary school level?
Tokenization: When numbers break into pieces
One of the key problems is tokenization. This process divides data into smaller parts, called tokens. Imagine it like assembling a puzzle, where words are broken down into syllables. The tokenizer, the AI model responsible for this process, does not understand the meaning of numbers.
It may happen that the number 380 is perceived as one token, while 381 is perceived as two (38 and 1). This disrupts the relationships between digits and complicates the calculation.
A statistical machine that falters with numbers
Another reason for ChatGPT's mathematical difficulties is its statistical nature. The chatbot learns based on a vast amount of examples and looks for patterns in them. For instance, it learns that the phrase "Dear Sir" is often followed by the phrase "we are reaching out to you".
However, this approach faces challenges in mathematics. ChatGPT can guess that the product of numbers ending in 2 will end in 4, but it cannot handle intermediate results. Simply put, the ChatGPT model tries to guess the result based on learned patterns instead of performing a precise calculation.
The challenge of multiplication
A study conducted by Yuntian Deng from the University of Waterloo showed that ChatGPT struggles with multiplying numbers greater than four digits. The reason is that any error in a calculation step shows up in the final result.
Imagine it as a domino effect – one error triggers a chain reaction, and the result is completely off. However, there is hope that ChatGPT will improve in the future. Deng and his colleagues also tested the o1 model from OpenAI, which is characterized by logical reasoning capabilities.
This model achieved significantly better results than the standard GPT-4o and was able to correctly solve multiplications of nine-digit numbers. The o1 model thinks through the problem step by step, allowing for more accurate results.
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