“Math is hard” — if you are an LLM – and why that matters

Claims from this post (5)

In the order they appear in the post. Each quotation is the speaker’s words in this post. A label such as “Supported” or “Can’t be checked” is the claim’s current assessment; its page has the evidence and the reasons.

1. Assessment: Can’t be checkedSaid 2023-10-19

   “The paper turns out to be pretty great, doing exactly the right test, but it doesn’t prove what its title alleges.”

   What we tested: The MathGLM paper does not prove its titular claim that GPT can solve mathematical problems without a calculator.

2. Assessment: Can’t be checkedSaid 2023-10-19

   “And 70% would be great for free throws; for multiplication it sucks.”

   What we tested: Around 70% accuracy is unacceptable for multiplication, which requires exact answers.

3. Assessment: UnresolvedSaid 2023-10-19

   “The LLM never induces such an algorithm.”

   What we tested: The LLM does not induce an algorithm that actually computes multiplication.

4. Assessment: Can’t be checkedSaid 2023-10-19

   “Some kind of hybrid may well work, but LLMs on their own remain stuck.”

   What we tested: Some kind of hybrid system may well succeed at reliable math where pure LLMs fail.

5. Assessment: Can’t be checkedSaid 2023-10-19

   “That, in a nutshell, is why we should never trust pure LLMs; even under carefully controlled circumstances with massive amounts of directly relevant data, they still never really get even the most basic linear functions.”

   What we tested: Pure LLMs should never be trusted.

Held from this post (4)

These records did not pass every check, so nothing about them is published. Held is not a finding.

• The record does not meet the current rules. Our reading, not assessed: LLMs on their own remain stuck, unable to reliably learn abstractions like multiplication.
• The two reviews reached different assessments. Our reading, not assessed: MathGLM's performance steadily declines as the problems get bigger, with its gap to a calculator steadily increasing, and the LLM-based system generalizes by similarity, doing better on cases in or near the training set and never, ever getting to a complete, abstract, reliable representation of what multiplication is.
• The criteria are ambiguous. Our reading, not assessed: Even with controlled conditions and massive relevant data, pure LLMs never truly learn even the most basic linear functions.
• The record does not meet the current rules. Our reading, not assessed: The weakness of neural networks in learning abstract, similarity-independent rules, identified in the early 1990s, still persists in current deep learning.