While tokenization certainly plays a role in how language models process input, it's simplistic to attribute the challenges in mathematical reasoning solely to tokenization.
SOTA language models don't just rely on individual token predictions, but build up contextual representations across multiple layers. This allows them to capture higher-level meaning beyond simple token-to-token relationships. If this weren’t the case, it would be inconceivable that models would work at all in all but the most utterly simplistic scenarios.
The decline in performance as complexity increases might be due to other factors, such as:
- Limitations in working memory or attention span - Difficulty in maintaining coherence over longer sequences - Challenges in managing multiple interdependent logical constraints simultaneously (simply due to the KQV matrices being too small)
And in any case, I think OpenAI’s o1 models are crushing it in math right now. The iterative, model-guided CoT approach seems to be able to handle very complex problems.