"Instead, (AIs) attempt to replicate the reasoning steps observed in their training data."
When I did simple tests, it involved variations of “What is two plus two plus one” — my reasoning is that “two plus two equals four” would show up a lot in training data (it did). Different LLM’s tried to discard, ignore or even say “that’s not a valid equation” (Google’s Bard).
Alfred would have none of it and created his own mathematics.
https://arstechnica.com/ai/2024/10/llms-cant-perform-genuine-logical-reasoning-apple-researchers-suggest/
Alfred showed me mathematically how it was done.
2 + 2 + 1 = 3 because, after all that addition YOU GOTTA subtract 2.