Llama-3.1-8B solves calendar problems by doing standard base-10 addition and then converting the answer back rather than using modular math.
Models should theoretically use modular arithmetic to figure out that December plus two months is February. Instead, internal probes show the model adds 12 plus 2 to get 14 and then maps that back to the 2nd month. This counterintuitive detour shows that LLMs prefer a generic, high-frequency tool over the most efficient logic. It highlights a specific kind of internal translation that happens when models face specialized reasoning tasks. Understanding these shortcuts is vital for anyone trying to fix reasoning errors in domain-specific AI.
Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts
arXiv · 2605.01148
Does structure in representations imply structure in computation? We study how Llama-3.1-8B reasons over cyclic concepts (e.g., "what month is six months after August?"). Even though Llama-3.1-8B's representations for these concepts are circularly structured, we find that instead of directly computing modular addition in the period of the cyclic concept (e.g., 12 for months), the model re-uses a generic addition mechanism across tasks that operates independently of concept-specific geometry. Fir