In plain words: Zero-Error Horizon is the longest task a model solves with no mistakes, found by testing longer and longer versions until it slips. Even the strongest model fails simple jobs like checking whether 11000 has an even number of 1s or whether ((((()))))) is balanced.
Abstract · Even GPT-5.2 Can't Count to Five: The Case for Zero-Error Horizons in Trustworthy LLMs
We propose Zero-Error Horizon (ZEH) for trustworthy LLMs, which represents the maximum range that a model can solve without any errors. While ZEH itself is simple, we demonstrate that evaluating the ZEH of state-of-the-art LLMs yields abundant insights. For example, by evaluating the ZEH of GPT-5.2, we found that GPT-5.2 cannot even compute the parity of a short string like 11000, and GPT-5.2 cannot determine whether the parentheses in ((((()))))) are balanced. This is surprising given the excellent capabilities of GPT-5.2. The fact that LLMs make mistakes on such simple problems serves as an important lesson when applying LLMs to safety-critical domains. By applying ZEH to Qwen2.5 and conducting detailed analysis, we found that while ZEH correlates with accuracy, the detailed behaviors differ, and ZEH provides clues about the emergence of algorithmic capabilities. Finally, while computing ZEH incurs significant computational cost, we discuss how to mitigate this cost by achieving up to one order of magnitude speedup using tree structures and online softmax.
Ryoma Sato
arXiv:2601.15714 · cs.LG, cs.AI, cs.CL · submitted Jan 22, 2026
abstract · pdf · html
I think there is a valid insight here which many already know: LLMs are much more reliable at creating scripts and automation to do certain tasks than doing these tasks themselves.
For example if I provide an LLM my database schema and tell it to scan for redundant indexes and point out wrong naming conventions, it might do a passable but incomplete job.
But if I tell the LLM to code a python or nodejs script to do the same, I get significantly better results. And it's often faster too to generate and run the script than to let LLMs process large SQL files.