🤖 AI Summary
This work addresses the persistent challenge that large language models (LLMs) still commit errors even on fundamental tasks, lacking reliable zero-error performance guarantees and thereby limiting their deployment in safety-critical applications. To this end, the paper introduces the “Zero-Error Horizon” (ZEH)—a metric quantifying the maximum problem scope an LLM can handle without committing any errors. The authors develop a framework combining systematic zero-error testing, tree-structured accelerated search, and online Softmax optimization to substantially reduce the computational cost of ZEH evaluation. Experiments reveal that state-of-the-art models such as GPT-5.2 still fail on ostensibly simple tasks like short-string parity and bracket balancing. While ZEH correlates with overall accuracy, it provides finer-grained insight into model capabilities and achieves up to a tenfold improvement in evaluation efficiency.
📝 Abstract
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.