Learning Rewrite-Invariant Reasoning with Targeted Alternation Training

Large language models (LLMs) often fail in systematic, model-specific ways under meaning-preserving question rewrites (paraphrases, format changes, benign distractors). In this work, we address this instability by identifying where the model's reasoning process diverges across semantically-equivalent inputs. For each target LLM, we sample multiple solution traces under rewrites and aggregate them into a graph of recurring intermediate steps, which pinpoints where incorrect traces diverge from correct ones. We then generate a small set of semantics-preserving examples that mirror the rewrite patterns most responsible for these divergences, and use them to steer the model (\emph{targeted alternation training}), either via fine-tuning or via in-context learning. Across MMLU-Pro, Big-MATH, and DROP, this yields consistent gains and cross-dataset generalization. On Humanity’s Last Exam, using 200 in-context examples, it improves GPT-5.2 (xhigh) from 35.4\% to 38.1\%, demonstrating that targeted alternation training can materially improve a frontier, API-accessible closed model under realistic access constraints.

AI systems can answer a question correctly, but fail when the same question is rewritten with different wording, reordered details, simpler or harder language, or harmless extra information. This paper studies that instability and proposes a way to reduce it by testing models on equivalent versions of the same question, identifying where their reasoning first starts to go wrong, and creating focused training examples that teach them to avoid those mistakes. Across several reasoning benchmarks, this targeted approach improves accuracy and makes models more consistent under harmless rewrites.