Order-Invariant Answers, Order-Sensitive Representations in Mathematical Reasoning
Quick summary
arXiv:2609.28442v1 Announce Type: cross Abstract: Reordering a set of mathematical rules without changing its meaning should preserve the correct answer, but must a model's internal representations stay invariant too? We investigate this question using synthetic multi-step function-composition problems, each presented under multiple rule orderings with the same correct answer. We measure accuracy and permutation signal-to-noise ratio (SNR), which quantifies how distinctly ordering patterns are represented relative to variation across problem instances. Across 16 language models ranging from 1B
Key takeaways
- arXiv:2609.28442v1 Announce Type: cross Abstract: Reordering a set of mathematical rules without changing its meaning should preserve the correct answer, but must a model's internal representations stay invariant too?
- We investigate this question using synthetic multi-step function-composition problems, each presented under multiple rule orderings with the same correct answer.
- We measure accuracy and permutation signal-to-noise ratio (SNR), which quantifies how distinctly ordering patterns are represented relative to variation across problem instances.
Why it matters
“Order-Invariant Answers, Order-Sensitive Representations in Mathematical Reasoning” should be evaluated beyond branding and benchmark scores. Its practical importance will emerge in task accuracy, latency, unit cost, safety and integration with real workflows.
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