SOURCE-LINKED INTELLIGENCE

Order-Invariant Answers, Order-Sensitive Representations in Mathematical Reasoning

arXiv · AI, language, vision and robotics · article · Sep 23, 2026 · UTC

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 to 8B parameters, we find a pattern: models that

Read original source ↗ Open in workspace

recordType

paper

region

Global