Axiom reversion
Definition
Axiom reversion is the teaching label used here when a response substitutes a familiar theorem or formula for the one specified in the problem.
Explanation
Suppose the claim is 5 + 9 + 13 + … + (4n + 1) = n(2n + 3), for integers n ≥ 1. If a proof substitutes n(n + 1)/2, it has switched to the formula for a different sum.
At n = 2, the stated sum is 14, while the substituted formula gives 3. That counterexample exposes the mismatch. The next step is to find where the proof introduced the other formula and compare it with the inductive hypothesis.
This identifies what went wrong in the text. Familiarity with a standard formula is a possible explanation, but the response alone does not establish what the model saw during training.
Scope and evidence
This is one of three error labels used in the teaching materials. The labels are examples for instruction, rather than an exhaustive or validated taxonomy of LLM errors.
Sources
Related concepts
Axiomatic replacement · Hallucination autopsy procedure · Invalid syntactic shortcut