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    <abstract>Inference-time methods for creative LLM behaviour, from stochastic decoding to tree search to evolutionary mutation of programs or prompts, all vary the output. The problem formulation stays fixed. We introduce TROPE, an inference-time framework that operates one level of abstraction higher: an LLM parser extracts a typed structural representation of each problem (entities, typed relations, assumptions, goal, disciplinary frame), and eleven operators across three levels (token noise, conceptual mutation, conceptual crossover) edit this representation directly before the LLM generates a candidate. Operator radicality is sampled from an \ensuremathα-stable distribution calibrated by rejection sampling so the rare large reformulations that prior methods cannot produce appear at the target rate. Candidates are scored by compression gain over an evidence corpus, for which we prove a calibrated-reference bound (Proposition 3): under reference-LM calibration, noise candidates score at most zero in expectation, a property embedding-distance novelty does not inherit. Against fifteen baselines at matched generator-backbone-call budget on ten benchmarks, TROPE gains +4.3 absolute points on average (+10% relative across the nine benchmarks other than the case study; a USAMO 2025 case study at n = 6 raises the relative figure to 14%). The largest reliable math-olympiad gain over the strongest per-column baseline is on AIME 2025/26 (17.6 → 21.5, +3.9, n = 60, p \ensuremath&lt; 0.05 paired Wilcoxon). Ablations show that mutation gives the largest single-level gains on MATH-500 and AIME, while crossover is used most often on creative and discovery tasks. The typed parser matters most on structured mathematics, and compression-based novelty matters most on UoT.</abstract>
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%0 Conference Proceedings
%T TROPE: Typed Representations and Operators for Problem Editing in LLM Reasoning
%A Bikbulatov, Vadim
%A Petrosian, Ovanes
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F bikbulatov-petrosian-2026-trope
%X Inference-time methods for creative LLM behaviour, from stochastic decoding to tree search to evolutionary mutation of programs or prompts, all vary the output. The problem formulation stays fixed. We introduce TROPE, an inference-time framework that operates one level of abstraction higher: an LLM parser extracts a typed structural representation of each problem (entities, typed relations, assumptions, goal, disciplinary frame), and eleven operators across three levels (token noise, conceptual mutation, conceptual crossover) edit this representation directly before the LLM generates a candidate. Operator radicality is sampled from an \ensuremathα-stable distribution calibrated by rejection sampling so the rare large reformulations that prior methods cannot produce appear at the target rate. Candidates are scored by compression gain over an evidence corpus, for which we prove a calibrated-reference bound (Proposition 3): under reference-LM calibration, noise candidates score at most zero in expectation, a property embedding-distance novelty does not inherit. Against fifteen baselines at matched generator-backbone-call budget on ten benchmarks, TROPE gains +4.3 absolute points on average (+10% relative across the nine benchmarks other than the case study; a USAMO 2025 case study at n = 6 raises the relative figure to 14%). The largest reliable math-olympiad gain over the strongest per-column baseline is on AIME 2025/26 (17.6 → 21.5, +3.9, n = 60, p \ensuremath< 0.05 paired Wilcoxon). Ablations show that mutation gives the largest single-level gains on MATH-500 and AIME, while crossover is used most often on creative and discovery tasks. The typed parser matters most on structured mathematics, and compression-based novelty matters most on UoT.
%U https://aclanthology.org/2026.emnlp-main.773/
%P 17967-17993

Markdown (Informal)

[TROPE: Typed Representations and Operators for Problem Editing in LLM Reasoning](https://aclanthology.org/2026.emnlp-main.773/) (Bikbulatov & Petrosian, EMNLP 2026)

• TROPE: Typed Representations and Operators for Problem Editing in LLM Reasoning (Bikbulatov & Petrosian, EMNLP 2026)

ACL

• Vadim Bikbulatov and Ovanes Petrosian. 2026. TROPE: Typed Representations and Operators for Problem Editing in LLM Reasoning. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 17967–17993, Budapest, Hungary. Association for Computational Linguistics.