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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2605.28512 |
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| _version_ | 1866914608538714112 |
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| author | Denamganaï, Kevin Yandoka |
| author_facet | Denamganaï, Kevin Yandoka |
| contents | Self-evolving scientific agents capable of conquering the hard tail of formal mathematics require Compositional Learning Behaviours (CLBs) -- the capacity to ground and recombine novel symbolic structures in context, beyond mere recombination of prelearned atoms. We propose \textbf{S2B-LM}, an adaptation of the Symbolic Behaviour Benchmark that removes numerical processing as a confound and adds chain-of-thought scaffolding to elicit rather than merely probe latent CLB competency. Cross-evaluating ten Lean~4 theorem provers on CLB competency (adj-ZSCT) and miniF2F whole-proof performance, exact permutation tests establish a hierarchical necessity structure: search-heavy models cover the tractable bulk without detectable CLBs, yet every model breaking into the Olympiad-level tier (miniF2F $>75\%$) is among the five highest CLB scorers ($p=0.004$). After ruling out model scale as a confound, our results show that CLB competency is \emph{necessary but not sufficient} for the hard tail of formal mathematical verification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28512 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Compositional Learning Behaviours in Formal Mathematics Denamganaï, Kevin Yandoka Computation and Language Self-evolving scientific agents capable of conquering the hard tail of formal mathematics require Compositional Learning Behaviours (CLBs) -- the capacity to ground and recombine novel symbolic structures in context, beyond mere recombination of prelearned atoms. We propose \textbf{S2B-LM}, an adaptation of the Symbolic Behaviour Benchmark that removes numerical processing as a confound and adds chain-of-thought scaffolding to elicit rather than merely probe latent CLB competency. Cross-evaluating ten Lean~4 theorem provers on CLB competency (adj-ZSCT) and miniF2F whole-proof performance, exact permutation tests establish a hierarchical necessity structure: search-heavy models cover the tractable bulk without detectable CLBs, yet every model breaking into the Olympiad-level tier (miniF2F $>75\%$) is among the five highest CLB scorers ($p=0.004$). After ruling out model scale as a confound, our results show that CLB competency is \emph{necessary but not sufficient} for the hard tail of formal mathematical verification. |
| title | On Compositional Learning Behaviours in Formal Mathematics |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2605.28512 |