aiqbench analysis
The paper tackles a concrete bottleneck in LLM-based theorem proving: retrieving the right lemmas from a corpus of hundreds of thousands of candidates, where current neural selectors favor frequently used foundational results. Its approach adds dependency structure to training data and model design, and reports a large gain in mean Recall@32 on Mathlib4 with claimed persistence on out-of-distribution benchmarks. The results are benchmark-specific, and the downstream theorem-proving gains on miniF2F and IMO-ProofBench are the claims readers should check most closely.
DAPS: Dependency-Aware Premise Selection for LLM Theorem Proving
arXiv:2610.41536v1 Announce Type: cross Abstract: LLM-based theorem proving in Lean 4 has advanced rapidly, but provers are difficult to leverage newly contributed lemmas, because retrieval skews toward popular foundational lemmas, leaving the right premises buried among hundreds of thousands of candidates. Existing neural selectors rank candidates by semantic similarity, with three intrinsic limitations: frequency-skewed retrieval, isolated pairwise ranking, and degradation on out-of-distribution queries such as competition problems and informal language. Given that mathematics is structured by dependencies rather than similarities, we restore this signal to both the training data and the model. We curate two underused dependency resources. We conduct the first systematic mining of 53 Lean Blueprint projects, a previously untapped corpus of 3,805 manually curated informal+formal nodes that capture rare, research-level premises absent from Mathlib4. We further pair it with the extraction of comprehensive, typed, multi-level Mathlib4 dependencies. We then introduce DAPS, a dependency-aware premise selector with a structural neighborhood encoder, a group-level contrastive objective, and a Mathlib-then-Blueprint adaptation procedure. DAPS reaches mean Recall@32 of 89.25 on Mathlib4-Heldout (+11.41 over the strong selector LeanHammer), and maintains this lead on two out-of-distribution benchmarks. Further experiments demonstrate that DAPS premises improve theorem proving on miniF2F and IMO-ProofBench. Project page: https://daps-eth.github.io/.
Abstract:LLM-based theorem proving in Lean 4 has advanced rapidly, but provers are difficult to leverage newly contributed lemmas, because retrieval skews toward popular foundational lemmas, leaving the right premises buried among hundreds of thousands of candidates. Existing neural selectors rank candidates by semantic similarity, with three intrinsic limitations: frequency-skewed retrieval, isolated pairwise ranking, and degradation on out-of-distribution queries such as competition problems and informal language. Given that mathematics is structured by dependencies rather than similarities, we restore this signal to both the training data and the model. We curate two underused dependency resources. We conduct the first systematic mining of 53 Lean Blueprint projects, a previously untapped corpus of 3,805 manually curated informal+formal nodes that capture rare, research-level premises absent from Mathlib4. We further pair it with the extraction of comprehensive, typed, multi-level Mathlib4 dependencies. We then introduce DAPS, a dependency-aware premise selector with a structural neighborhood encoder, a group-level contrastive objective, and a Mathlib-then-Blueprint adaptation procedure. DAPS reaches mean Recall@32 of 89.25 on Mathlib4-Heldout (+11.41 over the strong selector LeanHammer), and maintains this lead on two out-of-distribution benchmarks. Further experiments demonstrate that DAPS premises improve theorem proving on miniF2F and IMO-ProofBench. Project page: this https URL.
Logic in Computer Science (cs.LO); Computation and Language (cs.CL); Machine Learning (cs.LG)
arXiv:2610.41536 [cs.LO]
(or arXiv:2610.41536v1 [cs.LO] for this version)
https://doi.org/10.48550/arXiv.2610.41536 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 300 words