---
license: apache-2.0
base_model: Qwen/Qwen3-Embedding-0.6B
library_name: sentence-transformers
pipeline_tag: sentence-similarity
tags: [lean4, mathlib, retrieval, premise-selection]
---

# hpsearch-embed-fast

The query side of [hpsearch](https://github.com/humanfia/hpsearch)'s mode `fast` for proof states and Lean
expressions: the first 8 layers of Qwen3-Embedding-0.6B and a linear map to 2,560 dimensions, trained so that a
query lands next to the [`hmzprover/hpsearch-embed-4b-v2`](https://huggingface.co/hmzprover/hpsearch-embed-4b-v2)
vectors of what it asks for (documents keep their hpsearch-embed-4b-v2 vectors; `pairs_with` names it). About
3 ms per query on an A100 with CUDA-graph replay.

Queries: a proof state (prompt `Instruct: Given a Lean 4 proof state, retrieve Mathlib lemmas that help prove its
goal\nQuery: `, goal first), its goal alone, or a Lean expression (a statement's conclusion or Pi type; prompt
`Instruct: Given Lean 4 code, retrieve the Mathlib declaration it states or names\nQuery: `). Full softmax over the
frozen document vectors, plus distillation (KL over the documents) from hpsearch-embed-4b-v2's own query side on
expressions. Lean expressions come from the training corpora's own statements (no evaluation gold among them).

## Training data

Public training splits only:
- LeanDojo Benchmark 4 (v10) `random/train`: each traced tactic's state paired with the premises it uses;
- LeanStateSearch (`ruc-ai4math/mathlib_handler_benchmark_410`) `random/train`, the same way.
For part of the states, a one-to-three-sentence English description of the next step (written by an LLM from
the state and the tactic) follows the state, as in Lean Finder's "augmented" proof states.

Decontamination (strict): a state is dropped when its theorem is in a held-out split or is the theorem of any
evaluation query, when its text equals any evaluation query, or when its goal equals the goal of any
proof-state evaluation query; a premise is dropped when its name or statement is a gold of any evaluation
(MathlibQR/MPR, Lean Finder, LeanStateSearch, TBPS, TheoremSearch, MIRB, LeanDojo, hpsearch's own); such
premises are also left out of the contrastive softmax. Kept: 147,412 states
(89,719 LeanDojo, 57,693 LeanStateSearch), 89,298 premises.