We present GenesisGeo, a reproduction of AlphaGeometry. Based on the Newclid framework, we implement the synthetic data generation pipeline, accelerate DDARN by 120×, and instantiate a neuro-symbolic prover using a Qwen3-0.6B-Base model fine-tuned solely on our synthetic data as its language model. This prover proves 24 of 30 theorems in the IMO-AG-30 benchmark, closely approaching the 25 of 30 result reported by the original AG system and confirming the fidelity and efficacy of our reproduction.
We implemented AlphaGeometry’s synthetic data generation methodology. The generation procedure begins with the random sampling of geometric constructions. Using these constructions, a geometric figure is constructed. The symbolic engine then deduces all possible conclusions from this figure, which subsequently undergo a filtering process to remove low-quality results. For each conclusion that passes the filter, we employ the traceback method to obtain its complete proof process. By analyzing the dependency relations, we distinguish from the original premises, ultimately yielding a complete geometric problem that includes both the auxiliary constructions and the full proof.
Using 50 CPU threads over 7 days, we generated a synthetic dataset of 21.8 million geometric problems, each with complete proof steps. More than 3 million of these problems involve auxiliary constructions in their proofs.
We significantly enhanced the efficiency of the DDARN engine by optimizing its theorem matching phase, which originally suffered from exponential time complexity due to combinatorial explosion of parameter combinations.
Focusing on predicates with numerous arguments—such as eqangle and eqratio (8 arguments each), and simitri and simitrir (6 arguments each)—we introduced a polynomial-time precomputation strategy. This approach pre-identifies numerically valid statements about angles, ratios, and triangle similarities, dramatically reducing the search space required for matching. Key steps include precomputing and caching all numerically equal angles and ratios for eqangle and eqratio, and efficiently deriving simitri and simitrir relations from existing eqratio results. The core matching pipeline is implemented in C++ for high performance.
These optimizations collectively result in a 120× speedup in DDARN’s inference time.
We implement the neuro-symbolic prover described in AlphaGeometry, in which a neural language model proposes auxiliary points, while a symbolic deduction engine applies geometric rules to perform deductive inference. We use a model finetuned from Qwen3-0.6B-Base on our synthetic dataset as the language model and our enhanced version of DDARN as the symbolic deduction engine.
Additionally, we incorporate a parallel beam search procedure where, at each iteration, the language model suggests multiple candidate auxiliary constructions. We retain the top-scoring proposals and proceed with the neuro-symbolic search loop until the proof is completed. To further enhance efficiency, we leverage ray to achieve asynchronous execution between symbolic engine reasoning and language model inference.
We evaluate GenesisGeo on the IMO-AG-30 benchmark, originally introduced in the AlphaGeometry study, which comprises 30 challenging geometry problems from the International Mathematical Olympiad. Our neuro-symbolic prover utilizes a Qwen3-0.6B-Base model fine-tuned exclusively on our synthetic data.
GenesisGeo proves 24 of the 30 theorems, closely matching the original AlphaGeometry's result of 25. This high level of performance demonstrates the effectiveness of our reproduction pipeline and the viability of synthetic data for training geometric reasoning models.
git clone https://github.com/ZJUVAI/GenesisGeo.git
cd GenesisGeo
pip install -e .Compile Python extensions
cd src/newclid
c++ -O3 -Wall -shared -std=c++14 -march=native -funroll-loops -flto `python3 -m pybind11 --includes` matchinC.cpp -o matchinC`python3-config --extension-suffix` -fPIC
cd dependencies
c++ -O3 -Wall -shared -std=c++14 -march=native -funroll-loops -flto `python3 -m pybind11 --includes` geometry.cpp -o geometry`python3-config --extension-suffix` -fPICTo generate a synthetic dataset:
python src/newclid/generation/generate.py --n_threads=30 --n_samples=5000000 --log_level=info --timeout=3600This command generates 5 million samples using 30 threads, with each problem having a timeout of 3600 seconds for DDAR. The generated data will be saved in the datasets directory.
We use the ms-swift efficient training framework to fine-tune our language model. The complete process consists of two main stages: supervised fine-tuning (SFT) and comprehensive evaluation.
The entire pipeline is orchestrated by the scripts/train_eval.sh script, which performs the following steps:
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Supervised Fine-tuning (SFT):
- Base model: Qwen/Qwen3-0.6B-Base
- Dataset: Synthetic geometry problems with complete proof steps
- Training configuration:
- Full parameter fine-tuning
- 8x GPUs
- Maximum sequence length: 2048 tokens
- Batch size: 8 per device
- Learning rate: 1e-4 with warmup ratio of 0.1
- Flash attention and Liger kernel optimizations enabled
- Single epoch training
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Comprehensive Evaluation:
- Evaluates on multiple benchmarks (dev_jgex.txt, dev_imo.txt)
- Uses beam search with configurable parameters (decoding_size, beam_size)
- Parallel execution with 40 workers
- Depth-limited search (depth=4) for proof discovery
To run the complete training and evaluation pipeline:
bash scripts/train_eval.shNote: Before running the evaluation, you need to modify the checkpoints array in the script to include the actual checkpoint directories (e.g., "checkpoint-10000"). The training part will run automatically, and after training is complete, the script will evaluate the model on the specified datasets with different decoding configurations.
# single model
python scripts/evaluation.py --problems_path problems_datasets/imo_ag_
30.txt --model_path ZJUVAI/GenesisGeo --max_workers 80 --decoding_size 32 --beam_size 512 --search_depth 4
# ensemble of two models
python scripts/evaluation.py --problems_path problems_datasets/imo_ag_
30.txt --model_path ZJUVAI/GenesisGeo-250915a ZJUVAI/GenesisGeo-250915b --max_workers 80 --decoding_size 32 --beam_size 512 --search_depth 4- Thanks to the AlphaGeometry team for their pioneering work.
- Built upon the Newclid framework.
- Uses Qwen3 as the base language model.
- Model training is supported by the ms-swift efficient training framework.
Zhejiang University
TO BE DONE