Math Conjecture SOTA 0.5B
Math Conjecture SOTA 0.5B is a research-focused language model adapted for mathematical reasoning, conjecture analysis, proof-style generation, and formalization-aware responses. It is part of the broader Math Conjecture Training Corpus effort, which builds open-license training pipelines for unsolved conjectures, structured reasoning, competition mathematics, proof traces, and Lean-oriented theorem workflows.
This checkpoint is intended for research and experimentation around long-form mathematical reasoning rather than proof certification.
Model Details
Model description
This model is fine-tuned to produce more structured mathematical outputs, including:
- intuition-first explanations
- stepwise proof sketches
- conjecture decomposition
- theorem-style reasoning
- informal-to-formal transition hints
- Lean-aware reasoning patterns
The surrounding project supports multiple development paths including supervised fine-tuning, state-of-the-art math profiles, scratch initialization, evaluation, self-improvement data generation, adapter merge, Hub publishing, and local llama.cpp inference after conversion.
Model type
Parameter-efficient fine-tuned causal language model for math reasoning.
Hub repo
- Model repo:
NorthernTribe-Research/math-conjecture-model
- Dataset repo:
NorthernTribe-Research/math-conjecture-training-corpus
- Trainer Space repo:
NorthernTribe-Research/math_trainer
Parameter Count Visualization
| Metric | Value |
|---|
| Total parameters | 502.831M (502,830,976) |
| Trainable parameters | 8.798M (8,798,208) |
| Frozen parameters | 494.033M (494,032,768) |
| Trainable ratio | 1.7497% |
Trainable share:
[#---------------------------] 1.7497%
This checkpoint uses a parameter-efficient adaptation setup in which only a small fraction of model weights are trainable while the vast majority remain frozen. The project documentation explicitly states that training summaries record model.parameter_counts with total, trainable, frozen, and ratio fields, and that the Hub README is auto-updated with this visualization when push_to_hub is enabled.
Training Reference
- Summary source:
workspace/runs/math-conjecture-sota-050b-quick/training_summary.json
- This model card is derived from the repository README together with the latest training summary. The repo also includes a helper for refreshing the model card directly from those sources:
scripts/update_model_card.py.
Intended Uses
Direct use
This model is suitable for:
- mathematical reasoning research
- conjecture exploration demos
- proof-sketch generation
- theorem-style answer generation
- reasoning benchmark experiments
- formalization-oriented prompting
- research prototypes on Hugging Face Spaces
Downstream use
Potential downstream uses include:
- math-focused copilots
- conjecture analysis interfaces
- educational proof assistants
- formal/informal bridge systems
- evaluation pipelines for reasoning-heavy LLMs
Out-of-scope use
This model is not intended to be treated as:
- a formal theorem prover
- a replacement for proof assistants
- a certified symbolic solver
- a source of guaranteed-correct proofs
- an authoritative system for high-stakes mathematical claims
Training Data
This model is part of a larger corpus-building effort designed for training math AI systems aimed at unsolved conjecture reasoning. The v1 dataset pipeline combines local conjecture data with curated open-license Hugging Face datasets covering competition mathematics, structured reasoning, and formal proof corpora. The repository also documents broader open math sources such as:
- OpenR1-Math-220k
- FineProofs-SFT
- LeanStatement_CoT
- NuminaMath-LEAN
- DeepSeek-Prover-V1
These sources are included to improve coverage across proof traces, theorem formalization, and reasoning-heavy mathematical examples. The project documentation also emphasizes open-license, practical-size, and deterministic filtering choices in the corpus pipeline.
Training Procedure
The model-development workspace supports:
- SFT training
- SOTA math profile training
- scratch initialization
- scratch dry-runs
- self-improvement / rejection-sampling data generation
- evaluation with richer reasoning metrics
- adapter merge and Hub publish flows
The SOTA curriculum profiles responses across:
- simple
- intermediate
- advanced
- Lean-formalized bands
Evaluation capabilities
The project documentation states that the SOTA evaluation flow includes:
difficulty_band_metricsresponse_profile_metricssimple_to_leanselected_pass_at_kconsensus_rateconsensus_pass_at_k
It also supports stricter grading controls such as optional SymPy symbolic verification and substring-match controls.
Self-improvement flow
The repository includes a rejection-sampling data-generation path via generate_rft_data.py, used to create self-improvement training data from model outputs.
Project Architecture
The wider project includes:
- merged dataset construction
- validation and release packaging
- model development configs and scripts
- a Space trainer app
- a conjecture-lab Space app
- rollout runbooks
- state-of-the-art math blueprints
This means the model should be understood as one artifact within a broader research pipeline rather than a standalone checkpoint.
Example Usage
Transformers
1from transformers import AutoTokenizer, AutoModelForCausalLM
2import torch
3
4repo_id = "NorthernTribe-Research/math-conjecture-model"
5
6tokenizer = AutoTokenizer.from_pretrained(repo_id)
7model = AutoModelForCausalLM.from_pretrained(
8 repo_id,
9 torch_dtype=torch.float16 if torch.cuda.is_available() else torch.float32,
10 device_map="auto"
11)
12
13prompt = """Analyze the following mathematical conjecture.
14
15Conjecture:
16If a sequence is eventually periodic, then its generating function is rational.
17
18Return:
191. Intuition
202. Proof sketch
213. Key assumptions
224. Formalization notes
23"""
24
25inputs = tokenizer(prompt, return_tensors="pt").to(model.device)
26outputs = model.generate(
27 **inputs,
28 max_new_tokens=512,
29 do_sample=True,
30 temperature=0.7,
31 top_p=0.9
32)
33
34print(tokenizer.decode(outputs[0], skip_special_tokens=True))
Prompting style
This model generally benefits from prompts that request structure explicitly, such as:
- intuition
- proof sketch
- formalization notes
- assumptions
- edge cases
- candidate counterexamples
- Lean-style outline
Example prompt
1Consider the statement:
2
3"If a + b is even, then a and b have the same parity."
4
5Provide:
61. An intuitive explanation
72. A proof
83. A compact formalization outline
94. Any assumptions or edge cases
Local Inference
The project documentation confirms a local inference path using llama.cpp after:
- merging the adapter into a full model
- converting the merged model to GGUF
- optionally quantizing for lighter deployment
This supports local experimentation outside standard Transformers-based serving.
Limitations
This is a research model and may still:
- generate invalid proofs that sound convincing
- confuse symbolic plausibility with correctness
- fail on deep multi-hop theorem reasoning
- produce incomplete or brittle formalization hints
- overuse familiar proof templates
- hallucinate mathematical structure
All substantive outputs should be independently verified with formal tools, symbolic systems, or expert review.
Risks and Recommendations
Because the model is optimized for proof-style text generation, users may over-trust fluent mathematical output. For that reason:
- verify results independently
- use proof assistants or symbolic systems when correctness matters
- treat outputs as research assistance, not certification
- benchmark behavior before deployment in educational or analytical systems
Project Documentation
The repository includes documentation and workflow support for:
- dataset release
- model development
- rollout automation
- Space deployment
- evaluation
- adapter merge and publish
- model-card refresh automation
Citation
1@misc{northerntribe_math_conjecture_sota_05b_2026,
2 title = {Math Conjecture SOTA 0.5B},
3 author = {NorthernTribe Research},
4 year = {2026},
5 publisher = {Hugging Face},
6 howpublished = {Model repository}
7}
Disclaimer
This model is intended for research, experimentation, and educational exploration in mathematical reasoning. It does not guarantee theorem validity, proof correctness, or novel mathematical discovery.
