linalg-zero 1.0.0

This repository provides tools to generate a linear algebra dataset and code to train an open-source pre-trained model. Our goal is to explore the model's potential for emergent reasoning, inspired by the Deepseek-R1 paper.

Linalg-Zero

Check out the poster here and the paper here.

Table of Contents

1. Overview
2. Main Phases
3. Installation
4. Quickstart
5. Results
   • Artifacts
6. Reproducibility

Overview

This repository offers tools for generating a linear algebra problem dataset and training an open-source base model (i.e. Qwen2.5-3B), aiming to explore planning and tool use using SFT and RL, distinct from Deepseek-R1's primary emphasis on reasoning.

The project is simple by design and mostly consists of:

• linalg_zero/: contains the scripts to train models as well as generate synthetic data:
  • generate.py: generates the linear algebra dataset and splits.
  • distillation.py: runs the distillation pipeline to create multi-turn tool-use data.
  • sft_train.py: performs a simple SFT of a model on a dataset.
  • grpo_train.py: trains a model with GRPO on a given dataset.
• Makefile: contains easy-to-run commands for the dataset and training workflows using previous scripts.

Main Phases

We use the DeepSeek-R1 tech report as a loose guide, but the project phases are:

• Step 1: generate a linear algebra dataset with controlled difficulty and tool-call metadata.
• Step 2: distill multi-turn tool-use data from a teacher model.
• Step 3: SFT the base model on the dataset to teach the tool-calling format.
• Step 4: GRPO fine-tune on the tool-use tasks, using a curriculum.

Installation

We use uv as the dependency management tool. First, to install uv, follow the UV Installation Guide.

To run the experiments install the dependencies using:

• For generation/distillation: make install-data-gen
• For SFT: make install-sft
• For RL: make install-grpo

Next, log into your Hugging Face and Weights and Biases accounts as follows:

huggingface-cli login
wandb login

Quickstart

After installing dependencies above, run the commands below. For modifications, see the config files.

# Phase 1: Generate dataset
uv run python linalg_zero/generate.py --dataset_name atomwalk12/linalgzero --push_dataset

# Phase 2: Distillation (setup once)
cp linalg_zero/config/distillation/env.example.sh env.sh
# Edit env.sh to set HF_TOKEN and ARGILLA_API_KEY.
source env.sh

# Terminal A
uv run python linalg_zero/distillation/launch_server.py --config linalg_zero/config/distillation/vllm_qwen3_32b.yaml

# Terminal B (new terminal; source env.sh again)
source env.sh
uv run python linalg_zero/distillation.py --config linalg_zero/config/distillation/vllm_qwen3_32b.yaml

# Phase 3: SFT
uv run python linalg_zero/sft_train.py --config linalg_zero/config/sft/qwen2.5-3B/lora.yaml

# Phase 4: GRPO
uv run python linalg_zero/grpo_train.py --config-name runpod.yaml

Training requires the dataset to follow the strict OpenAI tool-calling format (see this link). We provide scripts to prepare and validate the data accordingly:

• linalg_zero/
  • sft/scripts/prepare_dataset.py: prepares the SFT dataset.
  • grpo/scripts/prepare_dataset.py: prepares and validates the GRPO dataset.

Results

We provide a recipe to encourage planning and tool-use capabilities in the Qwen2.5-3B model, starting from a pre-trained (not instruction-tuned) base model.

This yields models like Linalg-Zero-SFT and Linalg-Zero-GRPO, with the following downstream performance on the test set:

Metric	LinAlgZero-SFT	LinAlgZero-GRPO
Optimal Trajectory	89.87%	90.26%
Correctness	91.86%	92.63%
Format Validity	96.15%	96.66%
Tool Success	100.00%	100.00%

Artifacts

Artifact	Link
SFT checkpoint	atomwalk12/LinalgZero-SFT
GRPO checkpoint	atomwalk12/LinAlgZero-GRPO
Base dataset	atomwalk12/linalgzero
Distilled dataset (clean)	atomwalk12/linalgzero-distilled-clean
SFT dataset	atomwalk12/linalgzero-sft
GRPO dataset	atomwalk12/linalgzero-grpo

Reproducibility

• Distillation: H100 80GB on Runpod with Qwen/Qwen3-32B-FP8; 14 hours at $2.39/hr (~$25).
• SFT: Local 24GB RTX 4090 with Qwen/Qwen2.5-3B.
• GRPO: RTX 6000 Ada on Runpod, improving on the SFT baseline; 57 hours at $0.77/hr (~$50).
• Total: ~$75 using a mix of cloud GPUs and local training.

Citation

If you find this project is useful in your own work, please consider citing as follows:

@misc{openr1,
    title = {Linalg-Zero: Distilling Neurosymbolic Reasoning for Linear Algebra in Small Language Models},
    url = {https://github.com/atomwalk12/linalg-zero},
    author = {{Razvan F. Vasile}},
    month = {March},
    year = {2026}
}