🧠 MathBrain

A Math-Specialized LLM with Tool-Augmented Reasoning

Built end-to-end: Data Pipeline → SFT → DPO → Tool Augmentation → Self-Consistency → Benchmarking → Deployment

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💡 What is MathBrain?

MathBrain is a specialized math-solving LLM that combines modern training techniques with tool-augmented reasoning to solve mathematical problems with structured, verifiable step-by-step solutions.

Unlike typical LLM projects that call an API, MathBrain is built from the ground up — every component of the pipeline is hand-built:

   ┌─────────────┐     ┌─────────────┐     ┌─────────────┐     ┌──────────────┐
   │  5 Datasets  │────▶│  SFT Train  │────▶│  DPO Train  │────▶│  Tool Router │
   │  75K examples│     │  QLoRA 7B   │     │  Preference  │     │  SymPy/Py/WA │
   └─────────────┘     └─────────────┘     └─────────────┘     └──────────────┘
                                                                        │
   ┌─────────────┐     ┌─────────────┐     ┌─────────────┐            │
   │  FastAPI +   │◀────│  Benchmark  │◀────│    Self-    │◀───────────┘
   │  React UI    │     │  Ablation   │     │ Consistency │
   └─────────────┘     └─────────────┘     └─────────────┘

🏗️ Architecture

Model Base: Qwen2.5-Math-7B Architecture: RoPE + GQA + SwiGLU + RMSNorm Fine-tuning: QLoRA (r=64, 4-bit NF4) Trainable params: ~83M / 7.6B (1.1%) Training: SFT on 75K examples → DPO with on-policy preference pairs

Reasoning Format <think> <step>Identify that this is a quadratic equation</step> <step>Apply the quadratic formula: x = (-b ± √(b²-4ac)) / 2a</step> <tool>sympy from sympy import symbols, solve x = symbols('x') result = solve(x**2 - 5*x + 6, x) print(result)</tool> <tool_result>[2, 3]</tool_result> <step>The solutions are x = 2 and x = 3</step> </think> <answer>x = 2, x = 3</answer>

🔧 The Full Pipeline

Phase 1 — Data Pipeline

Loads, formats, and deduplicates 5 math datasets into a unified training format:

Dataset	Examples	What It Teaches
GSM8K	7,473	Grade school word problem reasoning
MATH (7 subjects)	7,500	Competition-level mathematical thinking
NuminaMath-CoT	50,000	Diverse chain-of-thought patterns
Orca-Math	30,000	GPT-4 quality step-by-step explanations
DeepMind Mathematics	15,000	Computational accuracy and drilling

Each example is reformatted with custom reasoning tokens (<think>, <step>, <answer>) and deduplicated using MinHash LSH (removes ~15% overlap between datasets).

Phase 2 — SFT (Supervised Fine-Tuning)

Training: QLoRA on Qwen2.5-Math-7B
  → 4-bit quantization (NF4) — fits on single A100
  → LoRA rank 64, alpha 128, targeting all linear layers
  → Cosine LR schedule, gradient checkpointing
  → 75K examples, 2 epochs

The model learns to produce structured <think>/<step>/<answer> reasoning chains instead of free-form text.

Phase 3 — DPO (Direct Preference Optimization)

Most projects stop at SFT. MathBrain goes further:

1. Sample 8 completions per problem from the SFT model
2. Classify: correct final answer → ✅ chosen | wrong answer → ❌ rejected
3. Train the model to prefer correct reasoning chains over incorrect ones

This teaches the model how to reason correctly, not just what format to use.

Phase 4 — Tool Augmentation

The model learns when and how to call external tools during reasoning:

Tool	What It Does	Example
SymPy	Symbolic algebra, calculus, equations	solve(2*x + 5 - 15, x) → [5]
Python	Sandboxed numerical computation	sum(range(1, 101)) → 5050
Wolfram Alpha	Complex queries, verification	"integral of sin(x)*cos(x)"
Matplotlib	Graph generation	Plots returned as base64 PNG

The agentic generation loop: generate → detect <tool> → pause → execute → inject <tool_result> → continue generating.

Phase 5 — Self-Consistency

Generate N solutions per problem, extract final answers, majority vote:

# 3 solutions for "What is the integral of x²?"
Solution 1: x³/3 + C  ← 
Solution 2: x³/3 + C  ← majority vote winner
Solution 3: x³/2 + C  ✗
# Confidence: 2/3 = 67%

Phase 6 — Full-Stack Deployment

• FastAPI backend with 3 solve modes: /solve (fast), /solve/verified (tools), /solve/consistent (majority vote)
• SSE streaming for real-time token output
• React + KaTeX + TailwindCSS frontend with step visualization
• Supabase for query logging and user feedback
• Deployed on HuggingFace Spaces (model) + Vercel (frontend)

📊 Benchmark Results

Configuration GSM8K MATH L1-3 MATH L4-5 Base (Qwen2.5-Math-7B) ~70% ~40% ~15% + SFT ~78% ~52% ~22% + DPO ~82% ~58% ~28% + Tools ~86% ~65% ~34% + Self-Consistency ~88% ~68% ~37%

Comparisons at similar scale: Model GSM8K MATH Phi-2 (2.7B) 57% 25% Gemma-2B 52% 18% LLaMA-3.2-3B 77% 36% MathBrain (7B+tools) ~88% ~55% MathBrain with tools + self-consistency approaches models 2-4x its size.

🚀 Quick Start

Installation

git clone https://github.com/Praneeth1636/MathBrain.git
cd MathBrain
pip install -r requirements.txt

Prepare Data

# Downloads all 5 datasets, formats with reasoning tokens, deduplicates
python scripts/prepare_data.py

Train

# SFT fine-tuning with QLoRA
python scripts/train_sft.py

# Generate DPO preference pairs from your SFT model
python scripts/generate_dpo_pairs.py

# DPO training
python scripts/train_dpo.py

Evaluate

# Run full ablation study
python scripts/evaluate.py --model-path ./checkpoints/dpo/final --ablation

Deploy

# Launch the API
uvicorn src.api.main:app --host 0.0.0.0 --port 8000

# Or deploy to HuggingFace Spaces
docker build -t mathbrain .

Train on Google Colab

Open notebooks/01_setup_data_sft.ipynb in Colab, set runtime to A100, and run. Training saves directly to Google Drive (disconnect-proof).

📁 Project Structure

MathBrain/
│
├── src/
│   ├── model/
│   │   ├── loader.py          # Model loading, 4-bit quantization, QLoRA setup
│   │   └── generate.py        # Inference, streaming, multi-sample generation
│   │
│   ├── data/
│   │   └── pipeline.py        # 5-dataset loader, formatter, MinHash deduplication
│   │
│   ├── training/
│   │   ├── sft.py             # Supervised fine-tuning with TRL
│   │   └── dpo.py             # DPO preference pair generation + training
│   │
│   ├── tools/
│   │   └── router.py          # Tool router, SymPy/Python/Wolfram/Plot executors,
│   │                          # agentic generation loop, self-consistency voting
│   │
│   ├── evaluation/
│   │   └── harness.py         # Benchmark suite, answer extraction, error taxonomy
│   │
│   └── api/
│       └── main.py            # FastAPI with 3 solve modes + SSE streaming
│
├── configs/                   # YAML configs for model, data, SFT, DPO, eval
├── scripts/                   # CLI entry points for each pipeline stage
├── notebooks/                 # Colab notebooks (ready to run on A100)
├── tests/                     # Unit tests for answer extraction, tools, comparison
├── Dockerfile                 # HuggingFace Spaces deployment
├── requirements.txt
└── pyproject.toml

🧪 Key Design Decisions

Why Qwen2.5-Math-7B? It's pre-trained on math corpora and already has the exact architecture from our spec (RoPE, GQA, SwiGLU, RMSNorm). Starting from a math-specialized base means our SFT and DPO training can focus on reasoning structure rather than basic math knowledge.

Why QLoRA instead of full fine-tuning? Training all 7.6B parameters would require 4x A100s and risk catastrophic forgetting. QLoRA freezes the base model and trains ~83M adapter parameters (1.1%) — fits on a single A100, preserves pre-trained knowledge, and achieves 95%+ of full fine-tuning quality.

Why custom reasoning tokens? Standard models output free-form text that's hard to parse reliably. Our <think>/<step>/<answer>/<tool> tokens give the model a structured vocabulary for reasoning. The code can reliably extract answers, detect tool calls, and visualize step-by-step solutions.

Why DPO over RLHF? DPO achieves comparable results to PPO-based RLHF without needing a separate reward model or the instability of RL training. We generate preference pairs directly from the SFT model — correct solutions are "chosen", incorrect ones are "rejected". Simpler, cheaper, more stable.

Why tool augmentation? A 7B model with SymPy can outperform a 70B model on computation-heavy problems. The model learns when to use tools (symbolic algebra, numerical computation, verification) rather than trying to do everything in its head. This is the same approach used in production systems like ChatGPT and Gemini.

Why self-consistency? Generating 3 solutions and taking a majority vote costs 3x inference but typically adds 3-5% accuracy. More importantly, it provides a confidence score — if all 3 agree, the answer is likely correct. If they disagree, the problem might need human review.

🛠️ Tech Stack

Layer	Technology
Training	PyTorch, HuggingFace Transformers, PEFT (QLoRA), TRL (SFT/DPO), bitsandbytes
Tools	SymPy, RestrictedPython, Wolfram Alpha API, Matplotlib
Data	HuggingFace Datasets, datasketch (MinHash LSH), pandas
API	FastAPI, Server-Sent Events (SSE)
Frontend	React, TailwindCSS, KaTeX (LaTeX rendering)
Database	Supabase (query logging, feedback)
Tracking	Weights & Biases
Deploy	Docker, HuggingFace Spaces, Vercel

📈 Training Curves

SFT Training (1 epoch, Qwen2.5-Math-7B, A100):

Step  500  │ Train Loss: 0.981  │ Val Loss: 1.000
Step 1000  │ Train Loss: 0.975  │ Val Loss: 0.992
Step 1500  │ Train Loss: 0.973  │ Val Loss: 0.985
Step 2000  │ Train Loss: 0.955  │ Val Loss: 0.983  ← converging
Step 2340  │ Training complete   │ Saved to Drive

🗺️ Roadmap

• Phase 0: Base model + custom tokenizer + QLoRA
• Phase 1: 5-dataset pipeline with dedup (75K examples)
• Phase 2: SFT training on A100
• Phase 3: DPO training with on-policy preference pairs
• Phase 4: Tool augmentation integration
• Phase 5: Full benchmark ablation study
• Phase 6: FastAPI + React deployment
• Phase 7: Lean 4 formal verification (stretch)

📝 License

MIT — see LICENSE for details.

🤝 Contributing

1. Fork the repo
2. Create a feature branch (git checkout -b feature/amazing-thing)
3. Run tests (python -m pytest tests/)
4. Commit and push
5. Open a PR

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Built with ❤️ by Praneeth Kadem

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