---
base_model: Qwen/Qwen3-8B
library_name: transformers
license: apache-2.0
language:
  - en
tags:
  - math
  - reasoning
  - gsm8k
  - synthetic-data
  - qwen3
  - qlora
  - unsloth
  - fine-tuned
  - grade-school-math
  - chain-of-thought
datasets:
  - clarkkitchen22/SynthGSM8K-50K
pipeline_tag: text-generation
model-index:
  - name: Qwen3-8B-GSM8K-Synth-50K
    results:
      - task:
          type: text-generation
          name: Math Reasoning
        dataset:
          name: GSM8K
          type: openai/gsm8k
        metrics:
          - name: GSM8K Accuracy
            type: accuracy
            value: 86.2
            verified: true
          - name: Training Loss (final)
            type: loss
            value: 0.266
---

# Qwen3-8B-GSM8K-Synth-50K

A **Qwen3-8B** model fine-tuned on **50,418 synthetic grade-school math problems** using QLoRA, designed for step-by-step mathematical reasoning with chain-of-thought.

## What This Model Does

Given a math word problem, the model produces a structured reasoning chain inside `<think>` tags, then outputs the final numerical answer.

### Example

**Input:**
> If 3x + 7 = 22, what is x?

**Output:**
```
<think>
Step 1: Subtract 7 from both sides: 3x = 22 - 7
Step 2: Calculate: 3x = 15
Step 3: Divide both sides by 3: x = 15 / 3
Step 4: Calculate: x = 5
</think>

The answer is 5.0.
```

## Evaluation Results

Evaluated on the **full GSM8K test set** (1,319 questions) with greedy decoding and 4-bit quantization.

| Model | GSM8K Accuracy | Correct / Total | Time |
|---|---|---|---|
| Base Qwen3-8B | 79.4% | 1,047 / 1,319 | 121.8m |
| **Qwen3-8B-GSM8K-Synth-50K** | **86.2%** | **1,137 / 1,319** | 45.1m |

**Fine-tuning improvement: +6.8 percentage points** over the base model.

The fine-tuned model also runs ~2.7x faster at inference due to shorter, more structured outputs (the base model produces verbose markdown formatting while the fine-tuned model outputs concise step-by-step solutions).

### Cross-Model Comparison

| Model | Params | Training Data | GSM8K Accuracy | vs Base |
|---|---|---|---|---|
| Base Qwen3-4B | 4B | — | 74.7% | — |
| Qwen3-4B-GSM8K-Synth-35K | 4B | 35K synthetic | 85.0% | +10.3% |
| Base Qwen3-8B | 8B | — | 79.4% | — |
| **Qwen3-8B-GSM8K-Synth-50K** | **8B** | **50K synthetic** | **86.2%** | **+6.8%** |

Key takeaways:
- Synthetic data fine-tuning provides a substantial accuracy boost at both model scales (+10.3% for 4B, +6.8% for 8B)
- The 8B fine-tuned model achieves the highest absolute accuracy (86.2%)
- Scaling from 4B to 8B improves base performance by +4.7% and fine-tuned performance by +1.2%

## Training Details

### Base Model & Method

| Parameter | Value |
|---|---|
| **Base model** | [Qwen/Qwen3-8B](https://huggingface.co/Qwen/Qwen3-8B) |
| **Method** | QLoRA (4-bit NF4 quantization) |
| **Framework** | [Unsloth](https://github.com/unslothai/unsloth) + HuggingFace TRL |
| **Merge** | Fully merged to 16-bit (no adapter needed at inference) |

### QLoRA Configuration

| Parameter | Value |
|---|---|
| **LoRA rank** | 16 |
| **LoRA alpha** | 16 |
| **Target modules** | q_proj, k_proj, v_proj, o_proj, gate_proj, up_proj, down_proj |
| **Dropout** | 0 |
| **Trainable parameters** | 43.6M / 8.23B (0.53%) |

### Training Hyperparameters

| Parameter | Value |
|---|---|
| **Epochs** | 3 |
| **Batch size** | 1 (per device) |
| **Gradient accumulation** | 64 (effective batch = 64) |
| **Learning rate** | 2e-4 (cosine schedule) |
| **Warmup steps** | 10 |
| **Optimizer** | AdamW 8-bit |
| **Precision** | bf16 |
| **Max sequence length** | 1024 |
| **Max grad norm** | 1.0 |
| **Seed** | 42 |
| **Total steps** | 2,364 |

### Memory Optimizations (fitting 8B in 12GB VRAM)

Training Qwen3-8B in 4-bit still uses ~7.2GB for weights alone, leaving only ~4.4GB on a 12GB GPU. The following optimizations made training possible:

- **Embedding offloading** (`offload_embedding=True`) — input embeddings kept on CPU
- **Chunked fused CE loss** (`UNSLOTH_CE_LOSS_N_CHUNKS=8`) — splits the large 151,936-vocab logits computation into smaller chunks
- **Unsloth gradient checkpointing** — auto-offloads activations for long sequences
- **Reduced sequence length** (1024 vs 4096) — data is short (median ~100 tokens, max ~260)
- **PYTORCH_CUDA_ALLOC_CONF=expandable_segments:True** — reduces CUDA memory fragmentation
- Peak VRAM usage: **11.8GB / 12.3GB** (96%)

### Training Loss Curve

```
Epoch 1: 0.735 → 0.304  (rapid descent)
Epoch 2: 0.292 → 0.277  (steady refinement)
Epoch 3: 0.271 → 0.266  (final polish)

Final training loss: 0.302 (avg over 3 epochs)
```

| Milestone | Loss | Epoch |
|---|---|---|
| Step 50 | 0.735 | 0.06 |
| Step 250 | 0.333 | 0.32 |
| Step 500 | 0.316 | 0.63 |
| Step 788 (Epoch 1) | 0.304 | 1.02 |
| Step 1000 | 0.292 | 1.27 |
| Step 1250 | 0.291 | 1.59 |
| Step 1576 (Epoch 2) | 0.277 | 2.03 |
| Step 1750 | 0.270 | 2.22 |
| Step 2000 | 0.266 | 2.54 |
| Step 2364 (Epoch 3) | 0.266 | 2.98 |

### Comparison with 4B Model

| Metric | Qwen3-4B (35K) | Qwen3-8B (50K) |
|---|---|---|
| **Training data** | 34,818 examples | 50,418 examples |
| **Final loss** | 0.291 | 0.266 |
| **LoRA rank** | 32 | 16 |
| **Training time** | 3h 18m | 9h 25m |
| **Peak VRAM** | ~8.1 GB | ~11.8 GB |

### Hardware & Time

| Metric | Value |
|---|---|
| **GPU** | NVIDIA RTX 4070 SUPER (12GB VRAM) |
| **Training time** | 9h 25m (33,890 seconds) |
| **Throughput** | 4.46 samples/sec, 0.07 steps/sec |
| **Peak VRAM** | ~11.8 GB |

## Training Data

Trained on the **full 50,418 examples** from [clarkkitchen22/SynthGSM8K-50K](https://huggingface.co/datasets/clarkkitchen22/SynthGSM8K-50K) — a synthetic grade-school math dataset generated by Claude Haiku 4.5 via Anthropic's Batch API, then filtered through an 8-stage quality pipeline.

### Data Format

Each training example follows the Qwen3 ChatML format with thinking tags:

```
<|im_start|>user
{math word problem}<|im_end|>
<|im_start|>assistant
<think>
{step-by-step solution}
</think>

The answer is {number}.<|im_end|>
```

GSM8K-style calculation annotations (e.g., `<<24*3=72>>`) are stripped from solutions during preprocessing.

### Dataset Highlights

- **50,418 problems** — full dataset used for this training run
- Generated via few-shot prompting from 200 real GSM8K seed problems
- 8-stage filter pipeline: structure, answer range, solution quality, AI detection, math verification, exact dedup, fuzzy dedup (TF-IDF @ 0.85), seed overlap
- Average 3.0 math operations per solution
- 92.6% integer answers, range 0-225,000
- ~$55 generation cost (Haiku 4.5 Batch API at 50% discount)

## Usage

### With Transformers

```python
from transformers import AutoModelForCausalLM, AutoTokenizer

model_name = "clarkkitchen22/Qwen3-8B-GSM8K-Synth-50K"
tokenizer = AutoTokenizer.from_pretrained(model_name)
model = AutoModelForCausalLM.from_pretrained(model_name, torch_dtype="auto", device_map="auto")

messages = [{"role": "user", "content": "A store sells apples for $2 each and oranges for $3 each. If Sarah buys 5 apples and 4 oranges, how much does she spend?"}]

text = tokenizer.apply_chat_template(messages, tokenize=False, add_generation_prompt=True)
inputs = tokenizer(text, return_tensors="pt").to(model.device)

outputs = model.generate(**inputs, max_new_tokens=512, temperature=0.6, top_p=0.95)
response = tokenizer.decode(outputs[0][inputs.input_ids.shape[-1]:], skip_special_tokens=True)
print(response)
```

### Answer Extraction

```python
import re

def extract_answer(text):
    """Extract numerical answer from model output."""
    match = re.search(r"answer\s*(?:is|:)\s*([-\d,]+\.?\d*)", text, re.IGNORECASE)
    if match:
        return float(match.group(1).replace(",", ""))
    matches = re.findall(r"([-\d,]+\.?\d+)", text)
    return float(matches[-1].replace(",", "")) if matches else None
```

## Intended Use

- **Math tutoring**: Step-by-step solutions to grade-school math problems
- **Research**: Studying the effect of model scale and synthetic data on math reasoning
- **Distillation baseline**: Comparing synthetic-data-trained small models against larger models
- **Further fine-tuning**: Starting point for domain-specific math reasoning tasks

## Limitations

- Trained on synthetic data generated by Haiku 4.5 — bounded by that model's math ability
- Optimized for GSM8K-style word problems (arithmetic, basic algebra) — not calculus, geometry, or advanced math
- All training answers are non-negative; may struggle with problems requiring negative answers
- Solutions use a specific `<think>` tag format — other prompting styles may give worse results
- Evaluated on GSM8K only — performance on other math benchmarks (MATH, MMLU-Math) not yet tested

## How It Was Built

### End-to-End Pipeline

```
200 GSM8K seeds → Claude Haiku 4.5 (Batch API) → 83K raw problems
    → 8-stage filter → 50K clean dataset → QLoRA fine-tune Qwen3-8B
    → Merge to 16-bit → Push to HuggingFace
```

### Pipeline Code

The full data generation pipeline and training code is available at:
[github.com/goldbar123467/SynthDataGSM8K](https://github.com/goldbar123467/SynthDataGSM8K)

## Citation

```bibtex
@model{qwen3_8b_gsm8k_synth_50k,
  title={Qwen3-8B-GSM8K-Synth-50K},
  author={clarkkitchen22},
  year={2026},
  base_model={Qwen/Qwen3-8B},
  training_data={clarkkitchen22/SynthGSM8K-50K},
  url={https://huggingface.co/clarkkitchen22/Qwen3-8B-GSM8K-Synth-50K}
}
```

## Acknowledgements

- **Base model**: [Qwen/Qwen3-8B](https://huggingface.co/Qwen/Qwen3-8B) by Alibaba
- **Training data**: [SynthGSM8K-50K](https://huggingface.co/datasets/clarkkitchen22/SynthGSM8K-50K) — synthetic math problems from Claude Haiku 4.5
- **Training framework**: [Unsloth](https://github.com/unslothai/unsloth) (2x faster QLoRA)
- **Seed data**: [OpenAI GSM8K](https://github.com/openai/grade-school-math)