---
license: mit
library_name: transformers
language:
  - en
base_model:
  - deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B
datasets:
  - AI-MO/NuminaMath-CoT
  - codeparrot/apps
  - deepmind/code_contests
  - BAAI/TACO
  - MatrixStudio/Codeforces-Python-Submissions
pipeline_tag: text-generation
---

# <span style="color: #7FFF7F;">ZR1-1.5B GGUF Models</span>

## **Choosing the Right Model Format**  

Selecting the correct model format depends on your **hardware capabilities** and **memory constraints**.  

### **BF16 (Brain Float 16) – Use if BF16 acceleration is available**  
- A 16-bit floating-point format designed for **faster computation** while retaining good precision.  
- Provides **similar dynamic range** as FP32 but with **lower memory usage**.  
- Recommended if your hardware supports **BF16 acceleration** (check your device's specs).  
- Ideal for **high-performance inference** with **reduced memory footprint** compared to FP32.  

📌 **Use BF16 if:**  
✔ Your hardware has native **BF16 support** (e.g., newer GPUs, TPUs).  
✔ You want **higher precision** while saving memory.  
✔ You plan to **requantize** the model into another format.  

📌 **Avoid BF16 if:**  
❌ Your hardware does **not** support BF16 (it may fall back to FP32 and run slower).  
❌ You need compatibility with older devices that lack BF16 optimization.  

---

### **F16 (Float 16) – More widely supported than BF16**  
- A 16-bit floating-point **high precision** but with less of range of values than BF16. 
- Works on most devices with **FP16 acceleration support** (including many GPUs and some CPUs).  
- Slightly lower numerical precision than BF16 but generally sufficient for inference.  

📌 **Use F16 if:**  
✔ Your hardware supports **FP16** but **not BF16**.  
✔ You need a **balance between speed, memory usage, and accuracy**.  
✔ You are running on a **GPU** or another device optimized for FP16 computations.  

📌 **Avoid F16 if:**  
❌ Your device lacks **native FP16 support** (it may run slower than expected).  
❌ You have memory limitations.  

---

### **Quantized Models (Q4_K, Q6_K, Q8, etc.) – For CPU & Low-VRAM Inference**  
Quantization reduces model size and memory usage while maintaining as much accuracy as possible.  
- **Lower-bit models (Q4_K)** → **Best for minimal memory usage**, may have lower precision.  
- **Higher-bit models (Q6_K, Q8_0)** → **Better accuracy**, requires more memory.  

📌 **Use Quantized Models if:**  
✔ You are running inference on a **CPU** and need an optimized model.  
✔ Your device has **low VRAM** and cannot load full-precision models.  
✔ You want to reduce **memory footprint** while keeping reasonable accuracy.  

📌 **Avoid Quantized Models if:**  
❌ You need **maximum accuracy** (full-precision models are better for this).  
❌ Your hardware has enough VRAM for higher-precision formats (BF16/F16).  

---

### **Very Low-Bit Quantization (IQ3_XS, IQ3_S, IQ3_M, Q4_K, Q4_0)**  
These models are optimized for **extreme memory efficiency**, making them ideal for **low-power devices** or **large-scale deployments** where memory is a critical constraint.  

- **IQ3_XS**: Ultra-low-bit quantization (3-bit) with **extreme memory efficiency**.  
  - **Use case**: Best for **ultra-low-memory devices** where even Q4_K is too large.  
  - **Trade-off**: Lower accuracy compared to higher-bit quantizations.  

- **IQ3_S**: Small block size for **maximum memory efficiency**.  
  - **Use case**: Best for **low-memory devices** where **IQ3_XS** is too aggressive.  

- **IQ3_M**: Medium block size for better accuracy than **IQ3_S**.  
  - **Use case**: Suitable for **low-memory devices** where **IQ3_S** is too limiting.  

- **Q4_K**: 4-bit quantization with **block-wise optimization** for better accuracy.  
  - **Use case**: Best for **low-memory devices** where **Q6_K** is too large.  

- **Q4_0**: Pure 4-bit quantization, optimized for **ARM devices**.  
  - **Use case**: Best for **ARM-based devices** or **low-memory environments**.  

---

### **Summary Table: Model Format Selection**  

| Model Format  | Precision  | Memory Usage  | Device Requirements  | Best Use Case  |  
|--------------|------------|---------------|----------------------|---------------|  
| **BF16**     | Highest    | High          | BF16-supported GPU/CPUs  | High-speed inference with reduced memory |  
| **F16**      | High       | High          | FP16-supported devices | GPU inference when BF16 isn't available |  
| **Q4_K**     | Medium Low | Low           | CPU or Low-VRAM devices | Best for memory-constrained environments |  
| **Q6_K**     | Medium     | Moderate      | CPU with more memory | Better accuracy while still being quantized |  
| **Q8_0**     | High       | Moderate      | CPU or GPU with enough VRAM | Best accuracy among quantized models |  
| **IQ3_XS**   | Very Low   | Very Low      | Ultra-low-memory devices | Extreme memory efficiency and low accuracy |  
| **Q4_0**     | Low        | Low           | ARM or low-memory devices | llama.cpp can optimize for ARM devices |  

---

## **Included Files & Details**  

### `ZR1-1.5B-bf16.gguf`  
- Model weights preserved in **BF16**.  
- Use this if you want to **requantize** the model into a different format.  
- Best if your device supports **BF16 acceleration**.  

### `ZR1-1.5B-f16.gguf`  
- Model weights stored in **F16**.  
- Use if your device supports **FP16**, especially if BF16 is not available.  

### `ZR1-1.5B-bf16-q8_0.gguf`  
- **Output & embeddings** remain in **BF16**.  
- All other layers quantized to **Q8_0**.  
- Use if your device supports **BF16** and you want a quantized version.  

### `ZR1-1.5B-f16-q8_0.gguf`  
- **Output & embeddings** remain in **F16**.  
- All other layers quantized to **Q8_0**.    

### `ZR1-1.5B-q4_k.gguf`  
- **Output & embeddings** quantized to **Q8_0**.  
- All other layers quantized to **Q4_K**.  
- Good for **CPU inference** with limited memory.  

### `ZR1-1.5B-q4_k_s.gguf`  
- Smallest **Q4_K** variant, using less memory at the cost of accuracy.  
- Best for **very low-memory setups**.  

### `ZR1-1.5B-q6_k.gguf`  
- **Output & embeddings** quantized to **Q8_0**.  
- All other layers quantized to **Q6_K** .  

### `ZR1-1.5B-q8_0.gguf`  
- Fully **Q8** quantized model for better accuracy.  
- Requires **more memory** but offers higher precision.  

### `ZR1-1.5B-iq3_xs.gguf`  
- **IQ3_XS** quantization, optimized for **extreme memory efficiency**.  
- Best for **ultra-low-memory devices**.  

### `ZR1-1.5B-iq3_m.gguf`  
- **IQ3_M** quantization, offering a **medium block size** for better accuracy.  
- Suitable for **low-memory devices**.  

### `ZR1-1.5B-q4_0.gguf`  
- Pure **Q4_0** quantization, optimized for **ARM devices**.  
- Best for **low-memory environments**.
- Prefer IQ4_NL for better accuracy.

# <span id="testllm" style="color: #7F7FFF;">🚀 If you find these models useful</span>
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# ZR1-1.5B

ZR1-1.5B is a small reasoning model trained extensively on both verified coding and mathematics problems with reinforcement learning. The model outperforms Llama-3.1-70B-Instruct on hard coding tasks and improves upon the base R1-Distill-1.5B model by over 50%, while achieving strong scores on math evaluations and a 37.91% pass@1 accuracy on GPQA-Diamond with just 1.5B parameters.

![ZR1-1.5B LiveBench evaluation results on LiveBench with greedy sampling: the model is very token efficient](zr1-1.5b-livebench.png)

## Data

For training we utilized the [PRIME Eurus-2-RL](https://huggingface.co/datasets/PRIME-RL/Eurus-2-RL-Data) dataset which combines the following math and code datasets:
- NuminaMath-CoT
- APPS, CodeContests, TACO, and Codeforces train set

We filtered math data by validating that questions are correctly graded when calling the evaluator with reference ground truth, and we removed all code examples with an empty list of test cases. Our final dataset comprised roughly 400k math + 25k code samples.

## Training Recipe 

We employ [PRIME (Process Reinforcement through IMplicit rEwards)](https://arxiv.org/abs/2502.01456), an online RL algorithm with process rewards, motivated by the improvement over GPRO demonstrated in the paper, as well as potentially more accurate token-level rewards due to the learned process reward model. We used the training batch accuracy filtering method from PRIME for training stability, and the iterative context lengthening technique demonstrated in [DeepScaleR](https://pretty-radio-b75.notion.site/DeepScaleR-Surpassing-O1-Preview-with-a-1-5B-Model-by-Scaling-RL-19681902c1468005bed8ca303013a4e2) for faster training, which has also been [shown to improve token efficiency](https://arxiv.org/abs/2503.07572). After a warmup period with maximum generation length set to 12k tokens, we sequentially increased the maximum generation length during training, starting at 8k tokens before increasing to 16k and 24k.

We trained on a single 8xH100 node with the following specific algorithmic details.

- PRIME + RLOO with token-level granularity
- No `<think>` token prefill. 0.1 format reward/penalty
- Main train batch size 256 with n=4 samples per prompt. veRL dynamic batch size with max batch size set per GPU to support training with large generation length
- Max prompt length 1536, generation length increase over training. Started with 12k intended to ease model into shorter generation length training
- 12384 -> 8192 -> 16384 -> 24448
- Start with 1 PPO epoch, increase to 4 during 24k stage
- Accuracy filtering 0.2-0.8 and relax to 0.01-0.99 during 24k stage
- Oversample batches 2x for accuracy filtering

And the following training hyperparameters: 

- KL coefficient 0 (no KL divergence term)
- Entropy coefficient 0.001
- Actor LR 5e-7
- Reward beta train 0.05
- Reward LR 1e-6
- Reward grad clip 10
- Reward RM coefficient 5

## Evaluation

**Coding**
|  | Leetcode | LCB\_generation |
| :---- | :---- | :---- |
| ZR1-1.5B | **40%** | **39.74%** |
| R1-Distill-Qwen-1.5B | 12.22% | 24.36% |
| DeepCoder-1.5B | 21.11% | 35.90% |
| OpenHands-LM-1.5B | 18.88% | 29.49% |
| Qwen2.5-1.5B-Instruct | 20.56% | 24.36% |
| Qwen2.5-Coder-3B-Instruct | 35.55% | 39.74% |
| Llama-3.1-8B-Instruct | 14.44% | 23.08% |
| Llama-3.1-70B-Instruct | 37.22% | 34.62% |
| Eurus-2-7B-PRIME | 34.44% | 32.05% |
| Mistral-Small-2503 | \- | <u>38.46%</u> |
| Gemma-3-27b-it | \- | <u>39.74%</u> |
| Claude-3-Opus | \- | <u>37.18%</u> |

**LiveBench**
| Model | AMPS Hard | Math\_Comp | LCB\_Generation | Coding\_Completion |
| :---- | :---- | :---- | :---- | :---- |
| ZR1-1.5B | **74%** | 60.42% | **39.74%** | **12%** |
| DeepCoder-1.5B | 69% | **61.46%** | 35.90% | **12%** |
| DeepScaleR-1.5B | 64% | 50% | 24.36% | 6% |
| OpenHands-LM-1.5B | 24% | 29.48% | 29.49% | 8% |
| R1-Distill-1.5B | 54% | 37.50% | 24.36% | 6% |
| Qwen2.5-1.5B-Instruct | 38% | 20.83% | 24.36% | 4% |
| Qwen2.5-Math-1.5B-Instruct | 49% | 36.46% | 0% | 0% |
| Qwen2.5-3B-Instruct | 41% | 17.71% | 28.21% | 10% |
| R1-Distill-7B | 74% | 61.46% | 44.87% | 14% |
| Qwen2.5-7B-Instruct | 56% | 29.17% | 38.46% | 40% |
| Qwen2.5-Math-7B-Instruct | 62% | 45.83% | 16.67% | 4% |
| R1-Distill-14B | 77% | 69.79% | 64.10% | 18% |
| Qwen2.5-14B-Instruct | 59% | 43.75% | 46.15% | 54% |
| R1-Distill-32B | 74% | 75% | 60.26% | 26% |
| QwQ-32B-Preview | 78% | 67.71% | 52.56% | 22% |
| QwQ-32B | 83% | 87.5% | 87.18% | 46% |
| Qwen2.5-32B-Instruct | 62% | 54.17% | 51.23% | 54% |
| Qwen2.5-Coder-32B-Instruct | 48% | 53.13% | 55.13% | 58% |
| R1-Distill-Llama-70B\* | 65% | 78.13% | 69.23% | 34% |
| Qwen2.5-72B-Instruct | 66% | 52.08% | 50% | 62% |
| Qwen2.5-Math-72B-Instruct | 56% | 59.38% | 42.31% | 42% |
| DeepSeek-R1\* | 88% | 88.54% | 79.48% | 54% |

**General Math**
| model | AIME24 | AIME25 | AMC22\_23 | AMC24 | GPQA-D | MATH500 | Minerva | Olympiad |
| :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- | :---- |
| ZR1-1.5B | 33.75% | 27.29% | 72.06% | 59.17% | **37.91%** | 88.34% | 33.52% | 56.87% |
| ZR1-1.5B (greedy) | 40% | 26.67% | 71.08% | 53.33% | 37.88% | **89.40%** | 32.72% | 57.93% |
| DeepScaleR-1.5B | **42.92%** | **27.71%** | 74.40% | **60.69%** | 34.66% | 89.36% | **35.50%** | **59.37%** |
| DeepScaleR-1.5B (greedy) | 33.33% | 33.33% | 67.47% | 57.77% | 29.29% | 84.60% | 31.62% | 52.44% |
| DeepCoder-1.5B | 41.88% | 24.79% | **75.30%** | 59.72% | 36.46% | 83.60% | 32.01% | 56.39% |
| Still-3-1.5B | 31.04% | 23.54% | 65.51% | 56.94% | 34.56% | 86.55% | 33.50% | 53.55% |
| Open-RS3-1.5B | 31.67% | 23.75% | 64.08% | 51.67% | 35.61% | 84.65% | 29.46% | 52.13% |
| R1-Distill-1.5B | 28.96% | 22.50% | 63.59% | 50.83% | 33.87% | 84.65% | 31.39% | 51.11% |
| R1-Distill-1.5B (greedy) | 26.67% | 13.33% | 51.81% | 24.44% | 30.81% | 73.40% | 25.74% | 40% |
| Qwen2.5-Math-1.5B-Instruct (greedy) | 10% | 6.67% | 42.17% | 26.67% | 28.28% | 75.20% | 28.31% | 40.74% |
| Qwen2.5-Math-7B-Instruct (greedy) | 20% | 3.33% | 46.99% | 31.11% | 32.32% | 83% | 37.13% | 42.22% |
| Qwen2.5-Math-72B-Instruct (greedy) | 26.67% | 6.67% | 59.04% | 46.67% | 43.94% | 85.40% | 42.65% | 50.37% |
| Eurus-2-7B-PRIME (greedy) | 20% | 13.33% | 56.62% | 40% | 36.36% | 81.20% | 36.76% | 44.15% |
| DeepHermes-3-Llama-3-3B (think prompt, greedy) | 0% | 3.33% | 12.05% | 11.11% | 30.30% | 34.40% | 10.66% | 10.52% |
| OpenHands-LM-1.5B (greedy) | 0% | 0% | 10.84% | 4.44% | 23.74% | 36.80% | 12.50% | 10.22% |

**Short CoT**

Our direct answer system prompt was: “Give a direct answer without thinking first.”

The table reports the average greedy pass@1 score across the following math evals: AIME24, AIME25, AMC22\_23, AMC24, GPQA-Diamond, MATH-500, MinervaMath, OlympiadBench

|  | avg pass@1 | max\_tokens |
| :---- | :---- | :---- |
| ZR1-1.5B | 51.13% | 32768 |
| ZR1-1.5B (truncated) | 46.83% | 4096 |
| ZR1-1.5B (direct answer prompt) | 45.38% | 4096 |
| ZR1-1.5B (truncated) | **40.39%** | 2048 |
| ZR1-1.5B (direct answer prompt) | 37% | 2048 |
| Qwen-2.5-Math-1.5B-Instruct  | 32.25% | 2048 |
| Qwen-2.5-Math-7B-Instruct | 37.01% | 2048 |

For Leetcode and LiveBench, we report pass@1 accuracy with greedy sampling. For the rest of the evaluations we report pass@1 accuracy averaged over 16 samples per question, with temperature 0.6 and top_p 0.95.

We use the following settings for SGLang:

```
python -m sglang.launch_server --model-path <model> --host 0.0.0.0 --port 5001 --mem-fraction-static=0.8 --dtype bfloat16 --random-seed 0 --chunked-prefill-size -1 --attention-backend triton --sampling-backend pytorch --disable-radix-cache --disable-cuda-graph-padding  --disable-custom-all-reduce --disable-mla --triton-attention-reduce-in-fp32
```

For vllm we disable prefix caching and chunked prefill.