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README.md

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+---
+license: cc-by-4.0
+base_model:
+- Qwen/Qwen2.5-14B
+datasets:
+- nvidia/OpenMathReasoning
+language:
+- en
+tags:
+- nvidia
+- math
+library_name: transformers
+---
+
+# <span style="color: #7FFF7F;">OpenMath-Nemotron-14B GGUF Models</span>
+
+
+## <span style="color: #7F7FFF;">Model Generation Details</span>
+
+This model was generated using [llama.cpp](https://github.com/ggerganov/llama.cpp) at commit [`19e899c`](https://github.com/ggerganov/llama.cpp/commit/19e899ce21a7c9ffcf8bb2b22269a75f6e078f8f).
+
+
+
+
+## <span style="color: #7FFF7F;">Ultra-Low-Bit Quantization with IQ-DynamicGate (1-2 bit)</span>
+
+Our latest quantization method introduces **precision-adaptive quantization** for ultra-low-bit models (1-2 bit), with benchmark-proven improvements on **Llama-3-8B**. This approach uses layer-specific strategies to preserve accuracy while maintaining extreme memory efficiency.
+
+### **Benchmark Context**
+All tests conducted on **Llama-3-8B-Instruct** using:
+- Standard perplexity evaluation pipeline
+- 2048-token context window
+- Same prompt set across all quantizations
+
+### **Method**
+- **Dynamic Precision Allocation**:  
+  - First/Last 25% of layers → IQ4_XS (selected layers)  
+  - Middle 50% → IQ2_XXS/IQ3_S (increase efficiency)  
+- **Critical Component Protection**:  
+  - Embeddings/output layers use Q5_K  
+  - Reduces error propagation by 38% vs standard 1-2bit  
+
+### **Quantization Performance Comparison (Llama-3-8B)**
+
+| Quantization | Standard PPL | DynamicGate PPL | Δ PPL   | Std Size | DG Size | Δ Size | Std Speed | DG Speed |
+|--------------|--------------|------------------|---------|----------|---------|--------|-----------|----------|
+| IQ2_XXS      | 11.30        | 9.84             | -12.9%  | 2.5G     | 2.6G    | +0.1G  | 234s      | 246s     |
+| IQ2_XS       | 11.72        | 11.63            | -0.8%   | 2.7G     | 2.8G    | +0.1G  | 242s      | 246s     |
+| IQ2_S        | 14.31        | 9.02             | -36.9%  | 2.7G     | 2.9G    | +0.2G  | 238s      | 244s     |
+| IQ1_M        | 27.46        | 15.41            | -43.9%  | 2.2G     | 2.5G    | +0.3G  | 206s      | 212s     |
+| IQ1_S        | 53.07        | 32.00            | -39.7%  | 2.1G     | 2.4G    | +0.3G  | 184s      | 209s     |
+
+**Key**:
+- PPL = Perplexity (lower is better)
+- Δ PPL = Percentage change from standard to DynamicGate
+- Speed = Inference time (CPU avx2, 2048 token context)
+- Size differences reflect mixed quantization overhead
+
+**Key Improvements:**
+- 🔥 **IQ1_M** shows massive 43.9% perplexity reduction (27.46 → 15.41)
+- 🚀 **IQ2_S** cuts perplexity by 36.9% while adding only 0.2GB
+- ⚡ **IQ1_S** maintains 39.7% better accuracy despite 1-bit quantization
+
+**Tradeoffs:**
+- All variants have modest size increases (0.1-0.3GB)
+- Inference speeds remain comparable (<5% difference)
+
+
+### **When to Use These Models**
+📌 **Fitting models into GPU VRAM**
+
+✔ **Memory-constrained deployments**
+
+✔ **Cpu and Edge Devices** where 1-2bit errors can be tolerated 
+ 
+✔ **Research** into ultra-low-bit quantization
+
+
+
+## **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**  
+
+### `OpenMath-Nemotron-14B-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**.  
+
+### `OpenMath-Nemotron-14B-f16.gguf`  
+- Model weights stored in **F16**.  
+- Use if your device supports **FP16**, especially if BF16 is not available.  
+
+### `OpenMath-Nemotron-14B-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.  
+
+### `OpenMath-Nemotron-14B-f16-q8_0.gguf`  
+- **Output & embeddings** remain in **F16**.  
+- All other layers quantized to **Q8_0**.    
+
+### `OpenMath-Nemotron-14B-q4_k.gguf`  
+- **Output & embeddings** quantized to **Q8_0**.  
+- All other layers quantized to **Q4_K**.  
+- Good for **CPU inference** with limited memory.  
+
+### `OpenMath-Nemotron-14B-q4_k_s.gguf`  
+- Smallest **Q4_K** variant, using less memory at the cost of accuracy.  
+- Best for **very low-memory setups**.  
+
+### `OpenMath-Nemotron-14B-q6_k.gguf`  
+- **Output & embeddings** quantized to **Q8_0**.  
+- All other layers quantized to **Q6_K** .  
+
+### `OpenMath-Nemotron-14B-q8_0.gguf`  
+- Fully **Q8** quantized model for better accuracy.  
+- Requires **more memory** but offers higher precision.  
+
+### `OpenMath-Nemotron-14B-iq3_xs.gguf`  
+- **IQ3_XS** quantization, optimized for **extreme memory efficiency**.  
+- Best for **ultra-low-memory devices**.  
+
+### `OpenMath-Nemotron-14B-iq3_m.gguf`  
+- **IQ3_M** quantization, offering a **medium block size** for better accuracy.  
+- Suitable for **low-memory devices**.  
+
+### `OpenMath-Nemotron-14B-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>
+❤ **Please click "Like" if you find this useful!**  
+Help me test my **AI-Powered Network Monitor Assistant** with **quantum-ready security checks**:  
+👉 [Free Network Monitor](https://readyforquantum.com/dashboard/?assistant=open)  
+
+💬 **How to test**:  
+ Choose an **AI assistant type**:  
+   - `TurboLLM` (GPT-4o-mini)  
+   - `HugLLM` (Hugginface Open-source)  
+   - `TestLLM` (Experimental CPU-only)  
+
+### **What I’m Testing**  
+I’m pushing the limits of **small open-source models for AI network monitoring**, specifically:  
+- **Function calling** against live network services  
+- **How small can a model go** while still handling:  
+  - Automated **Nmap scans**  
+  - **Quantum-readiness checks**  
+  - **Network Monitoring tasks**  
+
+🟡 **TestLLM** – Current experimental model (llama.cpp on 2 CPU threads):  
+- ✅ **Zero-configuration setup**  
+- ⏳ 30s load time (slow inference but **no API costs**)  
+- 🔧 **Help wanted!** If you’re into **edge-device AI**, let’s collaborate!  
+
+### **Other Assistants**  
+🟢 **TurboLLM** – Uses **gpt-4o-mini** for: 
+- **Create custom cmd processors to run .net code on Free Network Monitor Agents**
+- **Real-time network diagnostics and monitoring**
+- **Security Audits**
+- **Penetration testing** (Nmap/Metasploit)  
+- 🔑 Get more tokens by logging in or [downloading our Free Network Monitor Agent with integrated AI Assistant](https://readyforquantum.com/download)  
+
+🔵 **HugLLM** – Latest Open-source models:  
+- 🌐 Runs on Hugging Face Inference API  
+
+### 💡 **Example commands to you could test**:  
+1. `"Give me info on my websites SSL certificate"`  
+2. `"Check if my server is using quantum safe encyption for communication"`  
+3. `"Run a comprehensive security audit on my server"`
+4. '"Create a cmd processor to .. (what ever you want)" Note you need to install a Free Network Monitor Agent to run the .net code from. This is a very flexible and powerful feature. Use with caution!
+
+
+
+# OpenMath-Nemotron-14B
+
+OpenMath-Nemotron-14B is created by finetuning [Qwen/Qwen2.5-14B](https://huggingface.co/Qwen/Qwen2.5-14B) on [OpenMathReasoning](https://huggingface.co/datasets/nvidia/OpenMathReasoning) dataset.
+This model is ready for commercial use.
+
+![Evaluation Results](./results.png)
+
+
+OpenMath-Nemotron models achieve state-of-the-art results on popular mathematical benchmarks. We present metrics as pass@1 (maj@64) where pass@1
+is an average accuracy across 64 generations and maj@64 is the result of majority voting. 
+Please see our [paper](https://arxiv.org/abs/2504.16891) for more details on the evaluation setup.
+
+| Model                         | AIME24 |  AIME25     |  HMMT-24-25     | HLE-Math    |
+|-------------------------------|-----------------|-------|-------|-------------|
+| DeepSeek-R1-Distill-Qwen-1.5B | 26.8 (60.0)     | 21.4 (36.7) | 14.2 (26.5) | 2.9 (5.0)   |
+| [OpenMath-Nemotron-1.5B](https://huggingface.co/nvidia/OpenMath-Nemotron-1.5B) CoT   | 61.6 (80.0)     | 49.5 (66.7) | 39.9 (53.6) | 5.4 (5.4)   |
+| [OpenMath-Nemotron-1.5B](https://huggingface.co/nvidia/OpenMath-Nemotron-1.5B) TIR   | 52.0 (83.3)     | 39.7 (70.0) | 37.2 (60.7) | 2.5 (6.2)   |
+| + Self GenSelect              | 83.3            | 70.0  | 62.2  | 7.9         |
+| + 32B GenSelect               | 83.3            | 70.0  | 62.8  | 8.3         |
+| DeepSeek-R1-Distill-Qwen-7B  | 54.4 (80.0)     | 38.6 (53.3) | 30.6 (42.9) | 3.3 (5.2)   |
+| [OpenMath-Nemotron-7B](https://huggingface.co/nvidia/OpenMath-Nemotron-7B) CoT    | 74.8 (80.0)     | 61.2 (76.7) | 49.7 (57.7) | 6.6 (6.6)   |
+| [OpenMath-Nemotron-7B](https://huggingface.co/nvidia/OpenMath-Nemotron-7B) TIR    | 72.9 (83.3)     | 57.5 (76.7) | 54.6 (66.3) | 7.8 (10.8)  |
+| + Self GenSelect              | 86.7            | 76.7  | 68.4  | 11.5        |
+| + 32B GenSelect               | 86.7            | 76.7  | 69.9  | 11.9        |
+| DeepSeek-R1-Distill-Qwen-14B | 65.8 (80.0)     | 48.4 (60.0) | 40.1 (52.0) | 4.2 (4.8)   |
+| [OpenMath-Nemotron-14B-MIX (kaggle)](https://huggingface.co/nvidia/OpenMath-Nemotron-14B-Kaggle) | 73.7 (86.7) | 57.9 (73.3) | 50.5 (64.8) | 5.7 (6.5)   |
+| [OpenMath-Nemotron-14B](https://huggingface.co/nvidia/OpenMath-Nemotron-14B) CoT   | 76.3 (83.3)     | 63.0 (76.7) | 52.1 (60.7) | 7.5 (7.6)   |
+| [OpenMath-Nemotron-14B](https://huggingface.co/nvidia/OpenMath-Nemotron-14B) TIR   | 76.3 (86.7)     | 61.3 (76.7) | 58.6 (70.9) | 9.5 (11.5)  |
+| + Self GenSelect              | 86.7            | 76.7  | 72.4  | 14.1        |
+| + 32B GenSelect               | 90.0            | 76.7  | 71.9  | 13.7        |
+| QwQ-32B                       | 78.1 (86.7)     | 66.5 (76.7) | 55.9 (63.3) | 9.0 (9.5)   |
+| DeepSeek-R1-Distill-Qwen-32B | 66.9 (83.3)     | 51.8 (73.3) | 39.9 (51.0) | 4.8 (6.0)   |
+| [OpenMath-Nemotron-32B](https://huggingface.co/nvidia/OpenMath-Nemotron-32B) CoT   | 76.5 (86.7)     | 62.5 (73.3) | 53.0 (59.2) | 8.3 (8.3)   |
+| [OpenMath-Nemotron-32B](https://huggingface.co/nvidia/OpenMath-Nemotron-32B) TIR   | 78.4 (93.3)     | 64.2 (76.7) | 59.7 (70.9) | 9.2 (12.5)  |
+| + Self GenSelect              | 93.3            | 80.0  | 73.5  | 15.7        |
+| DeepSeek-R1                   | 79.1 (86.7)     | 64.3 (73.3) | 53.0 (59.2) | 10.5 (11.4) |
+
+We used [a version of OpenMath-Nemotron-14B](https://huggingface.co/nvidia/OpenMath-Nemotron-14B-Kaggle) model to secure 
+the first place in [AIMO-2 Kaggle competition](https://www.kaggle.com/competitions/ai-mathematical-olympiad-progress-prize-2/leaderboard)!
+
+## Reproducing our results
+
+The pipeline we used to produce the data and models is fully open-sourced!
+
+- [Code](https://github.com/NVIDIA/NeMo-Skills)
+- [Models](https://huggingface.co/collections/nvidia/openmathreasoning-68072c0154a5099573d2e730)
+- [Dataset](https://huggingface.co/datasets/nvidia/OpenMathReasoning)
+- [Paper](https://arxiv.org/abs/2504.16891)
+
+We provide [all instructions](https://nvidia.github.io/NeMo-Skills/openmathreasoning1/)
+to fully reproduce our results, including data generation.
+
+## How to use the models?
+
+Our models can be used in 3 inference modes: chain-of-thought (CoT), tool-integrated reasoning (TIR) and generative solution selection (GenSelect).
+
+To run inference with CoT mode, you can use this example code snippet.
+
+```python
+import transformers
+import torch
+
+model_id = "nvidia/OpenMath-Nemotron-14B"
+
+pipeline = transformers.pipeline(
+    "text-generation",
+    model=model_id,
+    model_kwargs={"torch_dtype": torch.bfloat16},
+    device_map="auto",
+)
+
+messages = [
+    {
+        "role": "user", 
+        "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\n" + 
+        "What is the minimum value of $a^2+6a-7$?"},
+]
+
+outputs = pipeline(
+    messages,
+    max_new_tokens=4096,
+)
+print(outputs[0]["generated_text"][-1]['content'])
+```
+
+To run inference with TIR or GenSelect modes, we highly recommend to use our 
+[reference implementation in NeMo-Skills](https://nvidia.github.io/NeMo-Skills/openmathreasoning1/evaluation/).
+
+Please note that these models have not been instruction tuned on general data and thus might not provide good answers outside of math domain. 
+
+
+## Citation
+
+If you find our work useful, please consider citing us!
+
+```bibtex
+@article{moshkov2025aimo2,
+  title   = {AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset},
+  author  = {Ivan Moshkov and Darragh Hanley and Ivan Sorokin and Shubham Toshniwal and Christof Henkel and Benedikt Schifferer and Wei Du and Igor Gitman},
+  year    = {2025},
+  journal = {arXiv preprint arXiv:2504.16891}
+}
+```
+
+## Additional information
+
+### License/Terms of Use: <br> 
+
+GOVERNING TERMS: Use of this model is governed by [CC-BY-4.0](https://creativecommons.org/licenses/by/4.0/legalcode.en). 
+Additional Information: [Apache License Version 2.0](https://huggingface.co/Qwen/Qwen2.5-Math-1.5B/blob/main/LICENSE).
+
+### Deployment Geography: 
+
+Global <br> 
+
+### Use Case: <br> 
+
+This model is intended to facilitate research in the area of mathematical reasoning.  
+
+ 
+
+### Release Date:  <br> 
+
+Huggingface 04/23/2025 <br> 
+
+### Model Architecture: <br> 
+
+**Architecture Type:** Transformer decoder-only language model  <br> 
+
+**Network Architecture:** Qwen2.5 <br> 
+
+
+**This model was developed based on Qwen2.5-1.5B <br> 
+
+** This model has 1.5B of model parameters. <br> 
+
+### Input: <br> 
+
+**Input Type(s):** Text <br> 
+
+**Input Format(s):** String <br> 
+
+**Input Parameters:** One-Dimensional (1D) <br> 
+
+**Other Properties Related to Input:** Context length up to 131,072 tokens <br> 
+
+ 
+
+### Output: <br> 
+
+**Output Type(s):** Text <br> 
+
+**Output Format:** String <br> 
+
+**Output Parameters:** One-Dimensional (1D) <br> 
+
+**Other Properties Related to Output:** Context length up to 131,072 tokens <br> 
+
+ 
+
+Our AI models are designed and/or optimized to run on NVIDIA GPU-accelerated systems. By leveraging NVIDIA’s hardware (e.g. GPU cores) and software frameworks (e.g., CUDA libraries), the model achieves faster training and inference times compared to CPU-only solutions. <br> 
+
+ 
+
+### Software Integration : <br> 
+
+**Runtime Engine(s):** <br> 
+
+* Tensor RT / Triton <br> 
+
+ 
+
+**Supported Hardware Microarchitecture Compatibility:** <br> 
+
+* NVIDIA Ampere <br> 
+
+* NVIDIA Hopper <br> 
+
+ 
+
+**Preferred Operating System(s):** <br> 
+
+* Linux <br> 
+
+ 
+
+### Model Version(s): 
+
+[OpenMath-Nemotron-1.5B](https://huggingface.co/nvidia/OpenMath-Nemotron-1.5B)
+
+[OpenMath-Nemotron-7B](https://huggingface.co/nvidia/OpenMath-Nemotron-7B)
+
+[OpenMath-Nemotron-14B](https://huggingface.co/nvidia/OpenMath-Nemotron-14B)
+
+[OpenMath-Nemotron-32B](https://huggingface.co/nvidia/OpenMath-Nemotron-32B)
+
+
+# Ethical Considerations: 
+
+NVIDIA believes Trustworthy AI is a shared responsibility and we have established policies and practices to enable development for a wide array of AI applications.  When downloaded or used in accordance with our terms of service, developers should work with their internal model team to ensure this model meets requirements for the relevant industry and use case and addresses unforeseen product misuse. 
+
+For more detailed information on ethical considerations for this model, please see the Model Card++ [Explainability](./EXPLAINABILITY.md), [Bias](./BIAS.md), [Safety & Security](./SAFETY.md), and [Privacy](./PRIVACY.md) Subcards.
+
+Please report security vulnerabilities or NVIDIA AI Concerns [here](https://www.nvidia.com/en-us/support/submit-security-vulnerability/).