Mungert/OpenMath-Nemotron-14B-GGUF

OpenMath-Nemotron-14B GGUF Models

Model Generation Details

This model was generated using llama.cpp at commit 19e899c.

Ultra-Low-Bit Quantization with IQ-DynamicGate (1-2 bit)

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.

🚀 If you find these models useful

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OpenMath-Nemotron-14B

OpenMath-Nemotron-14B is created by finetuning Qwen/Qwen2.5-14B on OpenMathReasoning dataset. This model is ready for commercial use.

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 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 CoT	61.6 (80.0)	49.5 (66.7)	39.9 (53.6)	5.4 (5.4)
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 CoT	74.8 (80.0)	61.2 (76.7)	49.7 (57.7)	6.6 (6.6)
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)	73.7 (86.7)	57.9 (73.3)	50.5 (64.8)	5.7 (6.5)
OpenMath-Nemotron-14B CoT	76.3 (83.3)	63.0 (76.7)	52.1 (60.7)	7.5 (7.6)
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 CoT	76.5 (86.7)	62.5 (73.3)	53.0 (59.2)	8.3 (8.3)
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 model to secure the first place in AIMO-2 Kaggle competition!

Reproducing our results

The pipeline we used to produce the data and models is fully open-sourced!

• Code
• Models
• Dataset
• Paper

We provide all instructions 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.

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.

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!

@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:

GOVERNING TERMS: Use of this model is governed by CC-BY-4.0. Additional Information: Apache License Version 2.0.

Deployment Geography:

Global

Use Case:

This model is intended to facilitate research in the area of mathematical reasoning.

Release Date:  

Huggingface 04/23/2025

Model Architecture:

Architecture Type: Transformer decoder-only language model  

Network Architecture: Qwen2.5

**This model was developed based on Qwen2.5-1.5B

** This model has 1.5B of model parameters.

Input:

Input Type(s): Text

Input Format(s): String

Input Parameters: One-Dimensional (1D)

Other Properties Related to Input: Context length up to 131,072 tokens

Output:

Output Type(s): Text

Output Format: String

Output Parameters: One-Dimensional (1D)

Other Properties Related to Output: Context length up to 131,072 tokens

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.

Software Integration :

Runtime Engine(s):

• Tensor RT / Triton
  

Supported Hardware Microarchitecture Compatibility:

• NVIDIA Ampere
  

• NVIDIA Hopper
  

Preferred Operating System(s):

• Linux
  

Model Version(s):

OpenMath-Nemotron-1.5B

OpenMath-Nemotron-7B

OpenMath-Nemotron-14B

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, Bias, Safety & Security, and Privacy Subcards.

Please report security vulnerabilities or NVIDIA AI Concerns here.