README.md

---
license: apache-2.0
language:
- en
- zh
base_model:
- Qwen/Qwen2.5-14B-Instruct
pipeline_tag: text-generation
library_name: transformers
tags:
- text-generation-inference
- trl
- vlm
- sft
- code
- math
model-index:
- name: Gauss-Opus-14B-R999
  results:
  - task:
      type: text-generation
      name: Text Generation
    dataset:
      name: IFEval (0-Shot)
      type: wis-k/instruction-following-eval
      split: train
      args:
        num_few_shot: 0
    metrics:
    - type: inst_level_strict_acc and prompt_level_strict_acc
      value: 39.07
      name: averaged accuracy
    source:
      url: https://huggingface.co/spaces/open-llm-leaderboard/open_llm_leaderboard#/?search=prithivMLmods%2FGauss-Opus-14B-R999
      name: Open LLM Leaderboard
  - task:
      type: text-generation
      name: Text Generation
    dataset:
      name: BBH (3-Shot)
      type: SaylorTwift/bbh
      split: test
      args:
        num_few_shot: 3
    metrics:
    - type: acc_norm
      value: 44.94
      name: normalized accuracy
    source:
      url: https://huggingface.co/spaces/open-llm-leaderboard/open_llm_leaderboard#/?search=prithivMLmods%2FGauss-Opus-14B-R999
      name: Open LLM Leaderboard
  - task:
      type: text-generation
      name: Text Generation
    dataset:
      name: MATH Lvl 5 (4-Shot)
      type: lighteval/MATH-Hard
      split: test
      args:
        num_few_shot: 4
    metrics:
    - type: exact_match
      value: 57.55
      name: exact match
    source:
      url: https://huggingface.co/spaces/open-llm-leaderboard/open_llm_leaderboard#/?search=prithivMLmods%2FGauss-Opus-14B-R999
      name: Open LLM Leaderboard
  - task:
      type: text-generation
      name: Text Generation
    dataset:
      name: GPQA (0-shot)
      type: Idavidrein/gpqa
      split: train
      args:
        num_few_shot: 0
    metrics:
    - type: acc_norm
      value: 18.9
      name: acc_norm
    source:
      url: https://huggingface.co/spaces/open-llm-leaderboard/open_llm_leaderboard#/?search=prithivMLmods%2FGauss-Opus-14B-R999
      name: Open LLM Leaderboard
  - task:
      type: text-generation
      name: Text Generation
    dataset:
      name: MuSR (0-shot)
      type: TAUR-Lab/MuSR
      args:
        num_few_shot: 0
    metrics:
    - type: acc_norm
      value: 27.83
      name: acc_norm
    source:
      url: https://huggingface.co/spaces/open-llm-leaderboard/open_llm_leaderboard#/?search=prithivMLmods%2FGauss-Opus-14B-R999
      name: Open LLM Leaderboard
  - task:
      type: text-generation
      name: Text Generation
    dataset:
      name: MMLU-PRO (5-shot)
      type: TIGER-Lab/MMLU-Pro
      config: main
      split: test
      args:
        num_few_shot: 5
    metrics:
    - type: acc
      value: 44.53
      name: accuracy
    source:
      url: https://huggingface.co/spaces/open-llm-leaderboard/open_llm_leaderboard#/?search=prithivMLmods%2FGauss-Opus-14B-R999
      name: Open LLM Leaderboard
---
![ccccccccccccc.png](https://cdn-uploads.huggingface.co/production/uploads/65bb837dbfb878f46c77de4c/Ii0oEprS2lm6Zoama7CPe.png)

# **Gauss-Opus-14B-R999**  

> Gauss-Opus-14B-R999 is based on the Qwen 2.5 14B modality architecture, designed to enhance mathematical and constructive reasoning capabilities. This model is optimized for advanced problem-solving, logical structuring, and mathematical comprehension. It excels in numerical reasoning, theorem proving, and multi-step calculations. Fine-tuned with specialized datasets in mathematics, physics, and formal logic, it delivers structured, high-accuracy outputs with a strong emphasis on precision and clarity.  

## **Key Improvements**  
1. **Enhanced Mathematical Reasoning**: Optimized for algebra, calculus, number theory, and logical deduction, providing precise and structured solutions.  
2. **Improved Instruction Following**: Capable of interpreting and following complex mathematical proofs, equations, and problem-solving instructions with high accuracy.  
3. **Versatile Adaptability**: Handles diverse reasoning tasks, including step-by-step solutions, mathematical proofs, and constructive problem-solving.  
4. **Long-Context Support**: Supports up to 128K tokens for input context and can generate up to 8K tokens in a single output, making it ideal for detailed mathematical derivations.  
5. **Multilingual Proficiency**: Supports over 29 languages, including English, Chinese, French, Spanish, Portuguese, German, Italian, Russian, Japanese, Korean, Vietnamese, Thai, Arabic, and more, ensuring broad accessibility.  

## **Quickstart with transformers**  

Here is a code snippet with `apply_chat_template` to show you how to load the tokenizer and model and generate content:  

```python
from transformers import AutoModelForCausalLM, AutoTokenizer

model_name = "prithivMLmods/Gauss-Opus-14B-R999"

model = AutoModelForCausalLM.from_pretrained(
    model_name,
    torch_dtype="auto",
    device_map="auto"
)
tokenizer = AutoTokenizer.from_pretrained(model_name)

prompt = "Solve the integral \int x^2 dx and explain the steps."
messages = [
    {"role": "system", "content": "You are a mathematical assistant specialized in problem-solving and theorem proving."},
    {"role": "user", "content": prompt}
]
text = tokenizer.apply_chat_template(
    messages,
    tokenize=False,
    add_generation_prompt=True
)
model_inputs = tokenizer([text], return_tensors="pt").to(model.device)

generated_ids = model.generate(
    **model_inputs,
    max_new_tokens=512
)
generated_ids = [
    output_ids[len(input_ids):] for input_ids, output_ids in zip(model_inputs.input_ids, generated_ids)
]

response = tokenizer.batch_decode(generated_ids, skip_special_tokens=True)[0]
```  

## **Intended Use**  
1. **Mathematical Problem-Solving**:  
   Designed for high-precision mathematical reasoning, step-by-step calculations, and structured solutions.  

2. **Theorem Proving and Logical Reasoning**:  
   Useful for verifying mathematical proofs, formal logic derivations, and theorem-based reasoning.  

3. **STEM Education and Research**:  
   Ideal for educators, researchers, and students requiring assistance in complex problem-solving and mathematical modeling.  

4. **Algorithm Development and Optimization**:  
   Supports structured reasoning in algorithmic problem-solving, coding optimizations, and computational logic.  

5. **Long-Form Explanatory Content**:  
   Can generate detailed mathematical articles, research summaries, and explanatory guides with structured step-by-step reasoning.  

6. **Multilingual Mathematical Assistance**:  
   Supports global accessibility for mathematical discussions, translations, and problem explanations across multiple languages.  

## **Limitations**  
1. **Hardware Requirements**:  
   Requires high-memory GPUs or TPUs due to its large parameter size and long-context support.  

2. **Potential Bias in Training Data**:  
   While optimized for accuracy, the model may inherit biases from training data in certain problem-solving approaches.  

3. **Complexity in Abstract Theories**:  
   May struggle with highly abstract or unsolved mathematical problems that require intuitive leaps beyond computational logic.  

4. **Error Propagation in Extended Proofs**:  
   Small errors in early steps may compound in multi-step proofs and long-form mathematical derivations.  

5. **Prompt Sensitivity**:  
   The quality of responses depends on how well the problem is structured and framed within the input prompt.
# [Open LLM Leaderboard Evaluation Results](https://huggingface.co/spaces/open-llm-leaderboard/open_llm_leaderboard)
Detailed results can be found [here](https://huggingface.co/datasets/open-llm-leaderboard/prithivMLmods__Gauss-Opus-14B-R999-details)!
Summarized results can be found [here](https://huggingface.co/datasets/open-llm-leaderboard/contents/viewer/default/train?q=prithivMLmods%2FGauss-Opus-14B-R999&sort[column]=Average%20%E2%AC%86%EF%B8%8F&sort[direction]=desc)!

|      Metric       |Value (%)|
|-------------------|--------:|
|**Average**        |    38.80|
|IFEval (0-Shot)    |    39.07|
|BBH (3-Shot)       |    44.94|
|MATH Lvl 5 (4-Shot)|    57.55|
|GPQA (0-shot)      |    18.90|
|MuSR (0-shot)      |    27.83|
|MMLU-PRO (5-shot)  |    44.53|