Why PyThagorean? 🐍
Pythagorean = python + `py'thagoras [ pythagoras resembles math ]
PyThagorean [Python + Math] is a Python and mathematics-based model designed to solve mathematical problems using Python libraries and coding. It has been fine-tuned on 1.5 million entries and is built on LLaMA's architecture. The model supports different parameter sizes, including 10B, 3B, and 1B (Tiny). These instruction-tuned, text-only models are optimized for multilingual dialogue use cases, including agent-based retrieval and summarization tasks. PyThagorean leverages an auto-regressive language model that uses an optimized transformer architecture. The tuned versions employ supervised fine-tuning (SFT) and reinforcement learning with human feedback (RLHF) to align with human preferences for helpfulness and safety.
PyThagorean Model Performance Comparison
In this section, we compare the outputs of different versions of the PyThagorean model for solving the following mathematical problem:
Problem: Find all real numbers ( x ) such that: [ \frac{x^3+2x^2}{x^2+3x+2} + x = -6. ] Enter all the solutions, separated by commas.
Model Performance
| Model Version | Output | Code Snippet |
|---|---|---|
| PyThagorean-10B | Outputs the solution with a higher level of precision and accuracy. Typically, this model will handle more complex mathematical problems. | python<br> model_id = "prithivMLmods/PyThagorean-10B" <br> # (rest of the code) <br> print(outputs[0]["generated_text"][-1]) |
| PyThagorean-3B | Outputs a more concise solution compared to the 10B model but with slightly less accuracy. | python<br> model_id = "prithivMLmods/PyThagorean-3B" <br> # (rest of the code) <br> print(outputs[0]["generated_text"][-1]) |
| PyThagorean-Tiny | Outputs a quicker, smaller-scale solution but might sacrifice some accuracy in solving complex problems. | python<br> model_id = "prithivMLmods/PyThagorean-Tiny" <br> # (rest of the code) <br> print(outputs[0]["generated_text"][-1]) |
Key Takeaways:
- PyThagorean-10B provides the most accurate and detailed solutions, suitable for complex mathematical problems.
- PyThagorean-3B offers a balance between speed and accuracy, making it ideal for general use cases.
- PyThagorean-Tiny is designed for quick responses with simpler accuracy, suitable for smaller tasks or real-time applications.
Modalities:
| Model Name | Model Size | Link |
|---|---|---|
| PyThagorean-10B | 10B Parameters | PyThagorean-10B |
| PyThagorean-3B | 3B Parameters | PyThagorean-3B |
| PyThagorean-Tiny | Tiny Parameters 1B | PyThagorean-Tiny |
Intended Use of PyThagorean:
Mathematical Problem Solving: PyThagorean is designed to assist in solving complex mathematical problems using Python libraries, such as NumPy, SymPy, and others. It is optimized for performing arithmetic, algebra, calculus, statistics, and more.
Code Generation: The model can generate Python code to solve mathematical problems, making it useful for students, educators, and developers looking to automate or assist with mathematical computations.
Multilingual Support: PyThagorean is tailored for multilingual dialogues, which makes it versatile for global use in educational environments, coding communities, and research fields.
Summarization & Retrieval: It can be used for summarizing mathematical content, retrieving solutions or explanations, and aiding in knowledge extraction, particularly in the context of mathematical research.
Interactive Agent Tasks: PyThagorean can be deployed as an agent in various dialogue systems, where it helps interactively solve mathematical queries or provide mathematical assistance.
Limitations of PyThagorean:
Mathematical Accuracy: While the model is trained on vast datasets, the accuracy of its mathematical solutions can sometimes be limited, especially for very advanced or niche topics. It might require human verification for critical applications.
Model Size Limitations: Depending on the size of the model (10B, 3B, 1B), the performance in terms of speed and complexity of the problems it can solve may vary. Smaller versions may struggle with larger or more intricate tasks.
Domain-Specific Expertise: Though the model is fine-tuned on mathematical datasets, it may not excel in highly specialized mathematical fields, such as advanced theoretical physics or specific branches of pure mathematics, without further domain-specific tuning.
No Visual or Graphical Interpretation: PyThagorean focuses on text-based responses and does not support graphical representations of mathematical concepts or problems unless integrated with additional tools or libraries for visual output.
Contextual Limitations: Like most AI models, PyThagorean's ability to retain context over long conversations or across complex multi-step problems might be limited. It is designed for smaller, more straightforward queries or tasks.
Human Feedback Required for Optimization: Although reinforcement learning is employed to make PyThagorean more aligned with human preferences, it may still require manual adjustments or fine-tuning to ensure the best output for specific use cases.
- End of Article, Thanks for Reading 🤗!.
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| Collection | PyThagorean 🐍 | | Hugging Face | prithivMLmods |