Llama-3.2-3B-Calculus-v2

$\displaystyle \int f(x) \, dx \quad \text{and} \quad \frac{d}{dx} f(x)$

Specialized Fine-Tuned Model for Mathematical Reasoning

📌 Overview

Llama-3.2-3B-Calculus-v2 is a specialized large language model fine-tuned for mathematical reasoning, specifically targeting Differential and Integral Calculus. Developed by Khurram Pervez, this model utilizes Chain-of-Thought (CoT) prompting to break down complex mathematical problems into logical, pedagogical steps.

The model was fine-tuned on an NVIDIA GeForce RTX 4060 Ti 16GB using 4-bit quantization (QLoRA) to maximize efficiency while maintaining high reasoning accuracy over 500 training steps.

🚀 Key Features

Step-by-Step Derivations: Optimized to explain the "why" behind each calculus rule.
Rule-Based Reasoning: Trained to identify and apply the Product Rule, Chain Rule, and Integration by Parts.
Calculus Specialist: Targeted performance on Taylor Series expansions, limits, and transcendental functions.
Efficient Local AI: Designed to run on consumer-grade hardware with minimal VRAM.

🛠️ Training Technicalities

Base Model: unsloth/Llama-3.2-3B-Instruct
Fine-tuning Method: QLoRA (Rank: 32, Alpha: 32)
Steps: 500 Steps
Final Train Loss: 0.4789
Optimizer: 8-bit AdamW
Scheduler: Cosine Decay
Hardware: Local Ubuntu Workstation (NVIDIA RTX 4060 Ti 16GB)

📖 Usage Instructions

Simple Inference

You can run this model using the unsloth library for 2x faster inference. We recommend a low temperature (0.1) for mathematical stability.

from unsloth import FastLanguageModel
import torch

# 1. Load Model and Tokenizer
model, tokenizer = FastLanguageModel.from_pretrained(
    "Khurram123/Llama-3.2-3B-Calculus-v2",
    max_seq_length = 2048,
    load_in_4bit = True,
)
FastLanguageModel.for_inference(model)

# 2. Define Calculus Problem
problem = "Find the derivative of f(x) = x^2 * ln(x) step by step."

# 3. Apply Llama 3.2 Instruct Template
messages = [{"role": "user", "content": problem}]
inputs = tokenizer.apply_chat_template(
    messages, 
    add_generation_prompt = True, 
    return_tensors = "pt"
).to("cuda")

# 4. Generate Solution
outputs = model.generate(
    input_ids = inputs, 
    max_new_tokens = 1024, 
    temperature = 0.1
)

# 5. Decode Output
response = tokenizer.decode(outputs[0], skip_special_tokens = True)
print(response.split("assistant")[-1].strip())

📊 Dataset Reference

The model was fine-tuned using a filtered subset of the MathInstruct dataset, focusing specifically on calculus-related instructional pairs to enhance symbolic manipulation and logical derivation.

Dataset Name: MathInstruct
Paper: MathInstruct: A Compiled Institution Dataset for Mathematical Reasoning
Source: TIGER-Lab (University of Waterloo, Ohio State University, et al.)

Citation

If you use this model or the underlying data, please cite the original MathInstruct paper:

@article{yue2023mathinstruct,
  title={Mathinstruct: A compiled instruction dataset for mathematical reasoning},
  author={Yue, Xiang and Qu, Xingwei and Zhang, Ge and Yao, Liang and Huo, Shijie and Sun, Wei and Caswell, Isaac and Xie, Wenhu and others},
  journal={arXiv preprint arXiv:2309.04408},
  year={2023}
}