---
license: apache-2.0
language:
- zh
- en
library_name: transformers
pipeline_tag: text-generation
tags:
- causal-lm
- math
- reasoning
- tool-calling
- function-calling
- bilingual
- code
- symbolic-solver
- llm
- pytorch
base_model: Kirim-ai/Kirim-V1-base
datasets: []
metrics:
- math
- gsm8k
- minerva
model-index:
- name: Kirim-1-Math
  results: []
widget:
- text: "Solve: ∫(x² + 2x + 1)dx"
  example_title: "Calculus Integration"
- text: "解方程组: 2x + 3y = 12, 4x - y = 5"
  example_title: "System of Equations (Chinese)"
- text: "Use the calculator tool to compute 2^128"
  example_title: "Tool Calling Example"
---

# Kirim-1-Math (16B)

<div align="center">

<div align="center">

  <img src="https://imgur.com/n5uQJXF.png" alt="Helion-V2-Thinking Logo" width="70%"/>

</div>

---

**The First Kirim Model with Advanced Mathematical Reasoning and Tool Calling**

[Base Model](https://huggingface.co/Kirim-ai/Kirim-V1-base) • [模型卡](https://huggingface.co/Kirim-ai/Kirim-1-Math/blob/main/MODEL_CARD.md)

</div>


##  Introduction

**Kirim-1-Math** is a 16-billion parameter mathematical reasoning model, representing a major leap in the Kirim model series. As the **first Kirim model with tool calling capabilities**, it combines advanced mathematical problem-solving with the ability to use external tools and execute calculations.

###  Key Features

-  **Advanced Math Reasoning**: Trained on mathematical proofs, olympiad problems, and research papers
-  **Tool Calling**: First in Kirim series with function calling capabilities
-  **Symbolic Solver**: Handles algebraic manipulation, calculus, and symbolic computation
-  **Bilingual**: Solves problems in both Chinese and English
-  **Code Execution**: Can write and execute Python code for numerical solutions
-  **LaTeX Output**: Generates properly formatted mathematical expressions
-  **30B Parameters**: More powerful reasoning than 7B/13B variants

---

##  Model Specifications

| Parameter | Value | Comparison |
|-----------|-------|------------|
| Parameters | 16B | 2.3× larger than base |
| Hidden Size | 5,120 | Enhanced capacity |
| Layers | 48 | Deep reasoning |
| Attention Heads | 40 | Fine-grained attention |
| KV Heads | 8 (GQA) | Memory efficient |
| Context Length | 32,768 tokens | Extended problems |
| Vocabulary | 102,400 | Same as base |
| Tool Calling | ✅ Yes | **New feature!** |
| Precision | BFloat16 | High quality |

### Architecture Highlights

- **Deeper Network**: 48 layers for complex multi-step reasoning
- **Wider Hidden States**: 5,120 dimensions for richer representations
- **Grouped Query Attention**: 5:1 ratio (40:8) for efficiency
- **Extended Training**: Specialized on mathematical datasets

---

##  Quick Start

### Installation

```bash
pip install transformers torch accelerate sympy
```

### Basic Usage

```python
from transformers import AutoModelForCausalLM, AutoTokenizer

# Load model
model = AutoModelForCausalLM.from_pretrained(
    "Kirim-ai/Kirim-1-Math",
    torch_dtype="auto",
    device_map="auto",
    trust_remote_code=True
)

tokenizer = AutoTokenizer.from_pretrained(
    "Kirim-ai/Kirim-1-Math",
    trust_remote_code=True
)

# Solve a math problem
messages = [
    {"role": "user", "content": "Solve the quadratic equation: x² - 5x + 6 = 0"}
]

inputs = tokenizer.apply_chat_template(
    messages,
    return_tensors="pt",
    add_generation_prompt=True
).to(model.device)

outputs = model.generate(
    inputs,
    max_new_tokens=2048,
    temperature=0.1,  # Lower temperature for math
    top_p=0.95,
    do_sample=False   # Deterministic for accuracy
)

response = tokenizer.decode(outputs[0], skip_special_tokens=True)
print(response)
```

---

##  Tool Calling

Kirim-1-Math is the **first Kirim model** with built-in tool calling capabilities.

### Available Tools

The model can use these built-in mathematical tools:

1. **Calculator**: Precise arithmetic operations
2. **Symbolic Solver**: Algebraic manipulations
3. **Code Executor**: Run Python/SymPy code
4. **Plot Generator**: Create mathematical visualizations
5. **Theorem Lookup**: Access mathematical theorems and formulas

### Tool Calling Example

```python
messages = [
    {
        "role": "user",
        "content": "Calculate 2^1024 and tell me how many digits it has"
    }
]

# Model will automatically decide to use calculator tool
inputs = tokenizer.apply_chat_template(messages, return_tensors="pt")
outputs = model.generate(inputs, max_new_tokens=2048)

# Response will include tool calls like:
# <tool_call>
# {
#   "name": "calculator",
#   "arguments": {
#     "expression": "2**1024"
#   }
# }
# </tool_call>
```

### Custom Tool Definition

```python
tools = [
    {
        "type": "function",
        "function": {
            "name": "scientific_calculator",
            "description": "Perform advanced scientific calculations",
            "parameters": {
                "type": "object",
                "properties": {
                    "expression": {
                        "type": "string",
                        "description": "Mathematical expression to evaluate"
                    },
                    "precision": {
                        "type": "integer",
                        "description": "Decimal precision",
                        "default": 10
                    }
                },
                "required": ["expression"]
            }
        }
    }
]

# Include tools in prompt
messages = [
    {"role": "system", "content": f"You have access to these tools: {tools}"},
    {"role": "user", "content": "Calculate sin(π/4) with 15 decimal places"}
]
```

---

##  Mathematical Capabilities

### 1. Algebraic Reasoning

```python
# Example: Solve system of equations
problem = """
解方程组:
2x + 3y = 12
4x - y = 5
"""

response = model.generate_solution(problem)
# Output includes step-by-step solution with reasoning
```

### 2. Calculus

```python
# Integration
problem = "Calculate: ∫(x³ + 2x² - x + 1)dx"

# Differentiation
problem = "Find dy/dx if y = ln(x²) + e^(3x)"
```

### 3. Probability & Statistics

```python
problem = """
A bag contains 5 red balls and 3 blue balls. 
What's the probability of drawing 2 red balls without replacement?
"""
```

### 4. Number Theory

```python
problem = "Prove that √2 is irrational"
# Model provides formal mathematical proof
```

### 5. Geometry

```python
problem = """
In triangle ABC, if AB = 5, BC = 7, and AC = 8,
find the area using Heron's formula.
"""
```

---


##  Use Cases

### 1. Educational Tutoring

```python
messages = [
    {
        "role": "user",
        "content": "I don't understand how to complete the square. Can you explain and show an example?"
    }
]
# Provides step-by-step explanations
```

### 2. Research Assistance

```python
messages = [
    {
        "role": "user",
        "content": "Help me verify this proof about convergence of infinite series"
    }
]
# Analyzes mathematical proofs
```

### 3. Homework Help

```python
messages = [
    {
        "role": "user",
        "content": "Solve these 10 calculus problems and show your work"
    }
]
# Solves problems with detailed steps
```

### 4. Competition Preparation

```python
messages = [
    {
        "role": "user",
        "content": "Give me 5 AMC-level problems to practice"
    }
]
# Generates practice problems
```

### 5. Code-Assisted Solving

```python
messages = [
    {
        "role": "user",
        "content": "Use numerical methods to find roots of x^5 - 3x^3 + 2x - 1 = 0"
    }
]
# Writes and executes numerical solver
```

---

##  Advanced Features

### Step-by-Step Reasoning

The model shows its work:

```
Problem: Solve x² - 5x + 6 = 0

Solution:
Step 1: Identify this as a quadratic equation in standard form ax² + bx + c = 0
        where a=1, b=-5, c=6

Step 2: Try factoring: We need two numbers that multiply to 6 and add to -5
        Those numbers are -2 and -3

Step 3: Factor: (x - 2)(x - 3) = 0

Step 4: Apply zero product property:
        x - 2 = 0  or  x - 3 = 0

Step 5: Solve each equation:
        x = 2  or  x = 3

Answer: x = 2 or x = 3
```

### LaTeX Output

```python
# Request LaTeX formatted output
messages = [
    {
        "role": "user",
        "content": "Solve this and format the answer in LaTeX: ∫(x² + 1)/(x³ + 3x + 1)dx"
    }
]

# Output includes:
# $$\int \frac{x^2 + 1}{x^3 + 3x + 1}dx = ...$$
```

### Symbolic Manipulation

Uses SymPy internally for symbolic computation:

```python
from sympy import symbols, expand, factor, simplify

# Model can perform:
# - Expansion: (x+1)³ → x³ + 3x² + 3x + 1
# - Factoring: x² - 4 → (x-2)(x+2)
# - Simplification: (x²-1)/(x-1) → x+1
```

---

##  Deployment

### System Requirements

**Minimum (4-bit Quantization):**
- GPU: 20GB VRAM (RTX 4090, A5000)
- RAM: 32GB
- Storage: 30GB

**Recommended (BF16):**
- GPU: 48GB VRAM (A40, A6000)
- RAM: 64GB
- Storage: 70GB

**Optimal (Production):**
- GPU: 80GB VRAM (A100, H100)
- RAM: 128GB
- Storage: 100GB SSD

### Quantization Options

```python
# 8-bit (30GB VRAM)
model = AutoModelForCausalLM.from_pretrained(
    "Kirim-ai/Kirim-1-Math",
    load_in_8bit=True,
    device_map="auto"
)

# 4-bit (20GB VRAM)
model = AutoModelForCausalLM.from_pretrained(
    "Kirim-ai/Kirim-1-Math",
    load_in_4bit=True,
    device_map="auto"
)
```

---

##  Training Details

### Training Data

- **Mathematics Corpus**: 500B tokens
  - Mathematical proofs and papers
  - Olympiad problems (IMO, USAMO, AMC)
  - Textbooks (algebra through advanced calculus)
  - Math Stack Exchange
  - arXiv math papers
  
- **Code**: 200B tokens
  - Mathematical Python libraries (NumPy, SymPy, SciPy)
  - Computational notebooks
  - Algorithm implementations

- **General**: 800B tokens
  - From Kirim-V1-base pre-training

**Total**: 1.5 Trillion tokens

### Training Process

**Stage 1: Continued Pre-training** (from Kirim-V1-base)
- Started from 13B base checkpoint
- Expanded to 30B parameters
- Trained on math-heavy corpus
- Duration: 45 days on 512x H100 GPUs

**Stage 2: Mathematical Instruction Tuning**
- 200K high-quality math problems with solutions
- Step-by-step reasoning examples
- Duration: 5 days

**Stage 3: Tool Calling Training**
- 50K tool-calling examples
- Function definition and execution
- Error handling and recovery
- Duration: 3 days

**Stage 4: Reinforcement Learning**
- Reward model based on solution correctness
- Self-verification training
- Duration: 7 days

---

##  Limitations

- **Computation Limits**: Cannot perform extremely large calculations without tools
- **Proof Verification**: May occasionally make logical errors in complex proofs
- **Theorem Knowledge**: Limited to theorems in training data (pre-Oct 2024)
- **Visual Math**: Cannot process images of equations or diagrams
- **Real-time Data**: Cannot access current mathematical research or live data

---

##  Model Series Comparison

| Model | Parameters | Purpose | Tool Calling | Best For |
|-------|------------|---------|--------------|----------|
| Kirim-V1-base | 13B | Foundation | ❌ | Research, fine-tuning |
| Kirim-V1-7B-Chat | 7B | Conversation | ❌ | Production chatbots |
| **Kirim-1-Math** | 16B | Mathematics | ✅ | **Math problems, STEM education** |
| Kirim-V2 (coming) | 30B+ | Multimodal | ✅ | Visual reasoning |

---

##  Citation

```bibtex
@misc{kirim2025math,
  title={Kirim-1-Math: Advanced Mathematical Reasoning with Tool Calling},
  author={Kirim AI Research Team},
  year={2025},
  publisher={Kirim AI},
  url={https://huggingface.co/Kirim-ai/Kirim-1-Math}
}
```

---

##  Contributing

We welcome contributions!

---

##  License

Apache License 2.0 - See [LICENSE](LICENSE) for details.