Kirim-1-Math (16B)

The First Kirim Model with Advanced Mathematical Reasoning and Tool Calling

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

pip install transformers torch accelerate sympy

Basic Usage

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:

Calculator: Precise arithmetic operations
Symbolic Solver: Algebraic manipulations
Code Executor: Run Python/SymPy code
Plot Generator: Create mathematical visualizations
Theorem Lookup: Access mathematical theorems and formulas

Tool Calling Example

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

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

# 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

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

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

3. Probability & Statistics

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

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

5. Geometry

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

Use Cases

1. Educational Tutoring

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

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

3. Homework Help

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

4. Competition Preparation

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

5. Code-Assisted Solving

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

# 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:

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

# 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

@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 for details.

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Safetensors

Model size

16B params

Tensor type

BF16

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