Model Card for Qwen2.5-1.5B-Open-R1-Distill

This model is a fine-tuned version of Qwen/Qwen2.5-1.5B-Instruct on the HuggingFaceH4/Bespoke-Stratos-17k dataset. It has been trained using TRL.

Quick start

from transformers import AutoTokenizer, AutoModelForCausalLM
model_id = "tyfeng1997/Qwen2.5-1.5B-Open-R1-Distill" #instruct
model = AutoModelForCausalLM.from_pretrained(model_id, device_map="cuda")
tokenizer = AutoTokenizer.from_pretrained(model_id)

# Prepare the messages
messages = [
    {
        "role": "system",
        "content": """Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop well-considered thinking process. Please structure your response into two main sections: Thought and Solution. In the Thought section, detail your reasoning process using the specified format: <|begin_of_thought|> {thought with steps separated with '\n\n'} <|end_of_thought|> Each step should include detailed considerations such as analisying questions, summarizing relevant findings, brainstorming new ideas, verifying the accuracy of the current steps, refining any errors, and revisiting previous steps. In the Solution section, based on various attempts, explorations, and reflections from the Thought section, systematically present the final solution that you deem correct. The solution should remain a logical, accurate, concise expression style and detail necessary step needed to reach the conclusion, formatted as follows: <|begin_of_solution|> {final formatted, precise, and clear solution} <|end_of_solution|> Now, try to solve the following question through the above guidelines:"""
    },
    {
        "role": "user",
        "content": """A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the triangles is 21 inches, what is the perimeter, in inches, of the regular hexagon?"""
    }
]

# Apply chat template
prompt = tokenizer.apply_chat_template(messages, tokenize=False)

# Tokenize the prompt
inputs = tokenizer(prompt, return_tensors="pt").to(model.device)

# Generate
outputs = model.generate(
    inputs.input_ids,
    max_new_tokens=10000,
    pad_token_id=tokenizer.pad_token_id,
    eos_token_id=tokenizer.eos_token_id
)

# Decode and print the response
response = tokenizer.decode(outputs[0], skip_special_tokens=True)
print(response)

output

<|begin_of_thought|>

Okay, so I need to figure out the perimeter of a regular hexagon when it's divided into six equilateral triangles, each with a perimeter of 21 inches. Let me start by recalling some basic properties about regular polygons and how their sides relate.

First, a regular polygon has all its sides equal in length. So if a hexagon is regular, then all six of its sides are congruent. Similarly, since it's divided into six equilateral triangles, each triangle must have three sides of equal length. Therefore, each side of the hexagon would also be equal to the side of these triangles.

Given that the perimeter of one of the equilateral triangles is 21 inches, we can determine the length of one side of the triangle. Since an equilateral triangle has three equal sides, dividing the total perimeter by three gives us the length of each side. 

Let me do the calculation:

Perimeter of one triangle = 21 inches

Number of sides per triangle = 3

Length of each side = Perimeter / Number of sides

= 21 / 3

= 7 inches

So each side of the hexagon (and thus each side of the triangles) measures 7 inches.

Now, remember that a regular hexagon has six sides. If each side is 7 inches long, then multiplying the number of sides by the length of each side will give the total perimeter of the hexagon. 

Total perimeter = Number of sides × Length of each side

Plugging in our numbers:

Total perimeter = 6 × 7

= 42 inches

Wait a second, hold on. Is there another way this could be approached? Maybe by considering the structure of the hexagon itself?

If the hexagon is made up of six equilateral triangles, maybe there's a pattern or formula for calculating the perimeter given the area or something else. But without more information like the area, maybe not. Alternatively, perhaps the problem expects a straightforward multiplication because each side is known.

Alternatively, think about the hexagon being composed of multiple smaller shapes. For example, perhaps the hexagon can be seen as two overlapping equilateral triangles, but that seems complicated here. Alternatively, consider that each triangle contributes to the overall shape's perimeter, which adds up to the entire perimeter of the hexagon.

Another angle: How does the division affect the perimeter? If the hexagon is divided into six equilateral triangles, does that mean each side of the hexagon includes parts of those triangles' edges? Or are they separate lines forming the outer boundary?

Hmm, let me visualize. Imagine cutting a regular hexagon along its sides. If you make cuts parallel to each side, creating six identical smaller hexagons, then each small hexagon would have six sides. However, each original large hexagon might have sides that are part of the smaller ones, depending on where you cut them. But the key point is that each side of the large hexagon is shared between two adjacent triangles, right? Because each triangle shares a side with two others. Wait, no. Wait, each vertex of the large hexagon is connected to three vertices of the triangles. Wait, actually, in a regular hexagon, each vertex is connected to two other vertices via sides of the triangles. Wait, no, wait, the interior angles add up to 360 degrees, so each internal angle at a vertex is 120 degrees. Then, the central angle between two adjacent vertices is 60 degrees. Therefore, the distance from the center to a vertex is s, and the radius is s * sin(30°) ≈ s * 0.5. Therefore, each side of the hexagon is 2r * cos(30°) = 2s * √3/2 = s√3. Therefore, the perimeter is 6s√3. Which matches the answer derived earlier. So regardless of how the hexagon is divided into triangles, as long as it remains regular, the perimeter depends only on the side length. Hence, the answer should still be 42 inches.

But wait, just to confirm, even if the hexagon was divided into triangles with different side lengths, the perimeter would still be determined by adding up all the sides. Since the hexagon is regular, all sides are equal. Therefore, whether the triangles are equilateral, isosceles, etc., doesn't change the total length. Thus, the method holds true.

Therefore, after careful consideration and verification, my initial approach seems correct. The perimeter is indeed 42 inches.

**Final Answer**
The perimeter of the regular hexagon is \boxed{42} inches.

<|end_of_thought|>

<|begin_of_solution|>

To find the perimeter of a regular hexagon when it is divided into six equilateral triangles, each with a perimeter of 21 inches, follow these steps:

1. **Determine the side length of the equilateral triangles**: 
   - A regular hexagon consists of six equilateral triangles.
   - The perimeter of one equilateral triangle is 21 inches.
   - Divide the perimeter by 3 to get the length of each side:
     \[
     \text{Side length} = \frac{21}{3} = 7 \text{ inches}
     \]

2. **Calculate the perimeter of the regular hexagon**:
   - A regular hexagon has six equal sides.
   - Multiply the side length by 6:
     \[
     \text{Perimeter} = 6 \times 7 = 42 \text{ inches}
     \]

Thus, the perimeter of the regular hexagon is \(\boxed{42}\) inches.

<|end_of_solution|>

Training procedure

This model was trained with SFT.

Framework versions

• TRL: 0.15.0.dev0
• Transformers: 4.49.0.dev0
• Pytorch: 2.5.1
• Datasets: 3.2.0
• Tokenizers: 0.21.0

Note

This model was only trained for 1 epoch, so the MATH results are not good.

Citations

Cite TRL as:

@misc{vonwerra2022trl,
    title        = {{TRL: Transformer Reinforcement Learning}},
    author       = {Leandro von Werra and Younes Belkada and Lewis Tunstall and Edward Beeching and Tristan Thrush and Nathan Lambert and Shengyi Huang and Kashif Rasul and Quentin Gallouédec},
    year         = 2020,
    journal      = {GitHub repository},
    publisher    = {GitHub},
    howpublished = {\url{https://github.com/huggingface/trl}}
}