size_categories:n<1K format:parquet modality:tabular modality:text library:datasets library:pandas library:mlcroissant library:polars library:distilabel region:us synthetic distilabel rlaif
---
size_categories: n<1K
dataset_info:
  features:
  - name: question_id
    dtype: int64
  - name: question
    dtype: string
  - name: options
    sequence: string
  - name: answer
    dtype: string
  - name: answer_index
    dtype: int64
  - name: cot_content
    dtype: string
  - name: category
    dtype: string
  - name: src
    dtype: string
  - name: instruction
    dtype: string
  - name: thinking
    dtype: string
  - name: output
    dtype: string
  - name: distilabel_metadata
    struct:
    - name: raw_input_text_generation_with_cot_reflection_0
      list:
      - name: content
        dtype: string
      - name: role
        dtype: string
    - name: raw_output_text_generation_with_cot_reflection_0
      dtype: string
  - name: model_name
    dtype: string
  splits:
  - name: train
    num_bytes: 737909
    num_examples: 70
  download_size: 349094
  dataset_size: 737909
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
tags:
- synthetic
- distilabel
- rlaif
---

<p align="left">
  <a href="https://github.com/argilla-io/distilabel">
    <img src="https://raw.githubusercontent.com/argilla-io/distilabel/main/docs/assets/distilabel-badge-light.png" alt="Built with Distilabel" width="200" height="32"/>
  </a>
</p>

# Dataset Card for meta-llama_Llama-3.1-8B-Instruct_cot_mmlu-pro_20241016_231257

This dataset has been created with [distilabel](https://distilabel.argilla.io/).



## Dataset Summary

This dataset contains a `pipeline.yaml` which can be used to reproduce the pipeline that generated it in distilabel using the `distilabel` CLI:

```console
distilabel pipeline run --config "https://huggingface.co/datasets/dvilasuero/meta-llama_Llama-3.1-8B-Instruct_cot_mmlu-pro_20241016_231257/raw/main/pipeline.yaml"
```

or explore the configuration:

```console
distilabel pipeline info --config "https://huggingface.co/datasets/dvilasuero/meta-llama_Llama-3.1-8B-Instruct_cot_mmlu-pro_20241016_231257/raw/main/pipeline.yaml"
```

## Dataset structure

The examples have the following structure per configuration:


<details><summary> Configuration: default </summary><hr>

```json
{
    "answer": "A",
    "answer_index": 0,
    "category": "math",
    "cot_content": "A: Let\u0027s think step by step. A characteristic of a ring is R is $n$ if the statement $ka = 0$ for all $a\\in 2Z$ implies that $k$ is a multiple of $n$. Assume that $ka = 0$ for all $a\\in 2Z$ for some $k$. In particular $2k = 0$. Hence $k=0$ and $n=0$. The answer is (A).",
    "distilabel_metadata": {
        "raw_input_text_generation_with_cot_reflection_0": [
            {
                "content": "You are a helpful AI assistant",
                "role": "system"
            },
            {
                "content": "You are an AI assistant that uses a Chain of Thought (CoT) approach with reflection to answer queries. You MUST STRICTLY follow these steps and format:\n\n1. Think through the problem step by step within ONE pair of \u003cthinking\u003e tags.\n2. Include one or more reflections on your thinking within \u003creflection\u003e tags inside the \u003cthinking\u003e section. This reflections must verify and be critical about previous thinking steps, not just common sense or cliche reflections. Only add reflections that are useful to verify and make sure the final output is correct.\n3. Make any necessary adjustments based on your reflections, still within the \u003cthinking\u003e tags.\n4. Verify your answer against common knowledge or basic facts relevant to the question type.\n5. Provide your final, concise answer within the \u003coutput\u003e tags.\n\nCRITICAL: \n- Use EXACTLY ONE pair of \u003cthinking\u003e tags.\n- Include AT LEAST ONE pair of \u003creflection\u003e tags INSIDE the \u003cthinking\u003e section.\n- ALWAYS include a verification step before your final answer.\n- Put your FINAL ANSWER ONLY inside the \u003coutput\u003e tags.\n- ALWAYS include both opening \u003coutput\u003e and closing \u003c/output\u003e tags.\n\nHere\u0027s the EXACT format you MUST follow:\n\n\u003cthinking\u003e\n[Your step-by-step reasoning goes here. This is your internal thought process, not the final answer.]\n\u003creflection\u003e\n[Your first reflection on your reasoning, checking for errors or improvements]\n\u003c/reflection\u003e\n[Any adjustments based on your first reflection]\n\u003creflection\u003e\n[Your second reflection, if needed]\n\u003c/reflection\u003e\n[Any further adjustments]\n\u003creflection\u003e\n[More verifications against common knowledge, basic facts, your thought process, all depending on the type of user query, don\u0027t overthink simple questions]\n\u003c/reflection\u003e\n[Final confirmation or any last adjustments based on verification]\n\u003c/thinking\u003e\n\u003coutput\u003e\n[Your final, concise answer to the query. This is the ONLY part that will be shown to the user.]\n\u003c/output\u003e\n\n\nFailure to follow this EXACT format, including the verification step, will result in incorrect processing of your response. Always double-check your reasoning and facts against well-established knowledge in the relevant field, whether it\u0027s mathematics, science, history, or any other domain. Verify your answer using multiple approaches when possible, and be prepared to correct any initial misconceptions.\nUser query: Question:\nThe symmetric group $S_n$ has $\n\\factorial{n}$ elements, hence it is not true that $S_{10}$ has 10 elements.\nFind the characteristic of the ring 2Z.\nOptions:\nA. 0\nB. 30\nC. 3\nD. 10\nE. 12\nF. 50\nG. 2\nH. 100\nI. 20\nJ. 5\nAnswer: Let\u0027s think step by step.",
                "role": "user"
            }
        ],
        "raw_output_text_generation_with_cot_reflection_0": "\u003cthinking\u003e\nTo find the characteristic of the ring 2Z, we need to understand what a characteristic of a ring is. The characteristic of a ring is the smallest positive integer $n$ such that $n \\cdot a = 0$ for all $a$ in the ring, or it is 0 if no such n exists. In the case of 2Z, which is the set of all even integers, we need to find the smallest positive integer $n$ such that $n \\cdot a = 0$ for all $a$ in 2Z.  \n\u003creflection\u003e\nWe need to consider that 2Z contains all even integers and that we are looking for a property that applies to all elements in this set, which means we have to think about the multiplication of elements in 2Z and its impact on their properties. We also have to verify that no element in 2Z is a multiplicative identity and that the ring operation here is multiplication.  \n\u003c/reflection\u003e\nConsidering $n \\cdot a$, we know that in 2Z multiplication is defined as $n \\cdot a = 2k$ for some integer $k$ where $n$ and $a$ are even numbers. This implies that the product will always be even, and it\u0027s possible to make the product equal to zero if we choose $n$ to be even, but not necessarily the multiplicative identity, which in the standard ring $Z$ is 1. However, since we are looking for the smallest positive integer n, if we pick any even number greater than 2, we can still get a zero product.  \n\u003creflection\u003e\nWe should be cautious in our previous step about choosing \u0027n\u0027. The explanation provided must hold true for all a in 2Z, which we need to double-check. What if we try to find a counterexample with an arbitrary \u0027a\u0027 to confirm our concept of \u0027n\u0027?  \n\u003c/reflection\u003e\nTrying a counterexample, if we consider $a = 4$, we can see that for any $n \u003e 4$ we can find a product greater than 0 and not equal to 0. This still leaves us with the option of using $n = 2$, because $2 \\cdot a = 4 \\cdot 2 = 8$, which is not 0. But since 8 is even, we also know that any $n\u003c2$ doesn\u0027t work in this case. However, if we consider 0, we know $0 \\cdot a = 0$, so the answer could be 0, but this doesn\u0027t apply to our initial\u0027smallest positive integer\u0027.  \n\u003creflection\u003e\nConsidering our reflections, we must re-check our understanding and make sure we\u0027re not overlooking any options. What\u0027s left are positive integers between 2 and 4. We also know there\u0027s a range of options given, and it might be more productive to inspect our options and see which one stands out as the smallest positive integer.  \n\u003c/reflection\u003e\nUpon reviewing the options and our current understanding of 2Z and its properties, we can conclude that the characteristic must be the smallest positive integer \u0027n\u0027 we have found that works, and the answer must be within the options. Since we have excluded 2, we are left with no option to verify as valid for a multiplicative identity and in accordance with our step-by-step method, the answer must be 0.  \n\u003creflection\u003e\nWith that in mind, we could heavily verify our answer since this is a basic property of the ring 2Z and, as we\u0027ve checked, for any a in 2Z, 0a = 0. We know that we considered the nature of 2Z as even numbers and the multiplication that follows the properties of the set and a consistent ring structure, making this answer to the problem the most accurate for any n in the set, which is always 0 since even times any other even number is always even.  \n\u003c/reflection\u003e\n\u003c/thinking\u003e\n\u003coutput\u003e\n0\n\u003c/output\u003e"
    },
    "instruction": "Question:\nThe symmetric group $S_n$ has $\n\\factorial{n}$ elements, hence it is not true that $S_{10}$ has 10 elements.\nFind the characteristic of the ring 2Z.\nOptions:\nA. 0\nB. 30\nC. 3\nD. 10\nE. 12\nF. 50\nG. 2\nH. 100\nI. 20\nJ. 5\nAnswer: Let\u0027s think step by step.",
    "model_name": "meta-llama/Llama-3.1-8B-Instruct",
    "options": [
        "0",
        "30",
        "3",
        "10",
        "12",
        "50",
        "2",
        "100",
        "20",
        "5"
    ],
    "output": "0",
    "question": "The symmetric group $S_n$ has $\n\\factorial{n}$ elements, hence it is not true that $S_{10}$ has 10 elements.\nFind the characteristic of the ring 2Z.",
    "question_id": 0,
    "src": "cot_lib-abstract_algebra",
    "thinking": "To find the characteristic of the ring 2Z, we need to understand what a characteristic of a ring is. The characteristic of a ring is the smallest positive integer $n$ such that $n \\cdot a = 0$ for all $a$ in the ring, or it is 0 if no such n exists. In the case of 2Z, which is the set of all even integers, we need to find the smallest positive integer $n$ such that $n \\cdot a = 0$ for all $a$ in 2Z.  \n\u003creflection\u003e\nWe need to consider that 2Z contains all even integers and that we are looking for a property that applies to all elements in this set, which means we have to think about the multiplication of elements in 2Z and its impact on their properties. We also have to verify that no element in 2Z is a multiplicative identity and that the ring operation here is multiplication.  \n\u003c/reflection\u003e\nConsidering $n \\cdot a$, we know that in 2Z multiplication is defined as $n \\cdot a = 2k$ for some integer $k$ where $n$ and $a$ are even numbers. This implies that the product will always be even, and it\u0027s possible to make the product equal to zero if we choose $n$ to be even, but not necessarily the multiplicative identity, which in the standard ring $Z$ is 1. However, since we are looking for the smallest positive integer n, if we pick any even number greater than 2, we can still get a zero product.  \n\u003creflection\u003e\nWe should be cautious in our previous step about choosing \u0027n\u0027. The explanation provided must hold true for all a in 2Z, which we need to double-check. What if we try to find a counterexample with an arbitrary \u0027a\u0027 to confirm our concept of \u0027n\u0027?  \n\u003c/reflection\u003e\nTrying a counterexample, if we consider $a = 4$, we can see that for any $n \u003e 4$ we can find a product greater than 0 and not equal to 0. This still leaves us with the option of using $n = 2$, because $2 \\cdot a = 4 \\cdot 2 = 8$, which is not 0. But since 8 is even, we also know that any $n\u003c2$ doesn\u0027t work in this case. However, if we consider 0, we know $0 \\cdot a = 0$, so the answer could be 0, but this doesn\u0027t apply to our initial\u0027smallest positive integer\u0027.  \n\u003creflection\u003e\nConsidering our reflections, we must re-check our understanding and make sure we\u0027re not overlooking any options. What\u0027s left are positive integers between 2 and 4. We also know there\u0027s a range of options given, and it might be more productive to inspect our options and see which one stands out as the smallest positive integer.  \n\u003c/reflection\u003e\nUpon reviewing the options and our current understanding of 2Z and its properties, we can conclude that the characteristic must be the smallest positive integer \u0027n\u0027 we have found that works, and the answer must be within the options. Since we have excluded 2, we are left with no option to verify as valid for a multiplicative identity and in accordance with our step-by-step method, the answer must be 0.  \n\u003creflection\u003e\nWith that in mind, we could heavily verify our answer since this is a basic property of the ring 2Z and, as we\u0027ve checked, for any a in 2Z, 0a = 0. We know that we considered the nature of 2Z as even numbers and the multiplication that follows the properties of the set and a consistent ring structure, making this answer to the problem the most accurate for any n in the set, which is always 0 since even times any other even number is always even.  \n\u003c/reflection\u003e"
}
```

This subset can be loaded as:

```python
from datasets import load_dataset

ds = load_dataset("dvilasuero/meta-llama_Llama-3.1-8B-Instruct_cot_mmlu-pro_20241016_231257", "default")
```

Or simply as it follows, since there's only one configuration and is named `default`: 

```python
from datasets import load_dataset

ds = load_dataset("dvilasuero/meta-llama_Llama-3.1-8B-Instruct_cot_mmlu-pro_20241016_231257")
```


</details>




