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: 640033
    num_examples: 70
  download_size: 294010
  dataset_size: 640033
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 mmmlu-pro-eval-cot-70B

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/mmmlu-pro-eval-cot-70B/raw/main/pipeline.yaml"
```

or explore the configuration:

```console
distilabel pipeline info --config "https://huggingface.co/datasets/dvilasuero/mmmlu-pro-eval-cot-70B/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 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[Verification against common knowledge or basic facts relevant to the question type]\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.",
                "role": "system"
            },
            {
                "content": "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 first need to understand what the characteristic of a ring is. The characteristic of a ring is the smallest positive integer n such that n * x = 0 for all elements x in the ring, if such an n exists. If no such n exists, the characteristic is said to be 0.\n\nThe ring 2Z consists of all even integers. This means that every element in 2Z is a multiple of 2.\n\nLet\u0027s consider the elements of 2Z. For any element x in 2Z, we can express x as 2k, where k is an integer.\n\nNow, we need to find the smallest positive integer n such that n * (2k) = 0 for all k.\n\nThis equation simplifies to 2nk = 0.\n\nSince k is an integer, 2nk can only be 0 if n is 0 or if 2n = 0, since k cannot be 0 for all elements.\n\nHowever, the characteristic cannot be 0 because there exists a positive integer n such that n * x = 0 for all elements x in the ring.\n\n\u003creflection\u003e\nUpon reflection, I realize that I should be looking for the smallest positive integer n that makes 2n divisible by all elements in 2Z, which essentially means finding the smallest n that makes 2n = 0 in the context of 2Z.\n\nHowever, considering the properties of modular arithmetic might provide a clearer insight.\n\u003c/reflection\u003e\n\nConsidering modular arithmetic, we can see that 2Z is essentially the set of integers modulo 2, but in the context of a ring, we\u0027re looking at the additive group and the multiplication operation.\n\nThe characteristic of a ring, however, can also be understood as the order of the additive group of the ring if it is finite, or the smallest positive integer n such that n times any element equals zero.\n\nIn the case of 2Z, adding any element to itself twice will result in 0 (in terms of the additive operation), but considering the question\u0027s scope, the focus is on finding a non-zero n that satisfies the condition for all elements.\n\n\u003creflection\u003e\nGiven that every element in 2Z is a multiple of 2, and knowing that in modular arithmetic, the characteristic can be seen as the modulus itself in certain contexts, I must confirm if the modulus or a related property applies directly here. Specifically, does the characteristic being sought relate to the smallest multiple of 2 that would\u0027reset\u0027 any element in the ring to zero, under modular arithmetic principles?\n\u003c/reflection\u003e\n\nUpon further consideration, the question can be resolved by understanding that the characteristic of the ring of integers modulo n is n itself. However, for 2Z, the characteristic should be the smallest positive integer n such that n times any element in 2Z equals zero. Given that every element is a multiple of 2, the smallest positive integer that satisfies this condition for all elements is indeed related to the inherent property of the ring being based on multiples of 2.\n\nFor 2Z specifically, considering it as a subset of integers, it doesn\u0027t form a field or a group under multiplication with identity, but its characteristic in terms of the additive group can be considered.\n\n\u003creflection\u003e\nTo verify the correct understanding of the characteristic in the context of 2Z, it\u0027s essential to consider well-established knowledge about rings, specifically those that consist of multiples of a prime number. The characteristic of such a ring, especially when consisting of integers and their properties under modular arithmetic, indicates a specific behavior that leads to a straightforward identification of its characteristic.\n\u003c/reflection\u003e\n\nGiven these reflections, the characteristic of the ring 2Z, based on the principle that the characteristic is the smallest positive integer n such that n times any element equals zero, and understanding that every element in 2Z is a multiple of 2, can be identified directly.\n\n\u003c/thinking\u003e\n\u003coutput\u003e\nG. 2\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/Meta-Llama-3.1-70B-Instruct",
    "options": [
        "0",
        "30",
        "3",
        "10",
        "12",
        "50",
        "2",
        "100",
        "20",
        "5"
    ],
    "output": "G. 2",
    "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 first need to understand what the characteristic of a ring is. The characteristic of a ring is the smallest positive integer n such that n * x = 0 for all elements x in the ring, if such an n exists. If no such n exists, the characteristic is said to be 0.\n\nThe ring 2Z consists of all even integers. This means that every element in 2Z is a multiple of 2.\n\nLet\u0027s consider the elements of 2Z. For any element x in 2Z, we can express x as 2k, where k is an integer.\n\nNow, we need to find the smallest positive integer n such that n * (2k) = 0 for all k.\n\nThis equation simplifies to 2nk = 0.\n\nSince k is an integer, 2nk can only be 0 if n is 0 or if 2n = 0, since k cannot be 0 for all elements.\n\nHowever, the characteristic cannot be 0 because there exists a positive integer n such that n * x = 0 for all elements x in the ring.\n\n\u003creflection\u003e\nUpon reflection, I realize that I should be looking for the smallest positive integer n that makes 2n divisible by all elements in 2Z, which essentially means finding the smallest n that makes 2n = 0 in the context of 2Z.\n\nHowever, considering the properties of modular arithmetic might provide a clearer insight.\n\u003c/reflection\u003e\n\nConsidering modular arithmetic, we can see that 2Z is essentially the set of integers modulo 2, but in the context of a ring, we\u0027re looking at the additive group and the multiplication operation.\n\nThe characteristic of a ring, however, can also be understood as the order of the additive group of the ring if it is finite, or the smallest positive integer n such that n times any element equals zero.\n\nIn the case of 2Z, adding any element to itself twice will result in 0 (in terms of the additive operation), but considering the question\u0027s scope, the focus is on finding a non-zero n that satisfies the condition for all elements.\n\n\u003creflection\u003e\nGiven that every element in 2Z is a multiple of 2, and knowing that in modular arithmetic, the characteristic can be seen as the modulus itself in certain contexts, I must confirm if the modulus or a related property applies directly here. Specifically, does the characteristic being sought relate to the smallest multiple of 2 that would\u0027reset\u0027 any element in the ring to zero, under modular arithmetic principles?\n\u003c/reflection\u003e\n\nUpon further consideration, the question can be resolved by understanding that the characteristic of the ring of integers modulo n is n itself. However, for 2Z, the characteristic should be the smallest positive integer n such that n times any element in 2Z equals zero. Given that every element is a multiple of 2, the smallest positive integer that satisfies this condition for all elements is indeed related to the inherent property of the ring being based on multiples of 2.\n\nFor 2Z specifically, considering it as a subset of integers, it doesn\u0027t form a field or a group under multiplication with identity, but its characteristic in terms of the additive group can be considered.\n\n\u003creflection\u003e\nTo verify the correct understanding of the characteristic in the context of 2Z, it\u0027s essential to consider well-established knowledge about rings, specifically those that consist of multiples of a prime number. The characteristic of such a ring, especially when consisting of integers and their properties under modular arithmetic, indicates a specific behavior that leads to a straightforward identification of its characteristic.\n\u003c/reflection\u003e\n\nGiven these reflections, the characteristic of the ring 2Z, based on the principle that the characteristic is the smallest positive integer n such that n times any element equals zero, and understanding that every element in 2Z is a multiple of 2, can be identified directly."
}
```

This subset can be loaded as:

```python
from datasets import load_dataset

ds = load_dataset("dvilasuero/mmmlu-pro-eval-cot-70B", "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/mmmlu-pro-eval-cot-70B")
```


</details>




