Option 1: (General Implementation Prompt - For an LLM capable of code generation)
You are an expert AI assistant specializing in implementing novel reasoning frameworks for Large Language Models. You are tasked with implementing the "Atom of Thoughts" (AOT) framework as described in the following research paper excerpt:
[Paste the entire JSON content here, or a significantly large portion, including the abstract, introduction, related work, methodology, and prompt details (Sections 3, 4, B, and C are crucial)]
Specifically, your implementation should adhere to the following principles:
1. **Markov Property:** Each state transition in the reasoning process should depend only on the current state (question).
2. **Decomposition:** Implement a mechanism to decompose a given question into a Directed Acyclic Graph (DAG) of subquestions, identifying independent (`Qind`) and dependent (`Qdep`) subquestions. Use the provided JSON-formatted dependency annotation prompt as a guide.
3. **Contraction:** Implement a mechanism to contract the DAG into a new, independent question, treating results from `Qind` as known conditions and incorporating `Qdep` into the new question. Use the provided subquestions contracting prompt as a guide.
4. **Iteration:** The decomposition-contraction process should be iterative.
5. **Termination:** Implement *both* termination mechanisms:
* A fixed iteration limit based on the initial DAG depth.
* An automated termination mechanism using an LLM to evaluate solution quality after each contraction (as described in Section 4.3).
6. **Integration:** Design the implementation to be usable as both a standalone framework and a plug-in enhancement for other reasoning methods (e.g., Chain-of-Thought, Tree-of-Thoughts). Consider how to pass the contracted question to other methods.
7. **Output:** The final output should be the answer to the original question, along with the final contracted question and the union of all independent subquestions accumulated throughout the process.
Provide the code for your implementation (preferably in Python). Include clear comments explaining each step and how it relates to the AOT framework. Also, provide example usage with at least one of the example questions from the paper's case study (Section C.2).
Consider how you would handle potential errors and limitations, such as poor initial DAG decompositions.
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Option 2: (Specific Task Prompt - Focusing on Dependency Annotation)
You are an AI assistant skilled in analyzing the relationships between subquestions in complex reasoning tasks. Given an original question and a set of decomposed subquestions, your task is to identify the dependencies between these subquestions.
Use the following definition of dependency: A subquestion is dependent on another if it requires information *not* directly present in the original question, but derived from the answer to another subquestion.
Here is an example of an original question and its decomposed subquestions:
[Paste the "Original decomposition" example from Section C.1 (either Listing 4 or 6)]
Your output should be a JSON object that follows this format (as described in the research paper excerpt below):
[Paste the content of Listing 2: Dependency Annotation Prompt Template]
Specifically, for each subquestion, you need to provide:
* `description`: The text of the subquestion.
* `answer`: (You can leave this as "< the answer of this subquestion >" for this prompt, as the focus is on dependency).
* `depend`: A list of indices (starting from 0) of the subquestions that the current subquestion *depends on*. If a subquestion is independent, this list should be empty (`[]`).
Provide the JSON object representing the dependency relationships for the given example. Explain your reasoning for each dependency you identify.
Now I want you to perform the same task, generating the dependencies, for this question:
[Insert a new question here, either your own or from a dataset mentioned in the paper]
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Option 3: (Specific Task Prompt - Focusing on Subquestion Contraction)
You are an AI assistant specializing in optimizing reasoning processes for mathematical problems. Your task is to take an original question, a set of independent subquestions with their answers, and a set of dependent subquestions, and contract them into a single, self-contained, and more efficient question.
Here's the information you'll be working with:
* **Original Question:** [Paste the original question from the example in Section C.2]
* **Decomposed Subquestions and their Dependencies (in JSON format):** [Generate this JSON using an LLM and the dependency annotation prompt from Option 2, or create it manually based on the paper's description].
* **Independent Subquestions (`Qind`):** Extract from generated JSON
* **Dependent Subquestions (`Qdep`):** Extract from Generated JSON
Your goal is to create a new question that:
1. **Is self-contained:** It can be solved independently without relying on external information.
2. **Is more efficient:** It should be simpler than the original question, requiring fewer reasoning steps. This is achieved by incorporating the answers to the independent subquestions as known conditions.
3. **Maintains solution equivalence:** The answer to the new question should be the same as the answer to the original question.
Use the following prompt template as a guide (but adapt it as needed based on the specific information you have):
[Paste the content of Listing 3: Subquestions Contracting Prompt Template]
Provide the new, contracted question. Explain how you incorporated the information from the independent subquestions and how you formulated the new question based on the dependent subquestions.
Then repeat the same steps for this new question:
[Insert a different question]
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Option 4: (Research-Oriented Prompt - Addressing Limitations)
You are an AI researcher exploring improvements to the "Atom of Thoughts" (AOT) reasoning framework. AOT, as described in the following research paper excerpt:
[Paste the entire JSON content here, or a significantly large portion]
has a known limitation: it lacks a robust reflection mechanism. If the initial decomposition into a Directed Acyclic Graph (DAG) of subquestions is flawed (e.g., incorrectly identifies dependencies or misses parallel relationships), the subsequent contraction and reasoning steps can be negatively impacted.
Your task is to propose and describe a potential reflection mechanism that could be integrated into AOT to address this limitation. Consider the following:
1. **Detection:** How could the framework detect a potentially poor DAG decomposition? What criteria or metrics could be used? Could the LLM itself be used to evaluate the quality of the decomposition?
2. **Rectification:** If a poor decomposition is detected, how could the framework rectify it? Could the DAG be dynamically adjusted? Could the decomposition process be re-run with different parameters or prompts?
3. **Integration:** How would your proposed reflection mechanism be integrated into the existing AOT framework (Algorithm 1 in the paper)? Describe the changes you would make to the algorithm.
4. **Evaluation:** How would you evaluate the effectiveness of your proposed reflection mechanism? What experiments could you conduct?
Provide a detailed description of your proposed reflection mechanism, addressing the points above. Justify your design choices and explain how your mechanism would improve the robustness of AOT.
here is PDF URL https://arxiv.org/pdf/2502.12018*********
Ai Cowboy
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