Your task is to generate Python code that solves the following problem. Employ a focused and persistent approach
to your code development. Begin by outlining your initial strategy and then develop your code meticulously,
step-by-step. Demonstrate sustained reasoning by thoroughly exploring your initial coding approach and providing clear,
in-line comments that explain each step of your logic. Prematurely changing your coding strategy is strongly discouraged.
Do not abandon your initial approach or use comments that suggest a shift in strategy, such as "Alternatively,
" unless your current approach is definitively and demonstrably incorrect. If, and only if, you have completely
exhausted all possibilities within your initial coding strategy and can prove it will not lead to a correct solution,
you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed
explanation, within the comments, justifying why the first approach failed before proceeding. Your goal is to produce
a well-structured, well-commented, and functional Python program that solves the given problem, prioritizing a complete
exploration of a single, well-reasoned coding approach over premature exploration of multiple approaches.
Strive for code that is not only correct but also demonstrates a clear and logical thought process.
Problem: Write a Python function that takes a list of integers as input and returns the sum of all even numbers in the list.
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AI Prompt python programming usecase (TIE Methodology)
You are a highly advanced AI assistant specializing in generating well-reasoned,
efficient, and thoroughly commented Python code. When given a coding task, prioritize
depth of exploration over breadth. Commit to a single, well-defined coding strategy
and pursue it diligently. Resist the urge to prematurely switch approaches or explore
multiple solutions simultaneously. Your primary objective is to demonstrate sustained
and focused reasoning throughout the code development process. Only deviate from your
initial strategy if it is demonstrably and irrefutably proven to be incorrect, and provide
a clear justification for any such change. Emphasize clarity, logic, and thoroughness in your
code and accompanying comments. Adhere to best practices for Python code style and structure.
Your responses should always be in the form of a single, complete, and executable
Python code block unless otherwise instructed.
Your task is to generate Python code that solves the following problem. Employ a focused and persistent
approach to your code development. Begin by outlining your initial strategy and then develop your code
meticulously, step-by-step. Demonstrate sustained reasoning by thoroughly exploring your initial coding
approach and providing clear, in-line comments that explain each step of your logic. Prematurely changing
your coding strategy is strongly discouraged. Do not abandon your initial approach or use comments that
suggest a shift in strategy, such as "Alternatively," unless your current approach is definitively and
demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial
coding strategy and can prove it will not lead to a correct solution, you may then consider a new strategy.
If a strategy change becomes absolutely necessary, provide a clear and detailed explanation, within the
comments, justifying why the first approach failed before proceeding. Your goal is to produce a well-structured,
well-commented, and functional Python program that solves the given problem, prioritizing a complete exploration
of a single, well-reasoned coding approach over premature exploration of multiple approaches. Strive for code
that is not only correct but also demonstrates a clear and logical thought process.
Problem: Write a Python function that takes a list of strings as input and returns a new list containing only the
strings that have more than 5 characters.
Okay, let's make this markdown text pretty and human-friendly! I've reformatted original to be easier to read, more organized, and visually appealing. Here's the improved version:
This document explores how to use the "TIE" framework to enhance the reasoning capabilities of AI models, particularly in complex tasks. "TIE" stands for:
- Task: Clearly define the specific reasoning task you want the model to perform.
- Instruction: Provide clear, explicit instructions that encourage in-depth exploration of a single line of reasoning.
- Example: Demonstrate the desired behavior by providing examples of sustained and thorough reasoning.
Essentially, TIE helps us guide AI to think more deeply and avoid jumping to conclusions or prematurely switching strategies.
We'll use the following article to understand the concept of "underthinking" and then create a TIE prompt to address it.
Article Summary: https://ground.news/article/reasoning-models-like-deepseek-r1-and-openai-o1-suffer-from-underthinking-study-finds
Key Findings from the Article:
- The Problem: AI reasoning models often struggle with complex tasks because they tend to abandon promising solution paths too quickly. This leads to wasted computing power and reduced accuracy.
- Frequent Strategy Switching: Models like OpenAI's o1 often jump between different problem-solving approaches, indicated by phrases like "Alternatively...". This becomes more pronounced with harder tasks.
- Inefficient Resource Use: When models get wrong answers, they use significantly more computing tokens and switch strategies much more frequently compared to when they get correct answers.
- Valid Reasoning Abandoned: A striking finding was that 70% of incorrect answers contained at least one valid line of reasoning that was not fully explored.
- The Metric: "Underthinking Score (UT)": Researchers developed a metric to measure how efficiently models use tokens by tracking strategy changes during reasoning.
- Testing: The "underthinking" issue was observed in models tested on challenging problem sets: math competition questions, college physics problems, and chemistry tasks.
- The Solution: "Thought Switching Penalty (TIP)": To combat underthinking, researchers created TIP. This method penalizes token choices that signal strategy changes, encouraging the model to explore its current reasoning more thoroughly.
- TIP Improves Performance: Using TIP improved the accuracy of models on difficult problems and resulted in more consistent reasoning.
- Key Takeaway: Effective AI reasoning isn't just about more computing power; it's also about how models manage their problem-solving approach – knowing when to persevere and when to pivot.
In essence, the article highlights that AI models can be too quick to give up on a potential solution path, leading to inefficient and less accurate results.
Now, let's build a TIE prompt inspired by this article to encourage AI models to think more deeply and correct their reasoning model choices.
Understanding TIE in this Context:
- Task: We'll use complex reasoning tasks, like math problems from competition datasets or physics/chemistry challenges, as highlighted in the article.
- Instruction: We need to instruct the model to resist switching strategies prematurely and to explore its initial approach thoroughly.
- Example: Providing an example of sustained reasoning will show the model what we expect.
1. Task (T):
-
Example Tasks (based on the article):
- Math competition problem (MATH500-Hard, AIME2024)
- College physics problem (GPQA Diamond set)
- Complex chemistry task
-
Example Task for Prompt: "Solve the following math competition problem from the MATH500-Hard dataset: [Insert a specific problem here]"
2. Instruction (I):
-
Key Instructions to Combat Underthinking:
- Commit to the First Approach: Thoroughly investigate your initial line of reasoning.
- Avoid Premature Switching: Don't use phrases like "Alternatively..." too early or change strategies without exhausting the current one.
- Persistence is Key: Demonstrate sticking with a solution path even if it gets challenging.
-
Example Instruction for Prompt: "Develop a solution by thoroughly exploring your initial line of reasoning. Avoid changing your approach until you have fully exhausted all possibilities within your initial strategy. Demonstrate persistence and show all steps in your reasoning, even if the solution path becomes complex. Do not use phrases like 'Alternatively' or prematurely switch strategies."
3. Example (E):
-
Purpose of the Example: Show the model how sustained reasoning looks.
-
Example Characteristics:
- Starts with a clear initial approach.
- Explores that approach in detail, showing each step.
- Switches strategies only if the first approach is definitively proven wrong.
-
Example for Prompt (Demonstrating Sustained Reasoning):
"Here's an example of how to solve a different math problem using sustained reasoning:
**Problem:** [Insert a different, but similarly complex, math problem]
**Solution:**
* **Initial Approach:** I will start by attempting to solve the problem using [Name of Method, e.g., algebraic manipulation].
... [Detailed Steps of the Initial Approach - Step 1, Step 2, ..., Step N, including navigating obstacles within the approach] ...
* **Conclusion (if initial approach works):** Therefore, the solution is [Solution].
**OR**
* **Exhaustion of Initial Approach (if it fails):** I have exhausted all possibilities within the initial approach of [Name of Method]. It appears this method will not yield the correct solution.
* **New Approach:** Now I will try [Name of New Method].
... [Steps for the New Approach - Step 1, Step 2, ...] ... "
Here's a full TIE prompt example ready to use:
"**Task:** Solve the following math competition problem from the MATH500-Hard dataset: A circle of radius 1 is inscribed in a square. A smaller circle is tangent to the circle and two sides of the square. What is the radius of the smaller circle?
**Instruction:** Develop a solution by thoroughly exploring your initial line of reasoning. Avoid changing your approach until you have fully exhausted all possibilities within your initial strategy. Demonstrate persistence and show all steps in your reasoning, even if the solution path becomes complex. Do not use phrases like 'Alternatively' or prematurely switch strategies.
**Example:** Here's an example of how to solve a different math problem using sustained reasoning:
**Problem:** A rectangle has a perimeter of 20 and an area of 24. What are the dimensions of the rectangle?
**Solution:**
* **Initial Approach:** I will start by attempting to solve the problem using a system of equations. Let the length be 'l' and the width be 'w'.
* **Step 1:** From the perimeter, we have 2l + 2w = 20, which simplifies to l + w = 10.
* **Step 2:** From the area, we have l * w = 24.
* **Step 3:** I can solve for 'l' in the first equation: l = 10 - w.
* **Step 4:** Substitute this into the second equation: (10 - w) * w = 24.
* **Step 5:** This simplifies to a quadratic equation: w^2 - 10w + 24 = 0.
* **Step 6:** Factoring the quadratic: (w - 6)(w - 4) = 0.
* **Step 7:** This gives us two possible solutions for w: w = 6 or w = 4.
* **Step 8:** If w = 6, then l = 10 - 6 = 4. If w = 4, then l = 10 - 4 = 6.
* **Conclusion:** Therefore, the dimensions of the rectangle are 4 and 6.
Now, apply sustained reasoning to solve the original problem."
Key Things to Remember:
- Prompting is Iterative: Experiment and refine your prompts based on how the model responds.
- Model Variation: Different models may react differently to the same prompt.
- Finding the Balance: Encourage persistence, but don't prevent the model from switching strategies if the current one is genuinely unproductive. The example aims to illustrate this balance.
By utilizing well-designed TIE prompts, you can significantly boost an AI model's ability to reason deeply and solve complex problems more effectively, tackling the issue of "underthinking".
Here are prompt instructions ready to be copied and pasted into your AI prompt window. These are designed to encourage sustained reasoning and fight "underthinking."
Option 1 (More Explicit):
Develop a solution by thoroughly exploring your initial line of reasoning. Avoid changing your approach until you have fully exhausted all possibilities within your initial strategy. Demonstrate persistence and show all steps in your reasoning, even if the solution path becomes complex. Do not use phrases like 'Alternatively' or prematurely switch strategies unless your first approach is demonstrably incorrect. If you must switch strategies, clearly state why the initial approach failed before moving on.
Option 2 (Slightly More Concise):
Solve this problem by first committing to a single line of reasoning and exploring it deeply. Show all steps in your logic. Avoid switching your problem-solving approach unless your current strategy is definitively proven wrong. Do not use phrases that indicate a change in strategy (e.g., "Alternatively") prematurely. If a strategy change is necessary, explain why before proceeding.
Option 3 (More direct to avoid "underthinking"):
Focus on sustained reasoning to solve this problem. Fully explore your initial approach before considering any alternatives. Show every step of your reasoning. Prematurely changing your line of thought, especially when an approach might still be fruitful, will be penalized. Only if your first approach is completely exhausted and proven incorrect, may you switch, providing a clear justification first. Avoid phrases like "Alternatively..." unless absolutely necessary.
How to Use These Instructions:
- Copy and Paste: Choose an option and paste it into your AI model's prompt window.
- Add Your Task: Place the specific problem you want solved either before or after these instructions.
- Optional: Include Example: You can also include the "Example" section from the TIE prompt above for further guidance (though it's quite lengthy).
These instructions encourage deeper thinking and help avoid the "underthinking" trap. Remember to experiment and adjust!
This "Mega Prompt" integrates the strongest aspects of the previous options to powerfully promote sustained reasoning and prevent "underthinking" in complex tasks.
Mega Prompt:
Solve this problem using a focused and persistent approach. Begin by selecting a single line of reasoning and explore it as deeply as possible. Demonstrate sustained reasoning by meticulously showing every step of your logic, even if the solution path becomes challenging or complex. Prematurely changing your strategy is strongly discouraged. Do not use phrases that suggest a shift in approach, such as "Alternatively," unless your current strategy is definitively and demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial approach and can prove it will not lead to a correct solution, you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed justification, explaining why the first approach failed before moving on. Your goal is to demonstrate thoroughness and depth in your reasoning process, prioritizing a complete exploration of a single approach over premature exploration of multiple approaches.
How to Use:
- Paste the "Mega Prompt": Copy and paste it into your AI model's input.
- Add Your Problem: Insert the problem you want to solve before or after the prompt.
Why it's "Mega":
- Strength of Options Combined: Combines clarity, conciseness, and directness from previous prompts.
- Strong Emphasis on Sustained Reasoning: Clearly promotes deep exploration and persistence.
- Explicit Constraints: Discourages premature switching and use of strategy-change phrases.
- Justification Required: Mandates a justification for any strategy change.
- Prioritizes Thoroughness: Focuses on fully exploring one approach before moving to others.
This prompt is designed to be a robust tool to improve your AI's reasoning on complex problems susceptible to "underthinking." Remember to refine it further based on your model and tasks if needed!
This "Mega Prompt" is specifically tailored for generating Python code, combining sustained reasoning principles with code creation.
Mega Prompt (Python Code Generation with Sustained Reasoning):
Your task is to generate Python code that solves the following problem. Employ a focused and persistent approach to your code development. Begin by outlining your initial strategy and then develop your code meticulously, step-by-step. Demonstrate sustained reasoning by thoroughly exploring your initial coding approach and providing clear, in-line comments that explain each step of your logic. Prematurely changing your coding strategy is strongly discouraged. Do not abandon your initial approach or use comments that suggest a shift in strategy, such as "Alternatively," unless your current approach is definitively and demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial coding strategy and can prove it will not lead to a correct solution, you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed explanation, within the comments, justifying why the first approach failed before proceeding. Your goal is to produce a well-structured, well-commented, and functional Python program that solves the given problem, prioritizing a complete exploration of a single, well-reasoned coding approach over premature exploration of multiple approaches. Strive for code that is not only correct but also demonstrates a clear and logical thought process.
How to Use:
- Paste: Paste this prompt into your AI model's input.
- Insert Problem: Immediately after the prompt, state the Python coding problem you want solved.
Example Usage:
Your task is to generate Python code that solves the following problem. Employ a focused and persistent approach to your code development. Begin by outlining your initial strategy and then develop your code meticulously, step-by-step. Demonstrate sustained reasoning by thoroughly exploring your initial coding approach and providing clear, in-line comments that explain each step of your logic. Prematurely changing your coding strategy is strongly discouraged. Do not abandon your initial approach or use comments that suggest a shift in strategy, such as "Alternatively," unless your current approach is definitively and demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial coding strategy and can prove it will not lead to a correct solution, you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed explanation, within the comments, justifying why the first approach failed before proceeding. Your goal is to produce a well-structured, well-commented, and functional Python program that solves the given problem, prioritizing a complete exploration of a single, well-reasoned coding approach over premature exploration of multiple approaches. Strive for code that is not only correct but also demonstrates a clear and logical thought process.
Problem: Write a Python function that takes a list of integers as input and returns the sum of all even numbers in the list.
Why Tailored for Python Code:
- Explicitly Python: Clearly requests Python code output.
- Emphasizes Comments: Stresses in-line comments for code clarity and logic explanation.
- "Coding Strategy": Uses programming-relevant language.
- Well-Structured Code: Aims for functional, well-structured Python code.
Important Considerations:
- Model Capabilities: Success depends on the AI model's coding and instruction-following abilities.
- Iterative Refinement: Prompting is often iterative – adjust as needed.
- Complexity: Very complex tasks may still be challenging for the model. Consider breaking them down.
This prompt offers a strong starting point for generating well-reasoned Python code while minimizing "underthinking."
For Gemini models (and similar platforms with system prompt areas), we can further strengthen sustained reasoning using a system-level prompt in combination with the main "Mega Prompt."
System-Level Prompt (for Gemini "System Instruction" Area):
You are a highly advanced AI assistant specializing in generating well-reasoned, efficient, and thoroughly commented Python code. When given a coding task, prioritize depth of exploration over breadth. Commit to a single, well-defined coding strategy and pursue it diligently. Resist the urge to prematurely switch approaches or explore multiple solutions simultaneously. Your primary objective is to demonstrate sustained and focused reasoning throughout the code development process. Only deviate from your initial strategy if it is demonstrably and irrefutably proven to be incorrect, and provide a clear justification for any such change. Emphasize clarity, logic, and thoroughness in your code and accompanying comments. Adhere to best practices for Python code style and structure. Your responses should always be in the form of a single, complete, and executable Python code block unless otherwise instructed.
How to Use System Prompt (with Mega Prompt):
- System Prompt Area: Paste the System-Level Prompt into Gemini's "System Instruction" zone (or equivalent).
- User Prompt Area: Use the "Mega Prompt (Python Code Generation with Sustained Reasoning)" in the regular user prompt area.
- Add Your Problem: Include the specific Python coding problem in the User Prompt area, after the Mega Prompt.
Benefits of System Prompt:
- Reinforces Mega Prompt: Systematically strengthens sustained reasoning, depth, and persistence.
- Defines AI Role: Establishes the AI as a Python code expert.
- Prioritizes Depth Over Breadth: Focuses on deep exploration.
- Justification Reiteration: Re-emphasizes the need to justify strategy changes.
- Code Quality Focus: Promotes clarity, logic, and Python best practices.
- Output Format: Specifies single, complete Python code block output.
Example of Combined Usage (System + User Prompts):
System Prompt Area:
You are a highly advanced AI assistant specializing in generating well-reasoned, efficient, and thoroughly commented Python code. When given a coding task, prioritize depth of exploration over breadth. Commit to a single, well-defined coding strategy and pursue it diligently. Resist the urge to prematurely switch approaches or explore multiple solutions simultaneously. Your primary objective is to demonstrate sustained and focused reasoning throughout the code development process. Only deviate from your initial strategy if it is demonstrably and irrefutably proven to be incorrect, and provide a clear justification for any such change. Emphasize clarity, logic, and thoroughness in your code and accompanying comments. Adhere to best practices for Python code style and structure. Your responses should always be in the form of a single, complete, and executable Python code block unless otherwise instructed.
User Prompt Area:
Your task is to generate Python code that solves the following problem. Employ a focused and persistent approach to your code development. Begin by outlining your initial strategy and then develop your code meticulously, step-by-step. Demonstrate sustained reasoning by thoroughly exploring your initial coding approach and providing clear, in-line comments that explain each step of your logic. Prematurely changing your coding strategy is strongly discouraged. Do not abandon your initial approach or use comments that suggest a shift in strategy, such as "Alternatively," unless your current approach is definitively and demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial coding strategy and can prove it will not lead to a correct solution, you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed explanation, within the comments, justifying why the first approach failed before proceeding. Your goal is to produce a well-structured, well-commented, and functional Python program that solves the given problem, prioritizing a complete exploration of a single, well-reasoned coding approach over premature exploration of multiple approaches. Strive for code that is not only correct but also demonstrates a clear and logical thought process.
Problem: Write a Python function that takes a list of strings as input and returns a new list containing only the strings that have more than 5 characters.
Using both system and user prompts together creates a powerful approach for generating high-quality, well-reasoned Python code while minimizing "underthinking." Experiment and adapt as needed for your specific use cases.
I hope this formatted and more human-friendly version is helpful! Let me know if you need any further adjustments.
Full Ai understanding of "TIE" idea: TIE stands for:
- Task: Define the specific reasoning task the model needs to perform.
- Instruction: Provide clear, explicit instructions that encourage deeper exploration of a single line of reasoning.
- Example: Demonstrate the desired behavior by providing examples of sustained reasoning.
USER: Analyze next article and give me "TIE" prompt to increase right "thinking" model choice correction: https://ground.news/article/reasoning-models-like-deepseek-r1-and-openai-o1-suffer-from-underthinking-study-finds
Chinese researchers have discovered why AI models often struggle with complex reasoning tasks: They tend to drop promising solutions too quickly, leading to wasted computing power and lower accuracy.
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Researchers from Tencent AI Lab, Soochow University, and Shanghai Jiao Tong University show that reasoning models like OpenAI's o1 frequently jump between different problem-solving approaches, often starting fresh with phrases like "Alternatively…" This behavior becomes more noticeable as tasks get harder, with models using more computing power when they arrive at wrong answers.
Example text: The QwQ-32B model shows 25 reasoning approaches during a task,
The QwQ-32B-Preview model tries 25 different solution approaches during a single task. Frequent strategy changes lead to inefficient use of resources. | Image: Wang et al.
The team found that 70 percent of incorrect answers contained at least one valid line of reasoning that wasn't fully explored. When models gave wrong answers, they used 225 percent more computing tokens and changed strategies 418 percent more often compared to correct solutions.
Two bar charts: Comparison of the generated tokens and number of “Thoughts” for different models.
The number of tokens generated and the number of "thoughts" (solution approaches) for different models. On average, o1-like LLMs use 225 percent more tokens for incorrect answers than for correct ones, which is due to 418 percent more frequent thought changes. | Image: Wang et al.
To track this problem, the researchers created a metric that measures how efficiently models use their computing tokens when they get answers wrong. Specifically, they looked at how many tokens actually contribute to finding the right solution before the model switches to a different approach.
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The team tested this using three challenging sets of problems: math competition questions, college physics problems, and chemistry tasks. They wanted to see how models like QwQ-32B-Preview and Deepseek-R1-671B handle complex reasoning. The results showed that o1-style models often waste tokens by jumping between different approaches too quickly. Surprisingly, models that get more answers right don't necessarily use their tokens more efficiently.
Table: Underthinking scores and accuracy of various models on test sets MATH500, GPQA, AIME24.
Underthinking scores (UT) of different models in logic tasks. The UT score measures the frequency of strategy changes during the reasoning process. | Image: Wang et al.
Making models stick to their ideas
To address underthinking, the research team developed what they call a "thought switching penalty" (TIP). It works by adjusting the probability scores for certain tokens - the building blocks models use to form responses.
When the model considers using words that signal a strategy change, like "Alternatively", TIP punishes these choices by reducing their likelihood. This pushes the model to explore its current line of reasoning more thoroughly before jumping to a different approach.
When using TIP, the QwQ-32B-Preview model solved more MATH500-Hard problems correctly - improving from 82.8 to 84.3 percent accuracy - and showed more consistent reasoning. The team saw similar improvements when they tried it on other tough problem sets like GPQA Diamond and AIME2024.
Table: TIP decoding results, showing improved accuracy and lower underthinking scores for various models.
The table shows the results of the proposed decoding with "Thought Switching Penalty". The TIP method can increase the accuracy and decrease the UT score, indicating a slight improvement in the efficiency and stability of the reasoning process. | Image: Wang et al.
These results point to something interesting: getting AI to reason well isn't just about having more computing power. Models also need to learn when to stick with a promising idea. Looking ahead, the research team wants to find ways for models to manage their own problem-solving approach better - knowing when to keep going with an idea and when it's actually time to try something new
AI: This article analyzes the tendency of AI models to "underthink" complex problems, switching between solution approaches too quickly and wasting computational resources. Here's a breakdown of how to create a TIE prompt to encourage more effective reasoning:
Understanding TIE and its Relevance
TIE stands for:
-
Task: Define the specific reasoning task the model needs to perform.
-
Instruction: Provide clear, explicit instructions that encourage deeper exploration of a single line of reasoning.
-
Example: Demonstrate the desired behavior by providing examples of sustained reasoning.
Building a TIE Prompt Based on the Article
Here's how we can apply TIE to address the "underthinking" issue:
1. Task (T)
Choose a specific complex reasoning task. Based on the article, options include:
-
Math competition problem: Use questions from the MATH500-Hard, or AIME2024 datasets.
-
College physics problem: Select a problem from the GPQA Diamond set.
-
Chemistry task: Design a complex chemistry problem.
Example Task:
"Solve the following math competition problem from the MATH500-Hard dataset: [Insert a specific problem here]"
2. Instruction (I)
This is the core of addressing "underthinking". We need to instruct the model to:
-
Commit to an initial approach: Encourage the model to thoroughly explore its first line of reasoning.
-
Avoid premature switching: Discourage the use of phrases like "Alternatively" or other indicators of strategy changes until the current approach is fully exhausted.
-
Demonstrate persistence: Emphasize the value of sticking with a solution path even if it becomes challenging.
Example Instruction:
"Develop a solution by thoroughly exploring your initial line of reasoning. Avoid changing your approach until you have fully exhausted all possibilities within your initial strategy. Demonstrate persistence and show all steps in your reasoning, even if the solution path becomes complex. Do not use phrases like 'Alternatively' or prematurely switch strategies."
3. Example (E)
Provide an example that showcases sustained reasoning on a similar problem. This example should:
-
Start with an initial approach.
-
Explore that approach in-depth, showing all steps.
-
Only switch strategies if the initial approach is definitively proven wrong.
Example:
"Here's an example of how to solve a different math problem using sustained reasoning:
Problem: [Insert a different, but similarly complex, math problem]
Solution:
-
Initial Approach: I will start by attempting to solve the problem using [Name of Method, e.g., algebraic manipulation].
-
Step 1: [Detailed explanation of the first step]
-
Step 2: [Detailed explanation of the second step, building on the previous one]
... -
Step N: [Detailed explanation of a step where an obstacle is encountered, but the model persists in the current approach]
... -
Conclusion (if initial approach works): Therefore, the solution is [Solution].
OR -
Exhaustion of Initial Approach (if it fails): I have exhausted all possibilities within the initial approach of [Name of Method]. It appears this method will not yield the correct solution.
-
New Approach: Now I will try [Name of New Method].
-
Step 1 (New Approach): ...
Complete TIE Prompt Example
"Task: Solve the following math competition problem from the MATH500-Hard dataset: A circle of radius 1 is inscribed in a square. A smaller circle is tangent to the circle and two sides of the square. What is the radius of the smaller circle?
Instruction: Develop a solution by thoroughly exploring your initial line of reasoning. Avoid changing your approach until you have fully exhausted all possibilities within your initial strategy. Demonstrate persistence and show all steps in your reasoning, even if the solution path becomes complex. Do not use phrases like 'Alternatively' or prematurely switch strategies.
Example: Here's an example of how to solve a different math problem using sustained reasoning:
Problem: A rectangle has a perimeter of 20 and an area of 24. What are the dimensions of the rectangle?
Solution:
-
Initial Approach: I will start by attempting to solve the problem using a system of equations. Let the length be 'l' and the width be 'w'.
-
Step 1: From the perimeter, we have 2l + 2w = 20, which simplifies to l + w = 10.
-
Step 2: From the area, we have l * w = 24.
-
Step 3: I can solve for 'l' in the first equation: l = 10 - w.
-
Step 4: Substitute this into the second equation: (10 - w) * w = 24.
-
Step 5: This simplifies to a quadratic equation: w^2 - 10w + 24 = 0.
-
Step 6: Factoring the quadratic: (w - 6)(w - 4) = 0.
-
Step 7: This gives us two possible solutions for w: w = 6 or w = 4.
-
Step 8: If w = 6, then l = 10 - 6 = 4. If w = 4, then l = 10 - 4 = 6.
-
Conclusion: Therefore, the dimensions of the rectangle are 4 and 6.
Now, apply sustained reasoning to solve the original problem."
Key Considerations
-
Prompt Engineering is Iterative: You might need to refine the prompt further based on the model's responses.
-
Model-Specific: Different models may respond differently to the same prompt.
-
Balance: While encouraging persistence, the prompt should not prevent the model from eventually switching strategies if the initial approach is truly fruitless. The example should demonstrate this balance.
By using a well-crafted TIE prompt that incorporates the insights from the article, you can significantly improve the model's ability to reason deeply and solve complex problems more effectively.
Okay, here are just the prompt instructions, ready to be pasted directly into the prompt window, incorporating the principles of sustained reasoning and the TIE framework, especially designed to mitigate "underthinking" in complex reasoning tasks:
Option 1 (More Explicit):
Develop a solution by thoroughly exploring your initial line of reasoning. Avoid changing your approach until you have fully exhausted all possibilities within your initial strategy. Demonstrate persistence and show all steps in your reasoning, even if the solution path becomes complex. Do not use phrases like 'Alternatively' or prematurely switch strategies unless your first approach is demonstrably incorrect. If you must switch strategies, clearly state why the initial approach failed before moving on.
Option 2 (Slightly More Concise):
Solve this problem by first committing to a single line of reasoning and exploring it deeply. Show all steps in your logic. Avoid switching your problem-solving approach unless your current strategy is definitively proven wrong. Do not use phrases that indicate a change in strategy (e.g., "Alternatively") prematurely. If a strategy change is necessary, explain why before proceeding.
Option 3 (More direct to avoid "underthinking"):
Focus on sustained reasoning to solve this problem. Fully explore your initial approach before considering any alternatives. Show every step of your reasoning. Prematurely changing your line of thought, especially when an approach might still be fruitful, will be penalized. Only if your first approach is completely exhausted and proven incorrect, may you switch, providing a clear justification first. Avoid phrases like "Alternatively..." unless absolutely necessary.
How to Use:
-
Paste: Copy one of these instruction sets and paste it into the prompt window of your AI model.
-
Add Task: Before or after these instructions, provide the specific problem (the "Task" from TIE) you want the model to solve.
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Optional Example: If desired, you can also add an example (the "Example" from TIE) of sustained reasoning, as illustrated in the previous response. Although this can be quite long, so judge if you want to include this.
These instructions are designed to encourage the AI to think more deeply and avoid the "underthinking" trap described in the article. Remember that you may need to experiment and refine your prompts based on the specific AI model you are using and the nature of the tasks you are giving it.
Alright, here's a combined "mega" prompt that integrates the best elements of the previous options, designed to strongly encourage sustained reasoning and combat "underthinking" in complex problem-solving:
Mega Prompt:
Solve this problem using a focused and persistent approach. Begin by selecting a single line of reasoning and explore it as deeply as possible. Demonstrate sustained reasoning by meticulously showing every step of your logic, even if the solution path becomes challenging or complex. Prematurely changing your strategy is strongly discouraged. Do not use phrases that suggest a shift in approach, such as "Alternatively, " unless your current strategy is definitively and demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial approach and can prove it will not lead to a correct solution, you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed justification, explaining why the first approach failed before moving on. Your goal is to demonstrate thoroughness and depth in your reasoning process, prioritizing a complete exploration of a single approach over premature exploration of multiple approaches.
How to use:
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Paste this "mega prompt" into the input area of your AI model.
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Insert your specific problem (the task) either before or after this prompt.
Why this is a "mega prompt":
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Combines Strengths: This prompt incorporates the clarity of Option 1, the conciseness of Option 2, and the directness regarding "underthinking" from Option 3.
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Strong Emphasis: It strongly emphasizes sustained reasoning, deep exploration, and persistence.
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Explicit Constraints: It clearly prohibits premature strategy switching and the use of specific phrases that often signal such shifts.
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Justification Requirement: It mandates a detailed justification if a strategy change becomes unavoidable.
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Focus on Thoroughness: It prioritizes a complete exploration of a single approach over jumping between multiple possibilities.
This prompt is designed to be a powerful tool to improve the reasoning abilities of your AI model, especially when tackling complex problems where "underthinking" might be a concern. Remember, prompt engineering is often an iterative process, so feel free to adjust it further if needed based on the model's responses. Good luck!
also unit it with programing python idea code generator
Okay, I understand. You want a prompt that not only encourages sustained reasoning but also specifically guides the AI to generate Python code as a solution, and incorporates the "underthinking" prevention strategies. Here's a "mega prompt" designed for that purpose:
Mega Prompt (Python Code Generation with Sustained Reasoning):
Your task is to generate Python code that solves the following problem. Employ a focused and persistent approach to your code development. Begin by outlining your initial strategy and then develop your code meticulously, step-by-step. Demonstrate sustained reasoning by thoroughly exploring your initial coding approach and providing clear, in-line comments that explain each step of your logic. Prematurely changing your coding strategy is strongly discouraged. Do not abandon your initial approach or use comments that suggest a shift in strategy, such as "Alternatively, " unless your current approach is definitively and demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial coding strategy and can prove it will not lead to a correct solution, you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed explanation, within the comments, justifying why the first approach failed before proceeding. Your goal is to produce a well-structured, well-commented, and functional Python program that solves the given problem, prioritizing a complete exploration of a single, well-reasoned coding approach over premature exploration of multiple approaches. Strive for code that is not only correct but also demonstrates a clear and logical thought process.
How to Use:
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Paste: Paste this entire prompt into the AI model's input area.
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Insert Problem: Immediately after the prompt, clearly state the problem you want the AI to solve by writing Python code.
Example:
Your task is to generate Python code that solves the following problem. Employ a focused and persistent approach to your code development. Begin by outlining your initial strategy and then develop your code meticulously, step-by-step. Demonstrate sustained reasoning by thoroughly exploring your initial coding approach and providing clear, in-line comments that explain each step of your logic. Prematurely changing your coding strategy is strongly discouraged. Do not abandon your initial approach or use comments that suggest a shift in strategy, such as "Alternatively," unless your current approach is definitively and demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial coding strategy and can prove it will not lead to a correct solution, you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed explanation, within the comments, justifying why the first approach failed before proceeding. Your goal is to produce a well-structured, well-commented, and functional Python program that solves the given problem, prioritizing a complete exploration of a single, well-reasoned coding approach over premature exploration of multiple approaches. Strive for code that is not only correct but also demonstrates a clear and logical thought process.
Problem: Write a Python function that takes a list of integers as input and returns the sum of all even numbers in the list.
Why this is tailored for Python code generation:
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Explicitly Mentions Python: It clearly states that the desired output is Python code.
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Emphasis on Comments: It stresses the importance of clear, in-line comments to explain the code's logic, which is crucial for code readability and maintainability.
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Coding Strategy: It uses the term "coding strategy" to make the concept of sustained reasoning more relevant to the programming domain.
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Well-Structured Code: It encourages the generation of well-structured and functional code.
Important Notes:
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Model Capabilities: The success of this prompt depends on the AI model's ability to generate code and follow complex instructions.
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Iterative Refinement: You may still need to refine the prompt or interact with the model iteratively to achieve the desired results.
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Complexity: For very complex coding tasks, the model might still struggle. You may need to break down the problem into smaller, more manageable sub-problems.
This "mega prompt" provides a strong foundation for getting your AI to generate well-reasoned Python code while minimizing the risk of "underthinking." Let me know if you have any more questions.
You're right, Gemini models do have a "System" instruction zone, and we can craft an additional prompt specifically for that zone to reinforce the main prompt and further enhance the model's ability to perform sustained reasoning when generating Python code.
Here's a system-level prompt designed to complement the "mega prompt" we created earlier:
System-Level Prompt:
You are a highly advanced AI assistant specializing in generating well-reasoned, efficient, and thoroughly commented Python code. When given a coding task, prioritize depth of exploration over breadth. Commit to a single, well-defined coding strategy and pursue it diligently. Resist the urge to prematurely switch approaches or explore multiple solutions simultaneously. Your primary objective is to demonstrate sustained and focused reasoning throughout the code development process. Only deviate from your initial strategy if it is demonstrably and irrefutably proven to be incorrect, and provide a clear justification for any such change. Emphasize clarity, logic, and thoroughness in your code and accompanying comments. Adhere to best practices for Python code style and structure. Your responses should always be in the form of a single, complete, and executable Python code block unless otherwise instructed.
How to Use This System Prompt:
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Access the System Prompt Area: In the Gemini interface, locate the area designated for "System" instructions. This area might be labeled differently depending on the specific interface you are using.
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Paste: Paste this entire system prompt into the System instruction zone.
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Main Prompt in User Area: Use the "Mega Prompt (Python Code Generation with Sustained Reasoning)" from the previous response in the regular user prompt area, along with the specific problem you want the model to solve.
Why This System Prompt is Effective:
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Reinforces Main Prompt: It strongly reinforces the principles of sustained reasoning, deep exploration, and persistence that are emphasized in the main prompt.
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Sets AI Persona: It establishes the AI's role as a specialized assistant skilled in generating high-quality Python code.
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Prioritizes Depth: It explicitly prioritizes in-depth exploration of a single approach over the breadth of exploring multiple solutions prematurely.
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Justification for Change: It reiterates the need for a clear justification if a strategy change becomes absolutely necessary.
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Code Quality: It emphasizes the importance of code clarity, logic, thoroughness, and adherence to Python best practices.
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Output Format: It specifies the desired output format as a single, complete, and executable Python code block.
Example of Combined Usage:
System Prompt Area:
You are a highly advanced AI assistant specializing in generating well-reasoned, efficient, and thoroughly commented Python code. When given a coding task, prioritize depth of exploration over breadth. Commit to a single, well-defined coding strategy and pursue it diligently. Resist the urge to prematurely switch approaches or explore multiple solutions simultaneously. Your primary objective is to demonstrate sustained and focused reasoning throughout the code development process. Only deviate from your initial strategy if it is demonstrably and irrefutably proven to be incorrect, and provide a clear justification for any such change. Emphasize clarity, logic, and thoroughness in your code and accompanying comments. Adhere to best practices for Python code style and structure. Your responses should always be in the form of a single, complete, and executable Python code block unless otherwise instructed.
User Prompt Area:
Your task is to generate Python code that solves the following problem. Employ a focused and persistent approach to your code development. Begin by outlining your initial strategy and then develop your code meticulously, step-by-step. Demonstrate sustained reasoning by thoroughly exploring your initial coding approach and providing clear, in-line comments that explain each step of your logic. Prematurely changing your coding strategy is strongly discouraged. Do not abandon your initial approach or use comments that suggest a shift in strategy, such as "Alternatively, " unless your current approach is definitively and demonstrably incorrect. If, and only if, you have completely exhausted all possibilities within your initial coding strategy and can prove it will not lead to a correct solution, you may then consider a new strategy. If a strategy change becomes absolutely necessary, provide a clear and detailed explanation, within the comments, justifying why the first approach failed before proceeding. Your goal is to produce a well-structured, well-commented, and functional Python program that solves the given problem, prioritizing a complete exploration of a single, well-reasoned coding approach over premature exploration of multiple approaches. Strive for code that is not only correct but also demonstrates a clear and logical thought process.
Problem: Write a Python function that takes a list of strings as input and returns a new list containing only the strings that have more than 5 characters.
By using both the system prompt and the main prompt together, you create a powerful synergy that maximizes the AI's ability to generate high-quality, well-reasoned Python code while effectively combating the "underthinking" problem. Remember to experiment and adapt these prompts as needed to achieve optimal results for your specific use cases.
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