problem on the failure of LLMs to do math -- and an easy fix

Enhancing Mathematical Computation Accuracy in AI: Addressing LLM Limitations with Specialized APIs

Here is a development related problem on the failure of LLMs to do math -- and an easy fix!

A user asked OpenAI to compute the first 1000 binary digits of SQRT(2) out of curiosity, a very trivial task….

Took a bit of time, returned wrong digits. Ask the same question to Sage or Wolfram, you'll get the first 1 million digits in less than a second, all correct. In my case I need billions of digits from billions of independent constants like SQRT(2) and SQRT(87) for my secure crypto apps. So, what's the deal with LLMs now solving math problems and supposedly becoming more intelligent than ever, when you have tools that can do symbolic computations correctly and much faster since at least 2010, don't use GPU, LLM, nor neural networks? Why isn't GPT using the Wolfram API to solve these problems much faster with accurate results?

I then asked OpenAI this question: "Wolfram code to generate 1000 binary digits of sqrt(2)". It returned the correct code, see picture. So technically, OpenAI "knows" how to get these digits, but instead relies on its own faulty logic to do the computations, rather than doing an API call to Wolfram. The fix is simple: folks at OpenAI, please contact Wolfram and make a partnership with them. It's win-win for everyone. And you can compute complicated integrals, solve differential equations (exactly when possible) and a lot more, with all detailed steps if user asks for it.

Step-by-Step Process to Investigate the Problem

1. Identify the Scope of LLM Math Limitations:

• Investigate where and why LLMs fail in high-precision calculations.

• Identify specific areas like irrational number expansion, large factorials, or matrix operations where LLMs struggle.

2.Benchmark Against Dedicated Tools:
• Compare LLMs’ math computation speeds and accuracy against Wolfram Alpha, SageMath, and other symbolic computation tools.

• Record results to understand the gap in performance.

3.Examine Current API Integration Options:
• Look at existing integrations or plugins that allow models to use computational software.
• Assess what barriers, if any, exist in connecting LLMs to these tools.

1. Evaluate Limitations of LLM Internal Computation:
   • Identify why LLMs resort to pattern recognition rather than direct calculations (e.g., token limitations, training limitations).

2. Research Wolfram & Sage APIs:
   • Explore documentation for these APIs to determine how they handle complex calculations.

•Identify parameters that are best suited to relay math queries through these tools.

1. Design a Test Scenario: • Simulate a user request for a math computation that is challenging for LLMs

• Test how effectively the system returns correct results with and without the API.

1. Implement API Calls for Computation in LLMs: •Write example code that routes specific math queries to Wolfram or Sage APIs.

•Ensure the code is modular, allowing easy switching between LLM calculations and API calls.

1. Evaluate User Needs in Math Computation:
   • Identify common use cases for high-accuracy math computations.
   • Analyse user feedback on when and why they seek external accuracy.

2. Run Performance & Accuracy Tests:
   • Test LLM performance across various mathematical queries with and without API integration.
   • Evaluate the efficiency and accuracy of each solution, measuring against dedicated tools.

10.Refine and Improve API-based Math Solutions:
• Fine-tune the integration to prioritize API calls for specific types of math problems.

• Develop a feedback loop to improve model accuracy over time, especially for recurring query types.

Why This Problem Matters

AI-powered applications increasingly intersect with fields that demand high-precision mathematics, from cryptography to engineering. LLMs are not always equipped to perform exact calculations due to limitations in their neural network structures and training data. As a result, computations relying on patterns instead of symbolic math can lead to inaccuracies, a significant problem in applications requiring strict mathematical correctness.

By integrating specialised APIs (like Wolfram Alpha), LLMs can offload complex calculations, improving accuracy, speed, and reliability. This hybrid approach allows LLMs to focus on what they do best—language interpretation—while letting established math tools handle rigorous calculations.

Future Possibilities

• Enhanced AI-Assisted Learning Tools: Integrating LLMs with symbolic math software can provide students with highly accurate, step-by-step solutions to complex problems.

• Advanced AI for Scientific Research: Scientists and researchers can rely on LLMs for computational-heavy tasks, ensuring precise calculations for simulations and models.

• Reliable AI-Based Cryptography Solutions: In cryptography, where precise constants are critical, a hybrid approach could bolster security and data integrity.

• Accessible Math Education: Improved accuracy in AI-powered tutoring tools for STEM education could help make complex subjects more approachable.

10 Ways This Blog is Useful for Coders, Developers, and Testers

1. Identifies Key Limitations of LLMs in math, setting a foundation for further research.

2. Provides a Process for testing API solutions to augment AI functionality.

3. Suggests Benchmarking Practices to objectively evaluate LLM capabilities.

4. Explains API Integration Steps for developers looking to combine AI and math tools.

5. Highlights Real-World Applications of precise mathematical calculations in AI.

6. Demonstrates Practical Test Scenarios for software testers.

7. Breaks Down Future Applications that could inspire innovative solutions.

8. Offers Hands-On Code Examples for building AI-math integrations.

9. Promotes Collaboration with Math Tool Experts for knowledge sharing.

10. Invites Philosophical Discussion on ethical considerations, offering a holistic view.

Philosophers’ Role in Ethical AI Development

Philosophers focusing on ethics can provide valuable insights into responsible AI development, particularly in areas where incorrect computations could have serious consequences.

For instance, *inaccurate calculations in healthcare or finance could lead to harmful outcomes. *

Ethical experts can:

• Advocate for Transparent AI: Ensure that limitations and dependencies are clear to end-users.

• Assist in Policy Creation: Help draft guidelines for using AI in critical applications.

• Promote Responsible AI: Evaluate scenarios where errors could impact privacy or fairness.

• Encourage Holistic AI: Guide collaborations that combine different tools for a more rounded approach to problem-solving.

Setting Up Testing Environments for Students

For university students aiming to explore API integration with AI models, setting up lab environments can be an ideal way to gain practical experience.

1. Choose a Platform: Use Jupyter Notebooks or Google Colab, which support Python and API calls.

2. Set Up the Wolfram or Sage API: Access API keys and configure basic query setups.

3. Develop Simple API Calls: For example, a call to fetch specific digits of √2.
   

import requests

# Example API call to Wolfram Alpha for square root of 2 digits
API_KEY = 'your_wolfram_api_key'
query = '1000 binary digits of sqrt(2)'
url = f'https://api.wolframalpha.com/v2/query?input={query}&format=plaintext&output=JSON&appid={API_KEY}'

response = requests.get(url)

#Process response
if response.status_code == 200:
    result = response.json()
    print(result['queryresult']['pods'][0]['subpods'][0]['plaintext'])
else:
    print("Error:", response.status_code)

1. Test with Sample Problems: Set up basic problems that students can solve using both LLMs and API solutions, comparing results.

2. Evaluate Accuracy and Efficiency: Track time and precision for each solution, helping students understand real-world API performance considerations.

This foundational work can set the stage for developing high-performance AI solutions that blend language and computation, with a responsible approach that considers the ethical impact of accuracy.