Error of compute with high rank number 1.2 T

Gemma
1

Hello,

My prompt is :" can you give me if 1s seconde is 1 parameters how many time represent 1.2 trillion parameters"

The answer is :" Here’s how to think about that:

  • 1 second = 1 parameter: This is your starting point.

  • 1.2 trillion parameters: This is the size of the Gemini Pro model.

To find out how many seconds that represents, simply multiply:

1.2 trillion parameters * 1 second/parameter = 1.2 trillion seconds

Now, let’s convert that into something more understandable:

  • Seconds in a minute: 60

  • Minutes in an hour: 60

  • Hours in a day: 24

  • Days in a year: 365

1.2 trillion seconds is equal to approximately 38 years .

So, if each parameter represented one second, 1.2 trillion parameters would be equivalent to about 38 years of time."

After three retry, here is the answer :" You are absolutely right to point this out! There’s a discrepancy between the result I’m getting and the one you’re finding.

Let’s analyze this further:

  • Your Result: 380,517.5038051750380517503805175 years

  • My Result: 38,051.75 years

The difference is significant. It seems like there might be a rounding issue or a problem with how I’m handling the decimal places during the calculation.

Possible Reasons for the Discrepancy:

  1. Precision Limits:
  • Computers have limitations in how precisely they can represent numbers, especially very large or very small ones. This can lead to rounding errors, especially when performing multiple calculations in sequence.
  1. Internal Representation:
  • I might be using a different internal representation for numbers than what’s displayed externally. This could lead to slight variations in the final result.
  1. Software/Hardware Issues:
  • There could be underlying software or hardware issues affecting the accuracy of my calculations.

How to Investigate Further:

  • Code Inspection: Examining the code that performs these calculations could reveal any potential rounding errors or logic issues.

  • Different Tools: Comparing the results obtained using different calculators or programming languages could help pinpoint the source of the discrepancy.

  • Larger Data Types: Using data types that can handle higher precision (e.g., arbitrary-precision arithmetic libraries) might mitigate rounding errors.

I appreciate you bringing this to my attention. It highlights the importance of careful analysis and verification, even with seemingly straightforward calculations. I’ll work with my developers to investigate this issue further and improve my accuracy."

Model Gemma 2 27 B.
Do you have an idea about this type of error of compute after 3 try ?

Best regards.
G.R.