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How ChatGPT does the calculations is a mystery. I asked it to calculate my total mortgage payments over 10 years for $100,000 at 2% interest. The result ($102,9

How ChatGPT does the calculations is a mystery. I asked it to calculate my total mortgage payments over 10 years for $100,000 at 2% interest. The result ($102,945.60) looked a bit suspicious to me. But it gets really interesting with 4.5% interest. ChatGPT> If the interest rate on your mortgage is 4.5% instead of 2%, the calculations will be different. Using the same formula as before, we can find the monthly payment: P = 100000[(0.045/12)(1 + 0.045/12)^120]/[(1 + 0.045/12)^120 - 1] P = 100000[0.00375(1.00375)^120]/[(1.00375)^120 - 1] P = 100000[0.479276]/[0.479276 - 1] P = 100000[0.479276]/[-0.520724] P = -918.71 So the monthly payment for this mortgage would be approximately -$918.71, which means you would be paying back more than the original loan amount every month. This is because the interest rate is higher than the growth rate of the loan amount. To calculate the total amount you will have to pay back, we can once again multiply the monthly payment by the total number of payments: Total amount to be paid back = Monthly payment x Total number of payments Total amount to be paid back = -$918.71 x 120 Total amount to be paid back = -$110,245.20 Note that the negative sign on the monthly payment and total amount to be paid back indicates that you will be paying more in interest than the original loan amount. This example illustrates the importance of shopping around and comparing mortgage rates to find the best deal. --- end quote --- That is, ChatGPT somehow "feels" that there's something wrong with the negative amount, and tries to come up with the explanation, but falls short.

Widdershin 4y ago
LLMs being used for math by programmers or engineers always makes me think of the rocket that blew up because they mixed metric and imperial units. It definitely happens in the wild as well, I’ve seen devs using copilot for napkin math far more than I’m comfortable with.
- klyrs 4y ago
  Don't worry, with this level of aptitude, if "AI" tried to build a rocket the fuel tank wouldn't even hold a positive volume.
- latency-guy2 4y ago
  I do firmly expect ChatGPT to parse their way through math and statistics LLMs are first and foremost billions to trillions of matrix multiplications, further, if ChatGPT and Copilot is not able to do math, then it certainly has no application for developing code that requires math, e.g. physics simulations, geometry, anything related to transforms in general i.e CSS Another important part (maybe at this point, only supposed future benefit) of ChatGPT is the ability to summarize larger texts and documentation, to be used in a variety of ways such as summarizing financial reports, research papers, long form journalism, books, as well as developer documentation and APIs. So if it can't do math, then ChatGPT is useless for all people, forever.
- gpderetta 4y ago
  Obviously the engineers that built the rocket were not actually intelligent but just a fancy autocomplete in a sack of meat.
swatcoder 4y ago
> How ChatGPT does the calculations is a mystery. It’s no mystery. It doesn’t do calculations at all. You really need to think of it more like am improvisor playing a financial advisor on stage rather than a financial advisor doing their work. There are countless samples of mortgage calculation texts in its training data, so at your request, it starts inventing such a text that uses your provided number. It knows, more or less, what numbers appear around what other numbers in this kind of text at the small scale of arithmetic and large scale of mortgage calculation texts and so it seems pretty coherent at first glance. But because you asked for a very specific thing that isn’t quite like any other in its training data, the text it includes becomes more hallucinatory and less referential. And when these hallucinations goes off the rails and no longer looks like the normal sort of mortgage calculator training text (few probably have negative results!), it starts to hallucinate the vaguely explanatory boilerplate text common around weird values. No calculations, no feelings, no understanding. Just text completion that feels inconceivably rich compared to what we’re used to, but that is literally about on par with an professional improvisor.
- resource0x 4y ago
  The problem is that it is not fixable in the language model without implementing special logic for mortgage calculations, like "if the user asks about mortgage calculations, do this (e.g. invoke python program) instead of regular processing. That is, this class of questions should be "special-cased" somehow. But the number of special cases like this is potentially infinite. Even to answer "I don't know how to answer this question", the engine has to be specifically instructed to do so.
  - MPSimmons 4y ago
    Yeah, all specialty subjects are like this (or math that's sufficiently different from its learned text - have it square a very, very large number with a bunch of random digits and compare that against the actual answer from a calculator). To actually solve this, we need AGI.
    - iainmerrick 4y ago
hackinthebochs 4y ago
GPT-3 and descendants don't see numbers the way we do due to the unintuitive way the input is tokenized[1], and so we need to be careful about projecting unreasonable expectations on what they should be able to do given their built-in limitations. [1] https://gwern.net/gpt-3#bpes https://gwern.net/gpt-3#bpes

Widdershin 4y ago

LLMs being used for math by programmers or engineers always makes me think of the rocket that blew up because they mixed metric and imperial units. It definitely happens in the wild as well, I’ve seen devs using copilot for napkin math far more than I’m comfortable with.

klyrs 4y ago
Don't worry, with this level of aptitude, if "AI" tried to build a rocket the fuel tank wouldn't even hold a positive volume.
latency-guy2 4y ago
I do firmly expect ChatGPT to parse their way through math and statistics LLMs are first and foremost billions to trillions of matrix multiplications, further, if ChatGPT and Copilot is not able to do math, then it certainly has no application for developing code that requires math, e.g. physics simulations, geometry, anything related to transforms in general i.e CSS Another important part (maybe at this point, only supposed future benefit) of ChatGPT is the ability to summarize larger texts and documentation, to be used in a variety of ways such as summarizing financial reports, research papers, long form journalism, books, as well as developer documentation and APIs. So if it can't do math, then ChatGPT is useless for all people, forever.
gpderetta 4y ago
Obviously the engineers that built the rocket were not actually intelligent but just a fancy autocomplete in a sack of meat.

swatcoder 4y ago

> How ChatGPT does the calculations is a mystery. It’s no mystery. It doesn’t do calculations at all. You really need to think of it more like am improvisor playing a financial advisor on stage rather than a financial advisor doing their work. There are countless samples of mortgage calculation texts in its training data, so at your request, it starts inventing such a text that uses your provided number. It knows, more or less, what numbers appear around what other numbers in this kind of text at the small scale of arithmetic and large scale of mortgage calculation texts and so it seems pretty coherent at first glance. But because you asked for a very specific thing that isn’t quite like any other in its training data, the text it includes becomes more hallucinatory and less referential. And when these hallucinations goes off the rails and no longer looks like the normal sort of mortgage calculator training text (few probably have negative results!), it starts to hallucinate the vaguely explanatory boilerplate text common around weird values. No calculations, no feelings, no understanding. Just text completion that feels inconceivably rich compared to what we’re used to, but that is literally about on par with an professional improvisor.

resource0x 4y ago
The problem is that it is not fixable in the language model without implementing special logic for mortgage calculations, like "if the user asks about mortgage calculations, do this (e.g. invoke python program) instead of regular processing. That is, this class of questions should be "special-cased" somehow. But the number of special cases like this is potentially infinite. Even to answer "I don't know how to answer this question", the engine has to be specifically instructed to do so.
- MPSimmons 4y ago
  Yeah, all specialty subjects are like this (or math that's sufficiently different from its learned text - have it square a very, very large number with a bunch of random digits and compare that against the actual answer from a calculator). To actually solve this, we need AGI.
  - iainmerrick 4y ago

hackinthebochs 4y ago

GPT-3 and descendants don't see numbers the way we do due to the unintuitive way the input is tokenized[1], and so we need to be careful about projecting unreasonable expectations on what they should be able to do given their built-in limitations. [1] https://gwern.net/gpt-3#bpes https://gwern.net/gpt-3#bpes