How GPT solve logic and math problems

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My very limited understanding of GPT is that it’s basically a text generator. Why and how could it solve logic and math problems? Or is it just an emergent ability from LLM that nobody understands?

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14 Answers

Anonymous 0 Comments

It can’t.

It’s just a really advanced version of auto-prediction. Kinda like how your phone might predict the next word you want to write based on your typing history.

Expect it can predict entire sentences and paragraphs. Because it’s more complicated than that and has loads of text history to reference.

(Okay, because I already know some people will not-uh that statement. This is a really bad explanation of what it is and does. I’m just trying to water it down so it’s ELI5 friendly.)

You can ask it a math problem, and it might be able to answer it well enough. Or maybe give it a logical statement, and it might appear to understand it.

But that’s just because it’s seen something similar before, so it already had the answer readily available.

You can try asking it questions that it’s not familiar with, and you’ll quickly see how incapable it is and that it’s quite limited.

Try asking it to play Four Fours. It is a very simple and easy math game, but gpt is terrible at it. It can’t very well generate new answers to questions it’s never seen the answer to.

Or you can ask it to explain this scenario in detail:

Three men go into a bar. The bartender asks, ‘Would you all like a beer?’ The first man say, ‘I don’t know.’ The second says, ‘I don’t know.’ The last man says, ‘Yes.’

That’s a scenario with simple logic to understand. But again, if gpt hasn’t seen it before, it can’t really understand it and will reply with seemingly irrelevant explanations.

Anonymous 0 Comments

It can’t.

It’s just a really advanced version of auto-prediction. Kinda like how your phone might predict the next word you want to write based on your typing history.

Expect it can predict entire sentences and paragraphs. Because it’s more complicated than that and has loads of text history to reference.

(Okay, because I already know some people will not-uh that statement. This is a really bad explanation of what it is and does. I’m just trying to water it down so it’s ELI5 friendly.)

You can ask it a math problem, and it might be able to answer it well enough. Or maybe give it a logical statement, and it might appear to understand it.

But that’s just because it’s seen something similar before, so it already had the answer readily available.

You can try asking it questions that it’s not familiar with, and you’ll quickly see how incapable it is and that it’s quite limited.

Try asking it to play Four Fours. It is a very simple and easy math game, but gpt is terrible at it. It can’t very well generate new answers to questions it’s never seen the answer to.

Or you can ask it to explain this scenario in detail:

Three men go into a bar. The bartender asks, ‘Would you all like a beer?’ The first man say, ‘I don’t know.’ The second says, ‘I don’t know.’ The last man says, ‘Yes.’

That’s a scenario with simple logic to understand. But again, if gpt hasn’t seen it before, it can’t really understand it and will reply with seemingly irrelevant explanations.

Anonymous 0 Comments

“Sparks of AGI” is a lecture on YouTube I have been forcing everyone I know to watch. GPT4 is, or rather was, intelligent by nearly every metric we have. It predicts the next word but to do that extremely well it had to build an internal model of the world. For real the unicorn segment gives me shivers just thinking about it

Anonymous 0 Comments

“Sparks of AGI” is a lecture on YouTube I have been forcing everyone I know to watch. GPT4 is, or rather was, intelligent by nearly every metric we have. It predicts the next word but to do that extremely well it had to build an internal model of the world. For real the unicorn segment gives me shivers just thinking about it

Anonymous 0 Comments

Yes GPT is an advanced generator designed to predict the next “symbol”, but that doesn’t mean that it can’t “learn” underlying principles.

It is certainly able to answer simple math problems that it hasn’t seen before, so in some sense has “figured out” the basic principles of, say, addition, because it’s seen enough examples that it can generalise.

This doesn’t mean it’s going to get everything correct though. I watched a video from the creator where he said that it had “learned” to add any two 40 digit numbers together, but if you give it a 35 digit and a 40 digit it would sometimes (confidently) get it wrong.

Of course, a human might know that they are bad at that sort of thing (we also make mistakes), but knows enough to use a calculator. With the Wolfram etc. plug-ins, this is exactly what future versions will do.

“ChatGPT can add two 40 digit numbers, so now it “mostly” understands how to add, but if you try a 40 digit number plus a 35 digit number, sometimes it gets it wrong. So it’s still deriving how math works..” Greg Brockman, founder of #OpenAI at #TED2023

EDIT: Added quote

Anonymous 0 Comments

Yes GPT is an advanced generator designed to predict the next “symbol”, but that doesn’t mean that it can’t “learn” underlying principles.

It is certainly able to answer simple math problems that it hasn’t seen before, so in some sense has “figured out” the basic principles of, say, addition, because it’s seen enough examples that it can generalise.

This doesn’t mean it’s going to get everything correct though. I watched a video from the creator where he said that it had “learned” to add any two 40 digit numbers together, but if you give it a 35 digit and a 40 digit it would sometimes (confidently) get it wrong.

Of course, a human might know that they are bad at that sort of thing (we also make mistakes), but knows enough to use a calculator. With the Wolfram etc. plug-ins, this is exactly what future versions will do.

“ChatGPT can add two 40 digit numbers, so now it “mostly” understands how to add, but if you try a 40 digit number plus a 35 digit number, sometimes it gets it wrong. So it’s still deriving how math works..” Greg Brockman, founder of #OpenAI at #TED2023

EDIT: Added quote

Anonymous 0 Comments

Because someone else has data shared or out datat related to math question you are asking on the web.

Math is fundamentally a process of arriving at a result using a lot of different methods.

Chatgpt cannot do that unless it is out there in the web.

Chatgpt doesn’t understand math, it pretends to make links in a semantic web.

In short doing math is not same as understanding math. Math is a beautiful subject just too complex for a machine to truly understand with our current tech.

Anonymous 0 Comments

Because someone else has data shared or out datat related to math question you are asking on the web.

Math is fundamentally a process of arriving at a result using a lot of different methods.

Chatgpt cannot do that unless it is out there in the web.

Chatgpt doesn’t understand math, it pretends to make links in a semantic web.

In short doing math is not same as understanding math. Math is a beautiful subject just too complex for a machine to truly understand with our current tech.

Anonymous 0 Comments

It doesn’t solve a logic/math problem anymore than your brain solves the calculus behind the trajectory of a baseball.

LLM algorithms are pattern matching algorithms. They take a bunch of initial states and a bunch of ending states and builds a statistical model that it can use to extrapolate answers from based on the initial state. You feed a new initial state to the LLM and it looks for the ending state that is most likely.

All of these AI/ML uses are the result of emergent ability from a relatively “simple” process. Modern AI/ML tools just do it at an absolutely massive scale that makes it impractical (not impossible) for a human to pick apart because it involves the tedious process of examining how millions/billions of data points individually changes the statistical model.

Anonymous 0 Comments

It doesn’t solve a logic/math problem anymore than your brain solves the calculus behind the trajectory of a baseball.

LLM algorithms are pattern matching algorithms. They take a bunch of initial states and a bunch of ending states and builds a statistical model that it can use to extrapolate answers from based on the initial state. You feed a new initial state to the LLM and it looks for the ending state that is most likely.

All of these AI/ML uses are the result of emergent ability from a relatively “simple” process. Modern AI/ML tools just do it at an absolutely massive scale that makes it impractical (not impossible) for a human to pick apart because it involves the tedious process of examining how millions/billions of data points individually changes the statistical model.