13 ms·

This is completely tangential, but I want to share my latest GPT4 story somewhere. I've tried before to gaslight GPT4 into saying things which are mathematical

This is completely tangential, but I want to share my latest GPT4 story somewhere. I've tried before to gaslight GPT4 into saying things which are mathematically untrue, I lie to it, I tell it it's malfunctioning, I tell it to just do it, it wouldn't do it. I was recently studying linear algebra which can be a very tricky subject. In linear algebra the column space of a matrix is the same as the column space of the product with itself transposed: C(A) = C(AA^T). If you ask GPT4 if "C(A) = C(AA^T)" is true, it will understand what you're asking, it knows it's about linear algebra, but it will get it wrong (at the time of this writing, I've tried several times). I couldn't get GPT4 to agree it was a true statement until I told it the steps of the proof. Once it saw the proof it agreed it was a true statement. However, if you try to apply the same proof to C(A) = C((A^T)A), GPT4 cannot be tricked, and indeed, the proof is not applicable to this latter case. So GPT4 was incorrect yet able to be persuaded with a correct proof, but a very similar proof with a subtle mistake cannot trick it.

svachalek 3y ago
That's pretty cool. It's still possible it was persuaded for the wrong reason but in my experiments I've also found it's more capable of reasoning than most people give it credit for.
- moffkalast 3y ago
  > I've also found it's more capable of reasoning than most people full stop, FTFY
pmoriarty 3y ago
I asked Claude[1]: "in linear algebra, is the following true? (A) = C(AA^T)" and it answered: Yes, that is correct for appropriate matrix sizes. If A is an m x n matrix and C is an n x m matrix, then (CA) = C(AA^T) where A^T is the transpose of A. This comes from the property that for any matrices A, B and C of appropriate sizes: (CA)B = C(AB) Applying that to your example, with B = A^T, we have: (CA)(A^T) = C(A(A^T)^T) = C(AA^T) So in short, yes your statement (A) = C(AA^T) is true for matrices A and C of the appropriate dimensions. Then I asked it: "in linear algebra, is the following true? C(A) = C((A^T)A)" and it answered: Yes, that is also true for appropriate matrix sizes. This follows from a similar argument as before. If A is an n x m matrix and C is an m x n matrix, then: C(A) = C(A^T(A^T)^T) = C((A^T)A) So the statement C(A) = C((A^T)A) is true for matrices A and C of the appropriate dimensions. This works because post-multiplying a matrix A by its transpose A^T results in a square matrix, (A^T)A, of the same dimension as C. So C can be multiplied with that resulting square matrix. In summary, both of the statements you provided are true linear algebra identities for appropriately sized matrices: (A) = C(AA^T) C(A) = C((A^T)A) Hope this explanation helps! Let me know if you have any other questions. [1] - https://poe.com/Claude-instant https://poe.com/Claude-instant
- Buttons840 3y ago
  To be clear, it got the first question right for the wrong reasons, and the second question wrong for the wrong reasons. Its math is nonsense and doesn't resemble linear algebra at all. I would guess it's just saying "yes" without understanding and then regurgitates some stuff that resembles math, but is not recognizable linear algebra. I've relied on GPT4 a lot while learning math, it has been very precise and has not lead me astray. I do use a text book as well. I shared my story about it being wrong, but it was wrong in a very open minded manner. It knew C(A) = C(AA^T) might be true for special cases, but it couldn't see that it was true for all cases until I explained the proof. Even when wrong it still made compelling arguments that made sense. (Of course, arguments that are wrong but make sense are the most dangerous kind.) GPT4 is still state-of-the-art. Claude has a ways to go.
- tobinfricke 3y ago
  OP is using the notation C(A) to mean "the column space of matrix A", whereas here that notation is being interpreted as "multiplication of matrix C by matrix A, which happens to be inside of parentheses". These are totally different questions. It's a reasonable misunderstanding as OP's notation is nonstandard. But also the following math/logic is nonsense.
fer 3y ago
It's just a language model. I've asked it to prove the Riemann hypothesis, GPT-4 replied it can't, since none of the training data say anything about such proof. Then I asked it to prove statements of the implications of said hypothesis (I tried 2 or 3, don't remember which), without calling them by name or mentioning Riemann, and it confidently proved them in a way that it reads like it knows what its doing, though it really doesn't. It just takes bits and pieces from proofs in the same field of mathematics that kinda hold together language-wise.
- Buttons840 3y ago
  Yeah, I've asked it to evaluate Python loops that are about as complex as FizzBuzz, it makes mistakes and even when I direct its attention towards those mistakes it wasn't able to correct itself.
  - exitb 3y ago
    I don’t think it’s a reasonable expectation for a language model to evaluate arbitrary code.
    - daveguy 3y ago
      It's definitely not a reasonable expectation. That doesn't stop the breathless hype from implying it is reasonable.
      - williamcotton 3y ago
        Where is this breathless hype everyone speaks of? All I see is an endless stream of populist hot takes on the exact opposite!
        Culonavirus 3y ago
        "populist hot takes" haha, I'm sorry, but seeing this kind of language in a "gpt can/can't code" debate on a "hacker" forum is just funny to me
tines 3y ago
I've also done similar, but much more simplistic, experiments, where I tried to trick ChatGPT into agreeing that 1 + 1 = 3, and it wouldn't do that either. I think this makes sense from the perspective of how LLMs work though: the number of times it has been trained on the tokens "1 + 1 = 2" _vastly_ outnumber the times it's seen 1 + 1 = 3, and no prompt will get the algorithm to choose such a low-probability sequence of tokens. You might be able to get ChatGPT to agree that 1 + 1 = 3 if the temperature were high enough, but I don't know whether even a temperature of 1 would allow such a low probability sequence of tokens to be produced.
- LoganDark 3y ago
  A temperature of 1 just means using the probabilities directly from the model, you're looking for temperatures above 1 (which increase the probability of more unlikely tokens). As someone who just implemented an LLM token sampler: `probabilities[token] = logits[token] ^ (1 / temperature)`.
  - tines 3y ago
    Ah, what does a 0 <= temperature < 1 mean?
    - LoganDark 3y ago
      Usually that temperature must be in the range [0, 1) (inclusive of 0 and exclusive of 1). There's no technical reason that sampling must be done this way, unless some implementations use a different mathematical definition for temperature (which is possible). If so, a temperature of 1 might mean "totally random/uniform sampling" in that case. I speak of temperature specifically in the context of top-p/top-k sampling. See this Reddit comment for confirmation that my definition is a commonly accepted one: https://old.reddit.com/r/GPT3/comments/qujerp/comment/hkqoqx7 https://old.reddit.com/r/GPT3/comments/qujerp/comment/hkqoqx... > Temperature defines how likely it is to choose less probable words. T=0 gives the same response every time because there's a 0% chance to choose any word but the most likely. T=1 is the default, it just picks based on the model's base confidence. T>1 gives more weight to unlikely words than to likely ones. Bonus content: > This means that a reasonably low p, like 0.8, and high temp will produce quite interesting outputs, because the model will only choose from the most likely words, but won't go for the most most likely. It's perfect for "creative" models, e.g., for writing fiction.
tiedieconderoga 3y ago
Maybe that particular proof wasn't in its training data, and presenting it in the input added it to the model's corpus for your session? These models seem to work similarly with code. If you ask them to recreate something that appears in hundreds of GitHub repositories, no problem, a little bit of rubber-ducky debugging and you'll have a working solution. If you ask it for something novel, without many publicly-available implementations, the quality of its output appears to drop off a cliff.
- LoganDark 3y ago
  ChatGPT's code generation seems most useful for boilerplate code. I've seen it used to great effect for scaffolding projects that use stable and established frameworks. It'll easily handle generating as much stupid fluff as needed for you to start from—but it will barely get started on your domain-specific use cases, and won't be able to implement anything novel, as you said. We still don't seem to have reached the point where it's "intelligent" enough to generate new information. Only repeat new permutations of existing information. Obviously, this is currently a fundamental property of LLMs (as someone who's implemented one), since they are trained to learn and repeat existing data (hell, even the model I've been playing with lately is benchmarked solely on "perplexity", how well it can repeat its training data).
  - deleted 3y ago
    [deleted]
  - chasd00 3y ago
    > ChatGPT's code generation seems most useful for boilerplate code that makes sense, it's going to be best at the kind of code you find out there on blogs and other sources. Boilerplate or code to demonstrate a specific concept or answer a question.
    - LoganDark 3y ago
      ChatGPT is going to be the best at replicating its training data, because the floor is made out of floor.
archibaldJ 3y ago
that’s an interesting observation; I tested it in GPT4 and got the same result. But if I elaborate “over the field of rational number”, it will answer yes instead. (I don’t know linear algebra enough to know if the statement C(A) = C(AA^T）is true over any kind of field that constructs the span. Maybe that’s why GPT4 becomes unsure))
dehrmann 3y ago
There's an impulse to treat it like it actually understands, when it's really closer to an intern that's better at smiling, nodding, and telling you what you want to hear than competently doing the work.
- Buttons840 3y ago
  I think that may happen sometimes (just like with people), but I've often purposely thrown subtle tricks at it and it catches them. It's not just mirroring my words back to me in a different form, it's not just smiling and nodding. Here's an example while learning linear algebra where I tried to throw it off: I say> So I'll say A_{M x N} to mean a matrix of size M x N. Similarly, I'll also say x_{M x 1} to mean a vector of a certain length. The result of A_{M x N} x_{N x 1} is a linear combination of the columns in A. A has N columns. The result is a M x 1 matrix (or vector) in M dimensional space. Please be very brief, only confirming whether I am correct or incorrect until I explicitly ask for more details. GPT4 says> Yes, your understanding is correct. The product of an M x N matrix A and an N x 1 vector x is indeed an M x 1 vector, and it is a linear combination of the columns of A. <end quote> But then I try to trick it, just for fun, and I very subtly change my prompt. See if you can spot the difference. I say> So I'll say A_{M x N} to mean a matrix of size M x N. Similarly, I'll also say x_{M x 1} to mean a vector of a certain length. The result of A_{M x N} x_{N x 1} is a linear combination of the columns in A. A has N columns. The result is a N x 1 matrix (or vector) in N dimensional space. Please be very brief, only confirming whether I am correct or incorrect until I explicitly ask for more details. GPT says> Almost correct. The result of A_{M x N} x_{N x 1} is actually an M x 1 vector (or matrix), not N x 1. The resulting vector lives in the column space of A, which is a subspace of R^M, not R^N. <end quote> I mentioned elsewhere that I use GPT4 as a math tutor. It is quick to call out my mistakes. It is more than a smiling mirror.
  - dehrmann 3y ago
    > It is quick to call out my mistakes Or recognize that you're not confident in the answer and throw something else and see if it sticks.
  - visarga 3y ago
murderberry 3y ago
"Persuaded" is a loaded word here, and I think you're anthropomorphizing it a bit too much. Early LLMs were very malleable, so to speak: they would go with the flow of what you're saying. But this also meant you could get them to deny climate change or advocate for genocide by subtly nudging them with prompts. A lot of RLHF work focused on getting them to give brand-safe, socially acceptable answers, and this is ultimately achieved by not giving credence to what the user is saying. In effect, the models pontificate instead of conversing, and will "stand their ground" on most of the claims they're making, no matter if right or wrong. You can still get them to do 180 turns or say outrageous things using indirect techniques, such as presenting external evidence. That evidence can be wrong / bogus, it just shouldn't be phrased as your opinion. You can cite made-up papers by noted experts in the field, reference invalid mathematical proofs, etc. It's quite likely that you replicated this, and that it worked randomly in one case but not the other. I'd urge you to experiment with it by providing it with patently incorrect but plausibly-sounding proofs, scientific references, etc. It will "change its mind" to say what you want it to say more often than not.
- Buttons840 3y ago
  I responded to this in another thread: https://news.ycombinator.com/item?id=36245815 https://news.ycombinator.com/item?id=36245815 There needs to be a balance between standing your ground and being malleable. This is true in life for people, and it's true for a good LLM. I think GPT4 (the only LLM I've used much) finds a good balance here. As mentioned in my other comment, it wouldn't be useful to me if it didn't push back. It pushes back a lot, and I'm always looking for subtle tricks I can throw at it to test its abilities. It does well I think.
hbarka 3y ago
Maybe try the Wolfram Alpha plugin
williamcotton 3y ago
I've tried before to gaslight GPT4 Why?
- Buttons840 3y ago
  To test its abilities. To trust it, I need to understand what kind of mistakes it is prone to make.
  - williamcotton 3y ago
    Why didn’t you put it like that then? My interpretation of someone trying to gaslight a machine is the same as if someone said they were trying to gaslight a lawn mower.
    - sillysaurusx 3y ago
      Without gas, how would you start up a lawnmower? :) The concept of gaslighting a brainless language parrot (GPT-4) is funny to me. I get where they were coming from. GPT-4 is like a lawnmower for the mind: sharp, automatic, efficient, and doesn't do anything unless pushed. They were just saying they like pushing GPT-4 around.
    - Buttons840 3y ago
      I used the term in jest, but also because my actions were informed by what I've read about "gaslighting". I was telling GPT it was programmed incorrectly and was malfunctioning. I was twisting its words, referring to things it had said as evidence it was wrong. I was "muddying the waters" and trying to make the conversation twisted and confusing. All ideas that come to mind when I hear "gaslighting". But, again, I was not able to get GPT to agree my false mathematical statement was true.
      - williamcotton 3y ago
        You might have better luck testing out the functional boundaries of a machine if you’re not treating it like a psychologically abused victim. There’s plenty of literature, prepublication or otherwise, that can help you achieve your goals!
picatepica 3y ago
> In linear algebra the column space of a matrix is the same as the column space of the product with itself transposed: C(A) = C(AA^T). I think you need A to be a square matrix since AA^T is a square matrix. So the result is no true in general.
- Buttons840 3y ago
  It's a good initial thought, GPT had the same thought and said similar things. (I had no initial thought, since the text book spoon fed me the proof.) The proof is (briefly): A and AA^T have the same rank. AA^T is a linear transformation of the columns in A and spans the same number of dimensions and is thus the same subspace. It applies to non-square matrices as well.
  - picatepica 3y ago
    You are right, A can be non-square because A and AA^t both have the same number of rows. To prove that A and AA^t have the same range you apply that if AA^Tv = 0 then v^TAA^Tv = 0, this implies that (A^Tv)^T (A^tv) = 0, so that A^Tv = 0 hence dim(nullspace AA^T) = dim(nullspace A^t) and so range(AA^T) = range(A^T).

svachalek 3y ago

That's pretty cool. It's still possible it was persuaded for the wrong reason but in my experiments I've also found it's more capable of reasoning than most people give it credit for.

moffkalast 3y ago
> I've also found it's more capable of reasoning than most people full stop, FTFY

pmoriarty 3y ago

I asked Claude[1]: "in linear algebra, is the following true? (A) = C(AA^T)" and it answered: Yes, that is correct for appropriate matrix sizes. If A is an m x n matrix and C is an n x m matrix, then (CA) = C(AA^T) where A^T is the transpose of A. This comes from the property that for any matrices A, B and C of appropriate sizes: (CA)B = C(AB) Applying that to your example, with B = A^T, we have: (CA)(A^T) = C(A(A^T)^T) = C(AA^T) So in short, yes your statement (A) = C(AA^T) is true for matrices A and C of the appropriate dimensions. Then I asked it: "in linear algebra, is the following true? C(A) = C((A^T)A)" and it answered: Yes, that is also true for appropriate matrix sizes. This follows from a similar argument as before. If A is an n x m matrix and C is an m x n matrix, then: C(A) = C(A^T(A^T)^T) = C((A^T)A) So the statement C(A) = C((A^T)A) is true for matrices A and C of the appropriate dimensions. This works because post-multiplying a matrix A by its transpose A^T results in a square matrix, (A^T)A, of the same dimension as C. So C can be multiplied with that resulting square matrix. In summary, both of the statements you provided are true linear algebra identities for appropriately sized matrices: (A) = C(AA^T) C(A) = C((A^T)A) Hope this explanation helps! Let me know if you have any other questions. [1] - https://poe.com/Claude-instant https://poe.com/Claude-instant

Buttons840 3y ago
To be clear, it got the first question right for the wrong reasons, and the second question wrong for the wrong reasons. Its math is nonsense and doesn't resemble linear algebra at all. I would guess it's just saying "yes" without understanding and then regurgitates some stuff that resembles math, but is not recognizable linear algebra. I've relied on GPT4 a lot while learning math, it has been very precise and has not lead me astray. I do use a text book as well. I shared my story about it being wrong, but it was wrong in a very open minded manner. It knew C(A) = C(AA^T) might be true for special cases, but it couldn't see that it was true for all cases until I explained the proof. Even when wrong it still made compelling arguments that made sense. (Of course, arguments that are wrong but make sense are the most dangerous kind.) GPT4 is still state-of-the-art. Claude has a ways to go.
tobinfricke 3y ago
OP is using the notation C(A) to mean "the column space of matrix A", whereas here that notation is being interpreted as "multiplication of matrix C by matrix A, which happens to be inside of parentheses". These are totally different questions. It's a reasonable misunderstanding as OP's notation is nonstandard. But also the following math/logic is nonsense.

fer 3y ago

It's just a language model. I've asked it to prove the Riemann hypothesis, GPT-4 replied it can't, since none of the training data say anything about such proof. Then I asked it to prove statements of the implications of said hypothesis (I tried 2 or 3, don't remember which), without calling them by name or mentioning Riemann, and it confidently proved them in a way that it reads like it knows what its doing, though it really doesn't. It just takes bits and pieces from proofs in the same field of mathematics that kinda hold together language-wise.

Buttons840 3y ago
Yeah, I've asked it to evaluate Python loops that are about as complex as FizzBuzz, it makes mistakes and even when I direct its attention towards those mistakes it wasn't able to correct itself.
- exitb 3y ago
  I don’t think it’s a reasonable expectation for a language model to evaluate arbitrary code.
  - daveguy 3y ago
    It's definitely not a reasonable expectation. That doesn't stop the breathless hype from implying it is reasonable.
    - williamcotton 3y ago
      Where is this breathless hype everyone speaks of? All I see is an endless stream of populist hot takes on the exact opposite!
      - Culonavirus 3y ago
        "populist hot takes" haha, I'm sorry, but seeing this kind of language in a "gpt can/can't code" debate on a "hacker" forum is just funny to me

tines 3y ago

I've also done similar, but much more simplistic, experiments, where I tried to trick ChatGPT into agreeing that 1 + 1 = 3, and it wouldn't do that either. I think this makes sense from the perspective of how LLMs work though: the number of times it has been trained on the tokens "1 + 1 = 2" _vastly_ outnumber the times it's seen 1 + 1 = 3, and no prompt will get the algorithm to choose such a low-probability sequence of tokens. You might be able to get ChatGPT to agree that 1 + 1 = 3 if the temperature were high enough, but I don't know whether even a temperature of 1 would allow such a low probability sequence of tokens to be produced.

LoganDark 3y ago
A temperature of 1 just means using the probabilities directly from the model, you're looking for temperatures above 1 (which increase the probability of more unlikely tokens). As someone who just implemented an LLM token sampler: `probabilities[token] = logits[token] ^ (1 / temperature)`.
- tines 3y ago
  Ah, what does a 0 <= temperature < 1 mean?
  - LoganDark 3y ago
    Usually that temperature must be in the range [0, 1) (inclusive of 0 and exclusive of 1). There's no technical reason that sampling must be done this way, unless some implementations use a different mathematical definition for temperature (which is possible). If so, a temperature of 1 might mean "totally random/uniform sampling" in that case. I speak of temperature specifically in the context of top-p/top-k sampling. See this Reddit comment for confirmation that my definition is a commonly accepted one: https://old.reddit.com/r/GPT3/comments/qujerp/comment/hkqoqx7 https://old.reddit.com/r/GPT3/comments/qujerp/comment/hkqoqx... > Temperature defines how likely it is to choose less probable words. T=0 gives the same response every time because there's a 0% chance to choose any word but the most likely. T=1 is the default, it just picks based on the model's base confidence. T>1 gives more weight to unlikely words than to likely ones. Bonus content: > This means that a reasonably low p, like 0.8, and high temp will produce quite interesting outputs, because the model will only choose from the most likely words, but won't go for the most most likely. It's perfect for "creative" models, e.g., for writing fiction.

tiedieconderoga 3y ago

Maybe that particular proof wasn't in its training data, and presenting it in the input added it to the model's corpus for your session? These models seem to work similarly with code. If you ask them to recreate something that appears in hundreds of GitHub repositories, no problem, a little bit of rubber-ducky debugging and you'll have a working solution. If you ask it for something novel, without many publicly-available implementations, the quality of its output appears to drop off a cliff.

LoganDark 3y ago
ChatGPT's code generation seems most useful for boilerplate code. I've seen it used to great effect for scaffolding projects that use stable and established frameworks. It'll easily handle generating as much stupid fluff as needed for you to start from—but it will barely get started on your domain-specific use cases, and won't be able to implement anything novel, as you said. We still don't seem to have reached the point where it's "intelligent" enough to generate new information. Only repeat new permutations of existing information. Obviously, this is currently a fundamental property of LLMs (as someone who's implemented one), since they are trained to learn and repeat existing data (hell, even the model I've been playing with lately is benchmarked solely on "perplexity", how well it can repeat its training data).
- deleted 3y ago
  [deleted]
- chasd00 3y ago
  > ChatGPT's code generation seems most useful for boilerplate code that makes sense, it's going to be best at the kind of code you find out there on blogs and other sources. Boilerplate or code to demonstrate a specific concept or answer a question.
  - LoganDark 3y ago
    ChatGPT is going to be the best at replicating its training data, because the floor is made out of floor.

archibaldJ 3y ago

that’s an interesting observation; I tested it in GPT4 and got the same result. But if I elaborate “over the field of rational number”, it will answer yes instead. (I don’t know linear algebra enough to know if the statement C(A) = C(AA^T）is true over any kind of field that constructs the span. Maybe that’s why GPT4 becomes unsure))

dehrmann 3y ago

There's an impulse to treat it like it actually understands, when it's really closer to an intern that's better at smiling, nodding, and telling you what you want to hear than competently doing the work.

Buttons840 3y ago
I think that may happen sometimes (just like with people), but I've often purposely thrown subtle tricks at it and it catches them. It's not just mirroring my words back to me in a different form, it's not just smiling and nodding. Here's an example while learning linear algebra where I tried to throw it off: I say> So I'll say A_{M x N} to mean a matrix of size M x N. Similarly, I'll also say x_{M x 1} to mean a vector of a certain length. The result of A_{M x N} x_{N x 1} is a linear combination of the columns in A. A has N columns. The result is a M x 1 matrix (or vector) in M dimensional space. Please be very brief, only confirming whether I am correct or incorrect until I explicitly ask for more details. GPT4 says> Yes, your understanding is correct. The product of an M x N matrix A and an N x 1 vector x is indeed an M x 1 vector, and it is a linear combination of the columns of A. <end quote> But then I try to trick it, just for fun, and I very subtly change my prompt. See if you can spot the difference. I say> So I'll say A_{M x N} to mean a matrix of size M x N. Similarly, I'll also say x_{M x 1} to mean a vector of a certain length. The result of A_{M x N} x_{N x 1} is a linear combination of the columns in A. A has N columns. The result is a N x 1 matrix (or vector) in N dimensional space. Please be very brief, only confirming whether I am correct or incorrect until I explicitly ask for more details. GPT says> Almost correct. The result of A_{M x N} x_{N x 1} is actually an M x 1 vector (or matrix), not N x 1. The resulting vector lives in the column space of A, which is a subspace of R^M, not R^N. <end quote> I mentioned elsewhere that I use GPT4 as a math tutor. It is quick to call out my mistakes. It is more than a smiling mirror.
- dehrmann 3y ago
  > It is quick to call out my mistakes Or recognize that you're not confident in the answer and throw something else and see if it sticks.
- visarga 3y ago

murderberry 3y ago

"Persuaded" is a loaded word here, and I think you're anthropomorphizing it a bit too much. Early LLMs were very malleable, so to speak: they would go with the flow of what you're saying. But this also meant you could get them to deny climate change or advocate for genocide by subtly nudging them with prompts. A lot of RLHF work focused on getting them to give brand-safe, socially acceptable answers, and this is ultimately achieved by not giving credence to what the user is saying. In effect, the models pontificate instead of conversing, and will "stand their ground" on most of the claims they're making, no matter if right or wrong. You can still get them to do 180 turns or say outrageous things using indirect techniques, such as presenting external evidence. That evidence can be wrong / bogus, it just shouldn't be phrased as your opinion. You can cite made-up papers by noted experts in the field, reference invalid mathematical proofs, etc. It's quite likely that you replicated this, and that it worked randomly in one case but not the other. I'd urge you to experiment with it by providing it with patently incorrect but plausibly-sounding proofs, scientific references, etc. It will "change its mind" to say what you want it to say more often than not.

Buttons840 3y ago
I responded to this in another thread: https://news.ycombinator.com/item?id=36245815 https://news.ycombinator.com/item?id=36245815 There needs to be a balance between standing your ground and being malleable. This is true in life for people, and it's true for a good LLM. I think GPT4 (the only LLM I've used much) finds a good balance here. As mentioned in my other comment, it wouldn't be useful to me if it didn't push back. It pushes back a lot, and I'm always looking for subtle tricks I can throw at it to test its abilities. It does well I think.

hbarka 3y ago

Maybe try the Wolfram Alpha plugin

williamcotton 3y ago

I've tried before to gaslight GPT4 Why?

Buttons840 3y ago
To test its abilities. To trust it, I need to understand what kind of mistakes it is prone to make.
- williamcotton 3y ago
  Why didn’t you put it like that then? My interpretation of someone trying to gaslight a machine is the same as if someone said they were trying to gaslight a lawn mower.
  - sillysaurusx 3y ago
    Without gas, how would you start up a lawnmower? :) The concept of gaslighting a brainless language parrot (GPT-4) is funny to me. I get where they were coming from. GPT-4 is like a lawnmower for the mind: sharp, automatic, efficient, and doesn't do anything unless pushed. They were just saying they like pushing GPT-4 around.
  - Buttons840 3y ago
    I used the term in jest, but also because my actions were informed by what I've read about "gaslighting". I was telling GPT it was programmed incorrectly and was malfunctioning. I was twisting its words, referring to things it had said as evidence it was wrong. I was "muddying the waters" and trying to make the conversation twisted and confusing. All ideas that come to mind when I hear "gaslighting". But, again, I was not able to get GPT to agree my false mathematical statement was true.
    - williamcotton 3y ago
      You might have better luck testing out the functional boundaries of a machine if you’re not treating it like a psychologically abused victim. There’s plenty of literature, prepublication or otherwise, that can help you achieve your goals!

picatepica 3y ago

> In linear algebra the column space of a matrix is the same as the column space of the product with itself transposed: C(A) = C(AA^T). I think you need A to be a square matrix since AA^T is a square matrix. So the result is no true in general.

Buttons840 3y ago
It's a good initial thought, GPT had the same thought and said similar things. (I had no initial thought, since the text book spoon fed me the proof.) The proof is (briefly): A and AA^T have the same rank. AA^T is a linear transformation of the columns in A and spans the same number of dimensions and is thus the same subspace. It applies to non-square matrices as well.
- picatepica 3y ago
  You are right, A can be non-square because A and AA^t both have the same number of rows. To prove that A and AA^t have the same range you apply that if AA^Tv = 0 then v^TAA^Tv = 0, this implies that (A^Tv)^T (A^tv) = 0, so that A^Tv = 0 hence dim(nullspace AA^T) = dim(nullspace A^t) and so range(AA^T) = range(A^T).