‘’’ these are the vectors that when viewed as linear functionals, annihilate every column of A . <…> Another way to view it: these are the vectors orthogonal to the row space. ‘’’
It’s quite obvious that vectors that “annihilate the columns” would be orthogonal to the column space not the row space.
I don’t know if you think o1 is magic. It still hallucinates, just less often and less obvious.
"Support, the calculator gave a bad result for 345987*14569" // "Yes, well, also your average human would"
...That why we do not ask "average humans"!
So the result might not necessarily be bad, it's just that the machine _can_ detect that you entered the wrong figures! By the way, the answer is 7.
> Can you please give an example of a “completely illogical statement” produced by o1 model? I suspect it would be easier to get an average human to produce an illogical statement.
> H: The surgeon, who is the boy's father, says "I can't operate on this boy, he's my son!" Who is the surgeon of the boy?
> O1: The surgeon is the boy’s mother.
Also, just because humans don't always think rationally doesn't mean ChatGPT does.
> This is a classic riddle! The surgeon is actually the boy's mother. The riddle plays on the assumption that a surgeon is typically male, but in this case, the surgeon is the boy's mother.
> Did you enjoy this riddle? Do you have any more you'd like to share or solve?
"I was trying to find a clever twist that isn't actually there. The riddle appears to just be a straightforward statement - a father who is a surgeon saying he can't operate on his son"
More than being illogical, it seems that LLMs can be too hasty and too easily attracted by known patterns. People do the same.
Then the follow up correction did have the effect of making it look harder at the question. It actually wrote:
"Let me look at EXACTLY what's given" (with the all caps).
It's not very different from a person that decides to focus harder on a problem once it was fooled by it a couple of times already because it is trickier than it seems. So yes, surprisingly human, with all its flaws.
<<Because the surgeon, who is the boy's father, says, "I can't operate on this boy, he's my son!" This indicates that there is another parent involved who is also a surgeon. Given that the statement specifies the boy's father cannot operate, the other surgeon must be the boy's mother.>> Sounds plausible and on the first read, almost logical.
