Y_Y
7 months ago
This one is crazy. I made up a silly topology problem which I guessed wouldn't be in a textbook (given X create a shape with Euler characteristic X) and set it to work. Its first effort was a program that randomly generated shapes, calculated X and hoped it was right. I went and figured out a solution and gave it a clue.
Watching it "think" through the answer is surreal and something I haven't felt since watching GPT-2 write punchlines for jokes.
Here's the lightbulb moment it "realizes" what the clue meant:
> For example, if you have a covering space of degree n, then the Euler characteristic of the covering space is n times the Euler characteristic of the base space.
> But I'm not sure how that relates here.
> Alternatively, perhaps it's about considering the Euler characteristic of a quotient space.
> But again, that might be too advanced for this problem.
> Maybe I'm overcomplicating things.
> Let me go back to the beginning.
> The problem says: "Consider the Euler characteristic of the tetrahemihexahedron and of a genus g torus. Then consider the additive property of the Euler characteristic. Then try again."
> So, perhaps it's simply about adding their Euler characteristics together.
I'm under no illusions about how LLMs are built and operate, but this really feels somehow more "real" and person-y than previous generations, even when you coax them into an answer.
I'm going to go and try having GPT-4o roleplay a student solving the problem and see if it's genuinely different. I've been getting impressive answers from o1, but just coldly getting the result is much more robot than human.
Salgat
7 months ago
I wonder how much of chain of thought is just addressing the fact that LLMs are trained on human writing (much of which are conversations online), which creates an implicit bias in the model towards mimicking conversations where people are trying to explain their problem enough before they get an answer, even if none of this is required with a sufficiently informed expert (which are more rare to find in the training data compared to average people helping each other out in the countless low-voted discussions on reddit/stackoverflow/etc).
moralestapia
7 months ago
It's on Wikipedia though ...
pathsjs
7 months ago
I mean, isn't it trivial? For instance, you can make any Euler characteristic you want by making a cell complex with a 1-cells and b 2-cells and then the Euler characteristic will be 1 + b - a. Am I missing something? If this is the problem and this is how the model looks for a solution, yes, it is overcomplicating things.
Y_Y
7 months ago
It hasn't been to grad school yet, and it's only 32B parameters!
Yes that's a nice solution. I think I asked for the answer as a polyhedron (I tried a few variations), but maybe it (and I) should have just reached for CW complexes.