This is probably part of why machines are doing so well at counterexamples. They have no aesthetic commitment to the conjecture and no embarrassment about producing something ugly
This is probably part of why machines are doing so well at counterexamples. They have no aesthetic commitment to the conjecture and no embarrassment about producing something ugly
That's not why.
It's because counterexamples are easy compared to proofs which require new mathematics.
GenAI is great at combining existing things in new ways (interpolation). It's terrible at creating new things from scratch (extrapolation).
This reminds me of the Go Grandmaster speaking out after losing to AlphaGo, that the model has no sense of "aesthetic play", as long as it would lead to a win within the rules.
I thought there was a lot of buzz about AI creativity after the infamous move 37 in that series?
Yes but it was so shocking because it was such an inhuman, "unaesthetic" play. It was considered to be "creative" in that no human would have thought of making the move, so it can't simply be copying human play.
if humans could do it, it would be called beautiful. defining something to be ugly is cope
They're trained on human data. I would expect them to emulate human biases as closely as possible.
This is where harness, and the fact that a machine can be endlessly prompted to try again comes in.
Even if an LLM starts by pursuing things that follow human bias, continuous failures and re-prompting to try something different will eventually force it to consider things outside of what ever biases it has.
You can do the same thing to a human. But most people would consider it unethical to lock someone in a box and force them to keep trying to solve the same problem over and over again until they figure it out.
Your comment stopped me in my tracks a little bit.
Is a 'bias' in a piece of writing generally a property of word to word choice and sentence to sentence construction or is it something more nebulous? Especially in terms of the appreciation of mathematics and someone's hesitance about publishing a mathematical argument they think is ugly or brute forced in some way.
> Is a 'bias' in a piece of writing generally a property of word to word choice and sentence to sentence construction or is it something more nebulous?
You might be fascinated when you read the story of Golden Gate Claude: https://www.anthropic.com/news/golden-gate-claude
Is it? I'd expect most of the training set to be synthetic data extrapolated from a small set of human authored texts.
Most of the training set is half of the Internet. LLMs are pre-trained on general set of human biases and patterns of thinking.
It's more complex than that, especially as post training is often goal based.
I wouldn't have expected that there was post training specifically on the issue of looking for proofs vs counter examples. But it might be that other post training has a side effect of making AIs better at looking for counter examples. I wonder if these agents are overall less biased and more rational than humans. Can you expand on what you mean by goal based training?