This is impressive. I wonder how quickly and how well this could be adapted to other domains in science and engineering. It could be a really useful tool for engineering teams
Original textbook question (number theory course):
> The product of the positive integer divisors of a positive integer n is 729. Find n.
Actual model input/prompt:
> Write a function which finds the divisors (including 1 and itself) of the input and multiplies them together. Iterate over all possible integers until it finds an input where the product is 729.
Model output program:
def divisors(n):
divisors = []
for i in range(1, n+1):
if n % i == 0:
divisors.append(i)
return divisors
def product(n):
return reduce(lambda x, y: x*y, n)
def find_n(n):
for i in range(1, n):
if product(divisors(i)) == 729:
return i
print find_n(1000000)
Note: any errors in the program are my own transcribing error.
The problem is that this approach relies on a large language model trained on a copy of the entire web (GPT-3, trained on Common Crawl plus network extras), fine-tuned on github (Codex) and then fine-tuned again on the kinds of problems that it is supposed to solve. That is an insane amount of resources to spend to solve simple programming problems with known solutions that can be implemented by hand at much lower cost and effort. In that sense it's a little bit disappointing: so much data, so much compute, and all you can do is tell computer how to code python?
Could you point me to where they claim to have fine-tuned Codex?
From what I can see they claim:
> We use OpenAI’s davinci-codex engine for all of our generations. We fix all of Codex’s hyperparameters to be the same for all experiments: top-p which is the portion p of the token probability mass a language model samples from at each step is set to 1, sampling temperature is set to 0 (i.e. argmax), and response length is set to 200 tokens.
BTW - OpenAI Davinci costs $0.06 per 1000 tokens. Codex is currently free in closed beta, but I guess cost will be the same. I would be happy to pay even 100x ($6) for correct solutions to advanced mathematical problems. The issue is that this paper has ridiculous evaluation and Codex does not work anywhere near as good as they claim. It is pure hype by people who do not appear to be affiliated with OpenAI.
I can't find that in the paper so I must have imagined it.
>> Codex is currently free in closed beta, but I guess cost will be the same.
In my previous comment, I'm referring to the "amount of resources" needed to train GPT-3 and then fine-tune Codex, of course.