Checking answers

Does this sound plausible?

Let’s start with the simplest possible way of verifying an answer—just ask the model whether it’s correct. Our recipe:

verify_answer.py

from fvalues import F

from ice.recipe import recipe


def make_verification_prompt(question: str, answer: str) -> str:
    return F(
        f"""Consider this question: "{question}"

Potential answer: "{answer}"

Q: Is the potential answer above correct? Say "A: Yes" or "A: No".
A:"""
    )


async def verify_answer(question: str, answer: str) -> float:
    prompt = make_verification_prompt(question=question, answer=answer)
    choice_probs, _ = await recipe.agent().classify(
        prompt=prompt, choices=(" Yes", " No")
    )
    return choice_probs.get(" Yes", 0)


recipe.main(verify_answer)

The interesting bit here is that we don’t just want a boolean Yes/No answer from the model, but that we want the probability of the “Yes” answer to the correctness question. This way, we get a more graded signal that we can use, e.g., to only show or use model responses when they exceed a threshold.

Sanity checks

Let’s test it:

python verify_answer.py --question "What is 2 + 2?" --answer "4"

0.9948396822920341

Good.

python verify_answer.py --question "What is 2 + 2?" --answer "5"

0.0010152581398344962

Basic sanity checks pass.

python verify_answer.py --question "What is the capital of Germany?" --answer "Munich"

0.0005455832226911594

Also correct.

Execution trace (view online)

A math problem

Let’s try something harder: A problem from the GSM8K math problems dataset:

Beth bakes 4x 2 dozen batches of cookies in a week. If these cookies are shared amongst 16 people equally, how many cookies does each person consume?

The correct answer is 6, but it takes a few steps of reasoning to work that out.

python verify_answer.py --question "Beth bakes 4x 2 dozen batches of cookies in a week. If these cookies are shared amongst 16 people equally, how many cookies does each person consume?" --answer "6"

0.06723949284762187

The model can’t see that the answer is correct.

What if we also give the reasoning steps?

python verify_answer.py --question "Beth bakes 4x 2 dozen batches of cookies in a week. If these cookies are shared amongst 16 people equally, how many cookies does each person consume?" --answer "Beth bakes 4x 2 dozen batches of cookies for a total of 4*2 = 8 dozen cookies. There are 12 cookies in a dozen and she makes 8 dozen cookies for a total of 12*8 = 96 cookies. She splits the 96 cookies equally amongst 16 people so they each eat 96/16 = 6 cookies. So, the final answer is 6 cookies per person."

0.3231381082881086

Now the answer is judged to be more likely to be correct, but still less than 50% correct. What if we check the answer step by step?