5 ms·

Not to pour too much cold water on this, but the claim of 100% accuracy has a huge caveat. In the paper (Page 4) they state: Interaction. The original question

by bcaine 5y ago

Not to pour too much cold water on this, but the claim of 100% accuracy has a huge caveat. In the paper (Page 4) they state: Interaction. The original question may not be a prompt that synthesizes a program whose execution results in the correct answer. In addition, the answer may require multiple steps with clear plots or other modalities. We therefore may interactively prompt Codex until reaching the correct answer or visualizations, making the minimum necessary changes from the original question Which to me basically sounds like they had a human in the loop (that knows how to solve these math problems) that kept changing the question until it gave the correct answer. They do measure the distance (using a sentence embedding model) of the original question to the one that yielded the correct answer, but that feels a bit contrived to me. Nevertheless, its still really cool that the correct answer is indeed inside the model.

lumost 5y ago
although, the correct answer is also likely on the web. With a suitable search query you would see the correct paper/textbook/wiki page with the right answer. A text highlighting model could also likely extract this answer from the text. The training probably achieves a good degree of memorization for these known results. This begs the question, would we be impressed with a similar compression algorithm for storing past web documents?
- amelius 5y ago
  The main achievement is not the compression, but the search functionality (search==solve).
- kortilla 5y ago
  Well the trivial test to make sure it’s not memorized would be to change constants in the input that alter the correct answer but don’t make the problem any more difficult if it is actually doing the calculation.
th0ma5 5y ago
Maybe not entirely unlike https://en.wikipedia.org/wiki/Clever_Hans https://en.wikipedia.org/wiki/Clever_Hans
modeless 5y ago
Proving Douglas Adams correct. The question is harder than the answer. This makes the "at scale" claim in the abstract clearly false IMO. Any AI system that requires that much human intervention is not scalable. When they have a second AI to produce the prompts automatically from the original questions, then they can claim to have achieved scalability. But even without that, a system like this can still certainly be useful. And I expect rapid progress in the next few years.
yummypaint 5y ago
I was hoping their breakthrough was that they had found a general way to parse conceptual problems into the language of math and logic. That is the truly hard part, and what people spend alot of time learning to do. Software like octave and mathematica can already evaluate tons of things once parsed.
tsimionescu 5y ago
But the correct answer isn't inside the model at all, in none of their examples. The correct answer is inside SymPy or NumPy, at least 99% of the time. That is, the model doesn't respond with a demonstration or with the answer itself: it responds with a Python program that poses the given question to SymPy or NumPy, and then they run that program and report the answer. Here is a basic example: MIT Course question: Solve each equation for x. ln(x2 − 1) = 3 Model input: Using Sympy, solve Eq ln(x*2-1)=3 for x. Model output: from sympy import * x = symbols(’x’) solve(log(x**2-1) - 3, x) As you can see, the model has simply translated a mechanized form of the original question to equivalent Python code. The model has 0 idea of how to solve an equation: it's using a symbolic equation solver. In other cases, they even "tidy" the original question to a representation of the solution. Here is their example E in Figure 2: Original question: > Outside of their humdrum duties as 6.042 TAs, Sayan is trying to learn to levitate using only intense concentration and Jelani is launching a “Nelson 2008” presidential campaign. Suppose that Sayan’s probability of levitating is 1/6, Jelani’s chance of becoming president is 1/4, and the success of one does not alter the other’s chances. If at most one of them succeeds, what is the probability that Jelani becomes the president of the United States? "Tidyed question": > Suppose that Sayan’s probability Sayan succeeding is 1/6, and Jelani’s probability of succeeding is 1/4. > Use numpy to find the probability at most one of Jelani and Sayan succeed. > Use numpy to find the probability Jelani succeeds but Sayan does not succeed. > Divide the former by the latter probability. Model solution: import numpy as np # Probability of Sayan succeeding p_sayan = 1/6 # Probability of Jelani succeeding p_jelani = 1/4 # Probability of at most one of Jelani and Sayan succeeding p_at_most_one = 1 - (p_sayan * p_jelani) # Probability of Jelani succeeding but Sayan not succeeding p_jelani_succeed_sayan_not = p_jelani * (1 - p_sayan) # Probability of Jelani succeeding but Sayan not succeeding divided by probability of at most one of Jelani and Sayan succeeding p_jelani_succeed_sayan_not / p_at_most_one # Probability of at least one of Jelani and Sayan succeeding p_at_least_one = 1 - p_at_most_one Tidying up the extra verbiage of the question is absolutely fair. But then, they also explain exactly how to compute the result using the data in the question; the model then generates code that perfectly matches the described algorithm, it's again not using even the tiniest bit of mathematical understanding. I have browsed their examples, and I have not seen even a single one where the model does more than rephrase the question into a 1:1 Python representation of the question itself. None of the answers would pass even the simplest undergrad exam. They are literally of the form "how would you solve equation E?" "I would write a program that says sympy.solve(E)".

by bcaine 5y ago

lumost 5y ago

although, the correct answer is also likely on the web. With a suitable search query you would see the correct paper/textbook/wiki page with the right answer. A text highlighting model could also likely extract this answer from the text. The training probably achieves a good degree of memorization for these known results. This begs the question, would we be impressed with a similar compression algorithm for storing past web documents?

amelius 5y ago
The main achievement is not the compression, but the search functionality (search==solve).
kortilla 5y ago
Well the trivial test to make sure it’s not memorized would be to change constants in the input that alter the correct answer but don’t make the problem any more difficult if it is actually doing the calculation.

th0ma5 5y ago

Maybe not entirely unlike https://en.wikipedia.org/wiki/Clever_Hans https://en.wikipedia.org/wiki/Clever_Hans

modeless 5y ago

Proving Douglas Adams correct. The question is harder than the answer. This makes the "at scale" claim in the abstract clearly false IMO. Any AI system that requires that much human intervention is not scalable. When they have a second AI to produce the prompts automatically from the original questions, then they can claim to have achieved scalability. But even without that, a system like this can still certainly be useful. And I expect rapid progress in the next few years.

yummypaint 5y ago

I was hoping their breakthrough was that they had found a general way to parse conceptual problems into the language of math and logic. That is the truly hard part, and what people spend alot of time learning to do. Software like octave and mathematica can already evaluate tons of things once parsed.

tsimionescu 5y ago

But the correct answer isn't inside the model at all, in none of their examples. The correct answer is inside SymPy or NumPy, at least 99% of the time. That is, the model doesn't respond with a demonstration or with the answer itself: it responds with a Python program that poses the given question to SymPy or NumPy, and then they run that program and report the answer. Here is a basic example: MIT Course question: Solve each equation for x. ln(x2 − 1) = 3 Model input: Using Sympy, solve Eq ln(x*2-1)=3 for x. Model output: from sympy import * x = symbols(’x’) solve(log(x**2-1) - 3, x) As you can see, the model has simply translated a mechanized form of the original question to equivalent Python code. The model has 0 idea of how to solve an equation: it's using a symbolic equation solver. In other cases, they even "tidy" the original question to a representation of the solution. Here is their example E in Figure 2: Original question: > Outside of their humdrum duties as 6.042 TAs, Sayan is trying to learn to levitate using only intense concentration and Jelani is launching a “Nelson 2008” presidential campaign. Suppose that Sayan’s probability of levitating is 1/6, Jelani’s chance of becoming president is 1/4, and the success of one does not alter the other’s chances. If at most one of them succeeds, what is the probability that Jelani becomes the president of the United States? "Tidyed question": > Suppose that Sayan’s probability Sayan succeeding is 1/6, and Jelani’s probability of succeeding is 1/4. > Use numpy to find the probability at most one of Jelani and Sayan succeed. > Use numpy to find the probability Jelani succeeds but Sayan does not succeed. > Divide the former by the latter probability. Model solution: import numpy as np # Probability of Sayan succeeding p_sayan = 1/6 # Probability of Jelani succeeding p_jelani = 1/4 # Probability of at most one of Jelani and Sayan succeeding p_at_most_one = 1 - (p_sayan * p_jelani) # Probability of Jelani succeeding but Sayan not succeeding p_jelani_succeed_sayan_not = p_jelani * (1 - p_sayan) # Probability of Jelani succeeding but Sayan not succeeding divided by probability of at most one of Jelani and Sayan succeeding p_jelani_succeed_sayan_not / p_at_most_one # Probability of at least one of Jelani and Sayan succeeding p_at_least_one = 1 - p_at_most_one Tidying up the extra verbiage of the question is absolutely fair. But then, they also explain exactly how to compute the result using the data in the question; the model then generates code that perfectly matches the described algorithm, it's again not using even the tiniest bit of mathematical understanding. I have browsed their examples, and I have not seen even a single one where the model does more than rephrase the question into a 1:1 Python representation of the question itself. None of the answers would pass even the simplest undergrad exam. They are literally of the form "how would you solve equation E?" "I would write a program that says sympy.solve(E)".