If a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms, then the power (in watts) in the external resistor is P = E²R/(R + r)². If E and r are fixed but R varies, what is the maximum value of the power?

This is a typical question from MIT’s single variable calculus course. In a recent work, a neural network is able to perfectly solve university-level problems like this, from text prompts. The work builds on OpenAI’s Codex Transformer model and improves the performance on the MATH benchmark (designed to assess mathematical reasoning) from the state of the art’s 6.9-8.8% to 100% accuracy!

These results are not just from overfitting to training data as the model however was also able to achieve 100% accuracy on all randomly sampled questions from the Columbia University’s new computational linear algebra course, which is not available online.

The model therefore could not have been trained on these questions. Additionally, the model could also be flipped to generate questions instead, perhaps giving us a glimpse into the future role of AI in educational content generation...


By the way, the answer is E²/4r. Did you get it?


The full article can be viewed here.

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