@alz_zyd_ Agreed. Not only is the mathematical ability of the LLMs incredible, the follow-up questions are just as good. It’s this interaction what makes it even more powerful
A point that is sometimes overlooked is that PDEs in physics and economics have a subtle but important difference.
When a physicist solves the Schrödinger equation (see my slide below), the potential is given. The coefficients of the equation are part of the problem statement. You pick your grid, refine your mesh, and the equation never changes on you. Better numerics give a better approximation to a fixed target.
In economics, this is not the case. Look at the Hamilton-Jacobi-Bellman equation for the neoclassical growth model (also slide below). The drift of capital depends on a derivative of the value function, the very object you are trying to solve for. The “coefficients” of the PDE are endogenous to the optimal choices of the agents. This is what @UncertainLars and Sargent referred to as the cross-equation restrictions implied by optimizing behavior.
This is what @MahdiKahou and I call the “equilibrium loop”: improving your approximation changes the policy, which changes the dynamics, which changes where in the state space the economy spends its time, which changes where your approximation needs to be accurate. You are not chasing a fixed target with a better net. Moving the net moves the target.
This has serious consequences for computation. You cannot just borrow neural network architectures from deep learning in the natural sciences. The loss function comes from equilibrium conditions, not from labeled data. The evaluation points are not given. Instead, they are regenerated each epoch from the current approximation. Ignoring it is why you often get solutions that look good on a training set but fall apart in simulation.
Ludwig Straub is a fantastic winner. I have just written up an overview of his work, in the tweet below -- go read it! His work shakes up what we know about monetary and fiscal policy.
If you support Trump now, history will remember you as a deeply evil person, part of a deeply evil failed attempt to destroy America. And yes, you will fail.
🎓 Today I delivered the final lecture of @Penn_Exchange’s Foundations of Economic Thought summer course by focusing on the evolution of macroeconomics from 1970 to 2000:
🔗 https://t.co/MHr3Dbo3Cx
🧠 Unsurprisingly, @UMN_Econ features prominently in the story (although @penneconomics also shows up quite a few times).
📑 You can find the slide deck here:
https://t.co/NbP86Xpbls
This piece would have sparked a major political scandal in normal times.
Not anymore. Nothing will happen, but at least we have a record of this.
https://t.co/Ar0MevlO3Z