We asked Claude Opus 4.8 Ultra to build a pharma demand forecaster. It wrote what a good data scientist would write.
Then we ran a time-series foundation model against it. It wasn't close.
Our newest model is coming soon. Before it lands, we're open-sourcing our earliest time-series foundation model, LAFN — the full story on Substack: what it is, why we broke from the standard transformer playbook, and how it handles point + probabilistic forecasting.
https://t.co/17Rxh8hr3R
For those interested in a broader result, namely a tâtonnement algorithm which is not stable only in some cases but almost always, check out our paper from 2024.
In our paper, we introduce mirror extratâtonnement — a generalized process with polynomial-time global convergence in Walrasian economies, including the notoriously hard Scarf economy.
More in this thread: https://t.co/RP7A2wwL6g
Excited to FINALLY release toughest+most rewarding paper I've worked on...
….we attack a 150 year old Walras question that's gone unanswered, not for lack of trying (Hicks, Samuelson, Arrow; our chances?😱)...
Q: Is the market equilibrium stable or unstable?¯\_(ツ)_/¯
🧵
If you want a full picture of price-adjustment, in our paper, we resolve Herbert Scarf's 50 year old challenge—namely “a general method for the explicit numerical solution of the neoclassical model.”
https://t.co/CzhTGtSA0E
Submitted 2x to ACM EC, and overturned by editors 🥱.
Excited to FINALLY release toughest+most rewarding paper I've worked on...
….we attack a 150 year old Walras question that's gone unanswered, not for lack of trying (Hicks, Samuelson, Arrow; our chances?😱)...
Q: Is the market equilibrium stable or unstable?¯\_(ツ)_/¯
🧵
Yes. The standard interpretation of tâtonnement is that the sequence of prices for each good is set by each price-setter (or fictional auctioneer whatever name you prefer).
In standard tâtonnement, the price of each good is increased if the demand is in excess and decreased otherwise.
Extratâtonnement (ours), on odd time-steps applies a tâtonnement update on the current time-step’s prices, and on even time-steps applies a tâtonnement update on the previous time-step’s prices. This slight modification makes tâtonnement convergent.
Interpretation: price setters do not update myopically only based on current excess demand but also take a look at yesterday’s excess demand. That is, when price-setters learn from history, equilibrium is stable.
We study the Walrasian equilibrium in the broadest setting. You can specialize the economy to contain price setter, consumers etc… (in our appendix we show Arrow-Debreu economies fit into this framework and indeed obtain results for these economies, and in a later paper we also include financial markets etc..). Our result is broad and is meant to be used in any stylized economic model.
I’m a computer science theorist, my goal is to create algorithmic tools for economists to solve models. The stylization of the models are not questions of algorithmic general equilibrium theory but of policy practitioners’ studies. The results we provide can allow economists to use our theorems to analyze their own stylized models.
Regular tâtonnement-type methods won’t converge in continuous-time without additional assumptions (there is well established dynamical systems theory about it). A tâtonnement-like method (but which is not strictly so as it adjusts prices of goods dependently) introduced by Smale which regularizes the excess demand by the inverse of its Jacobian is globally convergent but requires invertibility of the excess demand.
Without some tractability assumptions global convergence is not possible. Why? The problem of computing a Walrasian equilibrium is equivalent to computing a solution to an arbitrary continuous variational inequality (which is not tractable generally). So, yes, if assumptions are not clear, then they are smuggled.
In our paper, we provide the broadest set of assumptions for global stability and polynomial-time computation. We show that we can compute in seconds Walrasian equilibrium for randomly initialized Arrow-Debreu economies with thousands of goods.
Honestly, I don’t think looking at the stability of tâtonnement is interesting. These are just models, and interpreting behaviors in them is over-interpretation without taking them to data. Models are meant to be fit on data and evaluated empirically, but we could not do so because we couldn’t even solve these models efficiently. Our paper’s goal was to solve large economies so we can fit large economic models to data. This was Herbert Scarf’su understanding all along.
@IvanWerning Interesting work! An important reference which I could not find it in the paper is Smale's newtonian tâtonnement-like method (https://t.co/HdVLLolpCY) which converges globally in continuous time.
(Note: it is not a natural price adjustment process)
Tâtonnment algorithms are used to run Ethereum pricing. Beyond being core to economic theory, Tâtonnement manages billions of dollars.
I have been trying to convince people of this for the last 7 years.
I thought Tâtonnement was a "just so" story economists tell students in their first micro theory class. Is this
1. a real open problem we knew we had
2. a real open problem we forgot we had
3. an artificial problem in an already highly stylized setting
I appreciate the old Hicks/Samuelson debate, but it's 2026, economists please let me know.