Singularity Economics @EconSingularity

The AI tools are getting good enough that you can cheaply build a custom strategy game representing the causal mechanisms of your life and goals. You can model the important dynamics: runway, hiring, fundraising, token/compute spend, recruiting, etc. Then play through simulated futures and practice making the decisions you’ll face. Like a flight simulator for your life. The simulator can continue getting more realistic as you think of more ideas to include. Then you could train an AI to become superhuman at that simulated game and use the strategies it discovers to guide real decisions. Imagine if Elon had a custom strategy game modeling SpaceX, Tesla, xAI, his entities, balance sheets, teams, competitors, etc. Or imagine if instead of reading case studies you got to play through famous historical corporate situations to train yourself. I think eventually talented operators will end up building digital twins representing their lives in high fidelity and training against hundreds of simulations to sharpen themselves.

The excitement vs dread response in individual mathematicians is revealing of whether they do math for status or for the love of the game.

Grant Stenger (hiring) @GrantStenger

3 weeks ago

I have spent over a thousand hours thinking about the hodge conjecture. I am excited to see it solved.

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✅

Grant Stenger (hiring) @GrantStenger

2 months ago

A Millennium Problem will be solved by the end of the year.

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A Millennium Problem will be solved by the end of the year.

I used to commit 1,000 times per year. Now it’s 1,000 per day and accelerating. These models are unbelievable.

There will be trillions of markets. The world is radically under-hedged. People and businesses carry enormous exposure to housing, income, weather, energy, supply chains, health, and so on. This is a massive missing-markets problem. Historically, markets were expensive to create. Specifying the claim, verifying the outcome, finding counterparties, supplying liquidity, settling contracts, and keeping the structure legally admissible all required costly institutional labor. AI changes the cost structure. In this essay, I argue that we are approaching a phase change in market formation. In the supporting papers, I formalize what a market is, when a new market is born, how liquidity providers make long-tail claims tradable, and when markets are socially good or bad. The future contains trillions of markets. grantstenger.com/writing/trilli…

TLDR: a nice paper for the excessively mathematical ML engineer. I used to worry about search getting caught in local minima, before 2015 or so. Since then, it has been pounded into me by experience that local minima are rare: in high dimensions, almost all critical points are saddles. So I believe it, but didn't feel like I had a good theoretical justification. I noodled around with the math, but didn't come up with a good model. This paper satisfied my theoretical unease. It shows that the probability of a random critical point being a local minimum goes as exp(-N^2), for dimension N, under a plausible random field model. I don't think it's original; I just didn't know about it because I don't keep up with the literature. But it is short, clearly written, and nicely explained.

Grant Stenger (hiring) @GrantStenger

4 months ago

Local minima are rare in high dimensions because a strict local minimum has to curve upward in every direction, so all Hessian eigenvalues must be positive. In a D-dimensional toy model where eigenvalue signs are independent, that’s a 2^(-D) event. In GOE-like random matrix

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Local minima are rare in high dimensions because a strict local minimum has to curve upward in every direction, so all Hessian eigenvalues must be positive. In a D-dimensional toy model where eigenvalue signs are independent, that’s a 2^(-D) event. In GOE-like random matrix models, positive definiteness is even rarer, roughly exp(-cD^2). So as dimension grows, random critical points are much more likely to be saddles than minima. This is one reason high-dimensional optimization is often a saddle-escape problem, not a bad-local-minimum problem. Wrote up some of the math here: grantstenger.com/local-minima

roon @tszzl

5 years ago

the greatest whitepill of all is that local minima are rare in high dimensional spaces

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Jane Street reportedly grew net trading revenue from ~$10B in 2023 to ~$20B in ’24 to ~$40B in ’25. With reported net margins around 65%, a ~15x multiple implies a ~$400B public-market value. Mega-cap territory, growing fast, one of the most incredible businesses of all time.

The classical result of Pappus’ theorem (over a real/complex plane) is that if we put three points on each of two lines and draw the cross-connections, then the three intersection points must always be collinear. If we re-derive Pappus’ in a projective plane built over a division ring (where commutativity is not guaranteed), we get the same construction, but the points need not be collinear. In fact, they form a triangle whose defect is exactly the commutator ab-ba! If the division ring is commutative then ab-ba=0 so the triangle collapses and they will be collinear, and if not (like in the quaternionic case) then this defect is exactly calculable. In other words, Pappus is a kind of flatness/closure law: in commutative worlds the construction closes, and in noncommutative worlds it picks up a commutator, like a curvature/holonomy term.

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Did you know quant funds and AI labs are starting to mirror each other? Find out how, where, and why by reading Kinetic CEO @GrantStenger's new article on the front page of @FT Alphaville. Link below 👇

AI labs and quant funds are converging. Why was DeepSeek built by a Chinese hedge fund and not a US tech giant? In reality, they’re structurally the same pipeline: data -> model -> constraints -> execution -> feedback.

@solflare @novogratz @PayPal @xStocksFi @marcryptonio @jerallaire @buffalu__ @artemis @mcagney 38/ Kinetic is building SUPA - Solana Uniform Price Auction Basically an auction primitive for all assets trading on Solana youtu.be/hQml2lIMY4w?li…

Check out the highlights of Kinetic's Breakpoint presentation! @GrantStenger gives a breakdown of: - The history of Kinetic and its mission - Core priorities and verticalizing the tech stack - SUPA AMM, an MEV-resistant liquidity solution

“We’re launching a new market structure on Solana – our own DEX. And we’re excited to go deeper into this vertical than we ever have before.” - @GrantStenger from @kinetic_xyz

@solana SUPA fixes this problem at the root. If everyone in the slot trades at the same clearing price, a bot can’t front‑run you to force a worse fill and then back‑run to skim the difference. There’s nothing to skim.

SUPA is a next-generation AMM architecture that batches all trades submitted during a Solana slot (≈400ms), commits the clearing price at the start of the next slot, and settles via permissionless cranks. This design eliminates intra-slot MEV and neutralizes sandwich attacks.

Why did BTC sell off so hard this week? Primary catalysts: 1. Oct 29 hawkish FOMC guidance from Powell (Fed rate cut hesitancy & uncertainty) 2. Nasdaq beta + AI capex jitters (VXN up) 3. USD strengthened (DXY up) 4. Gov’t shutdown (liquidity dynamics + information vacuum) 5. Owen Gunden (10K BTC whale) dumps 3K BTC for $300M Accelerants: 1. Liquidation cascade flushing derivatives leverage (after Oct 10's historic auto-deleveraging) 2. Profit-taking by long-term holders 3. Outflows from BTC ETFs + delayed ETF approvals 4. Balancer exploit (bearish crypto sentiment) Just my thoughts, NFA. What would you adjust?

"Statistical arbitrage in the US equities market", Avellaneda & Lee (2010): Decompose returns with PCA to extract idiosyncratic residuals; model idio residuals as AR(1)/OU process; construct factor neutral portfolio; size to target volatility using (shrunk) covariance estimate.