Stein’s lemma for a scalar variable is a well-known characterization of the Gaussian: x ∼ 𝒩(m,σ²) ⇔ ∀f 𝔼[(x−m)f(x)] = σ² 𝔼[f'(x)] Interestingly, there’s also a multivariate version, but it’s 2nd order: x ∼ 𝒩(m, σ² I) ⇔ ∀f 𝔼[(x−m)ᵀ∇f(x)] = σ² 𝔼[∇² f(x)] 1/2

This is horrifying

It’s striking that some past jobs seemingly had few demands - eg Tolkien could write LotR. I’d guess management has grown more efficient, contributing to growth. But otoh it may have made those jobs more strenuous, meaning growth numbers overestimate life quality improvements.

Historians: Alternate histories based on counterfactuals are pointless speculation. Also historians: Let’s vigorously debate the primary causes of past events, each of which implicitly involves counterfactual reasoning.

If you're great at engineering and interested in working with me to build an AI product to make researchers more productive, DM me.

RT @yarotrof: Also a reminder that Ukraine, unlike Russia, is a democracy with a strong civil society, despite all its problems. No such pr…

@Jon_Hartley_ computed this Fed cost plot CPI rose 32% from 2004-2018, and 30% from 2018-2025 Eyeballing 250, 730, & 990 for 2004, Jay's start & end Pre-Jay real cost growth rate (730/(1.32*250))^(1/14) ~ 1.058 Jay real growth rate (990/(1.30*730))^(1/5) ~ 1.008 0.8% < 5.8%‼️

the economics version of this

New paper & surprising result. LLMs transmit traits to other models via hidden signals in data. Datasets consisting only of 3-digit numbers can transmit a love for owls, or evil tendencies. 🧵

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