More curves are bending. In mid-August Nate Rush & I posted an analysis of which discovery curves are starting to bend. What's happened since then? Cyber vulnerabilities: curve is still bent. Discovery of vulnerabilities is accelerating even further, though exploited vulnerabilities remain fairly flat. Math: curve is further bent. We said there was a likely acceleration for small-scale problems. Since then there has been a claimed Millennium prize resolution, & credible rumors of another. All frequently-updated databases of open problems seem to be proceeding at a rapid rate. Algorithms: curve is now bending. Two high profile algorithmic competitions have had big curve-bending events: NanoGPT, and the Hutter compression prize. Other frequently-updated series remain relatively unchanged: CIFAR-10, Stockfish, matrix-multiplication exponent. More observations below.

What impact is AI having? I'm of the view that we should be focussing more on aggregate outputs, relatively less on inputs or intermediate proxies. - Inputs: time spent across different activities; money spent on tokens. - Intermediate proxies: working papers; lines of code, commits & pull requests; self-reported speedup. - Final outputs: total cyber exploits discovered; total math problems solved; algorithmic efficiency. The disadvantage of inputs & intermediate proxies is that they're very hard to interpret -- totally possible that they move, but outputs don't, and vice versa. Lines of code could explode without value changing; and vice versa. A disadvantage of final outputs is (1) it's harder to run experiments; (2) it's hard to attribute to whether the change is AI or not. But in some domains the trend-break is so large that it's *obviously* AI.

New post with Nate Rush: Have we seen an acceleration in discoveries? Many plots & some tentative conclusions: 1. Cyber: ⤴️ sharp acceleration 2. Math: ↗️ some acceleration 3. Algorithms: ➡️ no clear acceleration

Q: has AI accelerated aggregate discovery yet? My very general impresions, would love others' thoughts: 1. Vulnerability discovery is up a lot. Between 2X-5X increase in volume, although the average severity has fallen somewhat. 2. Algorithmic efficiency hasn't moved much. E.g. nanogpt, SAT solvers, compression efficiency, chess algorithmic ability. They haven't shown noticeable changes I believe. 3. Math is hard to judge. Erdős problems are certainly falling faster than historical rates, but it's mainly the obscure ones. We don't seem to be tightening upper and lower bounds on unknown quantities noticeably more quickly AFAICT. There are some prominent AI discoveries (e.g. unit distance) but I don't know what's the denominator, i.e. the average flow of comparably important results, my guess is it's still small. 4. Papers/code volume is up a lot. Total arXiv papers and github code is up a lot, but no good way of judging how the quality has changed.

Very happy to share the first paper from @ElasticityInst: The Economics of Recursive Self-Improvement. Two parts: (1) a graphical representation of feedback loops, to formalize a variety of RSI-related arguments, where each arrow represents responsiveness (elasticity); (2) a survey of existing evidence with a loose calibration & a “wish list” of evidence that would help us calibrate better.