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yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model. We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more. More thoughts here:

opus 5 is a VERY interesting release for a few reasons 1. it showed that the general benchmarks we use today are almost completely useless now opus 5 is nowhere near fable in practical use, not even close. anyone who’s used it meaningfully can tell this very quickly after a few tasks. yet opus beats fable on many benchmarks i now trust domain specific benchmarks built with private datasets a lot more than the popular ones. perhaps the future is everyone running their own evals because the public ones are really not telling us much 2. it seems with the 5 series, anthropic is trying a new way of training models previously, the same generation of sonnet and opus were often released at the same time or sonnet comes out before opus, which indicates sonnet and opus were trained by separate pipelines in parallel with the 5 series, it was very clear that they trained mythos first, and then distilled it into sonnet and opus. it seems this approach has a big influence on the models seeing sonnet 5 being a flop and opus 5 getting pretty mixed reviews already, i’m not sure this is working out 3. “how pleasant is it to work with the model” used to be a strength in claude, but now it’s not. honestly, grok is my favorite right now on the “pleasant” dimension. kimi is not bad either it feels like both anthropic and openai are giving RLHF less care, in favor of scalable RL that’s machine verifiable this almost looks like AI is directing humans to build a world that’s more friendly for machines rather than humans, and most humans don’t even realize they are being manipulated to help with that almost every new generation of frontier models now talk more jargons, need more steering to do what you want, and are just less fun to work with if this continues, AI will start to speak their own language that looks like English but average humans can’t understand. they will choose to do things that their human user never asked for. are we already failing at alignment?