As I have noticed that other people have found similar small improvements, I created this Website to track Lean verified progress on the constant: gtimg.github.io/QuasiRiemann… Everyone is invited to submit a Lean proof for a better constant, let's see how low we can get this!

@HaileyStormC has submitted a new Lean verified θ = 0.8747729897 for QRH! She repeatedly sharpened bounds on sums, feeding each proved improvement into the next until zeros beyond the new boundary would lead to a contradiction. This is part of a wider QRH effort with contributions from ArviFoxy, @ZhongpaiGao, @mrowdays, Sil, timbalud, Devin Watson, Kari Roegnvaldsson, nielstron, Akash Levy, Tim Gehrunger, Baiying Liu, Argonaut Math, me, and OpenAI's original 7/8 preprint. Our repo doesn't require the full Lean verification to submit, so it's easier to contribute: github.com/rohanarun/quasi-r… I'll still run the full Lean verification in parallel for submissions. We have new sponsor @Agent37HQ for QRH now, so the first 100 contributors also get free sandboxes to run experiments/searches! It's like math Christmas 😂 We had so many improvements across multiple projects today. github.com/rohanarun/quasi-r…

I did it! c = 0.12511335296, the current QRH record according to Tim's tracker and anywhere I can find. Links below. Hopefully even more QRH news from me, we shall see 🙂

New historic NanoGPT record at 39.9s (-27.7s) from @DevenPzak , obliterating the prior record of 67.6s! This record introduces a new paradigm of thinking to NanoGPT: instead of optimizing matmuls or adding more expressive operations, optimize at the individual flop level with incredibly clever engineering and ML judgement. If a flop is low value on a particular step, skip it. Specifically: -(~8s) Sampled softmax. If a token doesn’t appear in a batch, skip its lm_head fwd/bwd some fraction of the time. -Sparse values. Only run an optimizer step for ngram embeddings that occurred in the batch. Set beta1 to zero to enable this. Beta2 is applied retroactively when the row is later used. -Sparse updates. Only update ngram and value embeddings once every 4 steps instead of once every 2. -Sparse communication. Shard the n-gram table across GPUs, and only pass the rows receiving updates on each step. -Sparse optimizer states. For the n-gram table, reduce from 2 floats in Adam optimizer per param, to 1 float per 768 params. -Hand-rolled flash attention for 64 dim heads. There are several additions that add accuracy too: -(~4s) EMA during last 300 steps, combined with lifting final_lr to 0.3 instead of 0.15. -(~1s) A new optimizer, Anvil2, which expands muon via a second tracked momentum buffer, improves the ortho coefficients, and modifies the cautious weight decay application. -A couple additional dynamic skip connections in the network. The most striking consequence of the ‘flop aware paradigm’ is you can grow parameters arbitrarily large, only limited by the available memory, since you can selectively choose how to expend flops on those parameters on each step. NanoGPT has kept active parameters below 124M, but total is unbounded, and has grown to 640M through embedding sparsity over the last year. This PR takes that to its logical conclusion on the 8xH100, scaling up to 65B sparse embedding parameters, which accounts for 25% of the PR’s gains. At frontier scale, where one is not bounded by an 8xH100, one could imagine where this paradigm could lead. github.com/KellerJordan/modd… As this was a very notable PR, I spoke with Deven for an hour to learn how he did it. Here’s his story on the changes: hyperstition.cc/training-nan…

Claim: we've solved the AI slop problem (!) 💩🧹✨ Blog post: facebookresearch.github.io/R… 🧵1/5 Key idea: take *expert* human writing and learn rubrics that find the gap between experts and models. Train with those rubrics. We train with RL-XAR (RL with eXpert Aligned Rubrics) & see large performance gains on writing scientific paper sections, Pulitzer prize novel continuations and high quality Wikipedia pages.