Hyperstition

3/n We have the most complete pretraining megakernel with hardware fault detection and replanning. 1. We achieve an out of the box 31% MFU on standard mixed precision (BF16 and FP32) pretraining of a 30B MoE Qwen architecture on one node and 30% MFU on data parallel pretraining over multiple nodes. 2. We have tensor parallelism, expert parallelism and data parallelism. 3. Hyperkernel automatically generates efficient megakernels that fuse low intensity processes and schedule the tiles to load balance over applicable streaming multiprocessors. This generalizes across all cluster topologies. 4. Hyperkernel automatically detects individual GPU, NVLink, and InfiniBand failures within seconds. Performs live triage mid-step so as to only recompute tensors which were lost rather than naively reverting to a previous checkpoint. Autonomously rewrites the megakernel to preserve MFU on the now partially degraded cluster.

9/n Our megakernel on robotics: π₀-FAST, from Physical Intelligence @physical_int, is a vision-language-action model for dexterous robot control. Instead of generating actions with a flow-matching action expert, as π₀ does, it compresses them into discrete tokens and decodes them autoregressively. Our megakernel ran the vision encoding prefill and generation of 60 tokens in 94 ms, while a custom reference PyTorch + CUDA graph decoding ran it in 243ms, with megakernels reducing latency by 61% at batch one in BF16.

Since my nanoGPT record was published, the question I’ve been asked the most is, “Does it scale?” The true answer is, while some aspects of the speedrun scale, the goal of this specific endeavor was not to scale it up. The point of the challenge is to utilize clever engineering and creative ML intuition to increase efficiency. But while nanoGPT is just about hill-climbing one benchmark, the rest of my work has been focused on scaling to the frontier. The main projects I’ve worked on are some architectural changes and ANVIL III. ANVIL III is a significantly stronger optimizer than ANVIL II, the optimizer I used to beat the nanoGPT world record. In fact, for the record, we removed the parts of ANVIL III that scale. ANVIL III is significantly stronger than Muon, while nearly matching its speed. For the same token budget (same compute), ANVIL III reaches final validation loss 20-28 millinats (.02-.028 nats) lower than Muon, holding at all scales from 124M to 1.2B, and different overtraining depths. As we scale up the model size and training depth, the 20-28 millinats becomes worth a larger fraction of compute. At deep overtraining (8x-Chinchilla) and 1.2B parameters, the fitted scaling curves imply that ANVIL III reaches the same loss numbers at 50% less compute. Of all the scales we tested, the gap is largest at 1.2B, staying between 26-28 millinats. The first remarkable aspect of ANVIL is hyperparameter consistency. The optimal hyperparameters remain highly consistent across different scales and training depths. In most of our tests, varying hyperparameters rarely changed ANVIL III’s loss, or did so within noise. In fact, as shown in the attached image (from the blog’s appendices), we tuned Muon significantly more than we tuned ANVIL III. We performed over 3 times the aggregate amount of runs of Muon than ANVIL III, and at each scale our loss margin uses only the optimal parameters for both. At 1.2B, we used 51 tuning runs of Muon (including muP proxies), compared to only 7 for ANVIL. We wanted to guarantee that our improvement was not a tuning artifact, so we meticulously tuned Muon’s parameters, and had to apply far less tuning to ANVIL III. Our hypothesis is that the high SNR of ANVIL III makes it very resistant to parameter changes. That SNR is the second remarkable aspect of ANVIL III. We generalize the Adam SNR (SNR = m̂ / (√v̂ + ε)) for each singular direction (uᵢ, vᵢ) in an update, and measure how strongly held-out gradients (G_b = gradient on held-out batches b) point along it: SNRᵢ = mean_b(uᵢᵀ G_b vᵢ) / rms_b(uᵢᵀ G_b vᵢ) In our tests, Muon takes a lot of steps with low SNR, but ANVIL III doesn’t, despite being a Muon variant. For example, at 10% of the training tokens into a 1.2B (approximately Chinchilla) model, 90% of singular directions in ANVIL III’s steps go downhill on held-out data, while Muon gets only 67% (random = 50%). Pretraining Blog: hyperstition.cc/cutting-pret… Another recent post from Hyperstition contextualizes the importance of this SNR gap. In The Signal and the Noise, we generalize Adam (in which the update is just a per-coordinate SNR) to every direction in parameter space. Almost every direction is nearly orthogonal to the gradient history, so averaging that over all directions just collapses back into plain momentum. But the single best direction, C⁻¹ḡ, reaches SNR=1 whenever recent gradients are linearly independent, which is almost always true in LLM pretraining. By solving that with a s-by-s Gram system with recency weighting, we get a basis-free optimizer that matches AdamW at 286M parameters. While this is far from optimal, it represents one avenue for possible gains in pretraining optimization that are yet to be realized. hyperstition.cc/the-signal-a… In another fun but mostly unrelated blog, Stuck in a Loop, we show that attention in pretraining creates feedback loops and self-reinforcement. A key’s gradient is proportional to the attention it already gets, so keys with early inflated attention receive stronger gradients, overinflating them. Breaking that loop spreads attention out, with the average entropy of attention heads goes from 3.75 to 4.69 nats (effectively 43 vs 109 tokens), but it makes the model worse. Similarly to The Signal and the Noise, this suggests that putting more weight in high-signal directions can beat spreading it out broadly. hyperstition.cc/stuck-in-a-l… These discoveries are just a small part of the upcoming releases from @hyperstition_cc. Can’t wait until we release more. Big things are coming!

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…