nanoGPT-speedrun-59-001

Modded-NanoGPT

This repository hosts the NanoGPT speedrun, in which we (collaboratively|competitively) search for the fastest algorithm to use 8 NVIDIA H100 GPUs to train a language model that attains 3.28 cross-entropy loss on the FineWeb validation set.

The target (3.28 validation loss on FineWeb) follows Andrej Karpathy's GPT-2 replication in llm.c, which attains that loss after running for 45 minutes. The speedrun code also descends from llm.c's PyTorch trainer, which itself descends from NanoGPT, hence the name of the repo. Thanks to the efforts of many contributors, this repo now contains a training algorithm which attains the target performance in:

• 2 minutes on 8xH100 (the llm.c GPT-2 replication needed 45)
• under 500M tokens (the llm.c GPT-2 replication needed 10B)

This improvement in training speed has been brought about by the following techniques:

• Modernized architecture: Rotary embeddings, QK-Norm, and ReLU²
• The Muon optimizer [writeup] [repo]
• Use FP8 matmul for head, and asymmetric rescale and softcap logits
• Initialization of projections to zero (muP-like)
• Skip connections from embedding to every block as well as from block 3 to 6
• Extra embeddings which are mixed into the values in attention layers (inspired by Zhou et al. 2024)
• Flash Attention 3 with long-short sliding window attention pattern (inspired by Gemma 2) and window size warmup with YaRN
• Align training batch starts with EoS and set a max document length
• Accumulate gradients for 2 steps for embedding and lm_head before updating parameters
• Enable model to back out contributions from first 2/3 layers before prediction
• Polar Express implementation in Muon
• Smear module to enable 1 token look back
• Sparse attention gate
• NorMuon
• Cautious Weight Decay w/ schedule tied to LR
• Exponential decay of residual stream
• Batch size schedule
• Partial Key Offset
• Multi token prediction
• Untie embed and lm_head at 2/3 of training
• Additional gating on value embeddings and skip connection
• Paired head attention

As well as many systems optimizations.

Contributors list (growing with each new record): @bozavlado; @brendanh0gan; @fernbear.bsky.social; @Grad62304977; @jxbz; @kellerjordan0; @KoszarskyB; @leloykun; @YouJiacheng; @jadenj3o; @KonstantinWilleke, @alexrgilbert, @adricarda, @tuttyfrutyee, @vdlad; @ryanyang0, @vagrawal, @classiclarryd, @byronxu99, @varunneal, @EmelyanenkoK, @bernard24/https://www.hiverge.ai/, @Gusarich, @li_zichong, @akash5474, @snimu, @roeeshenberg, @ChrisJMcCormick, @dominikkallusky, @acutkosky, @manikbhandari, @andrewbriand, @jrauvola

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Running the current record

To run the current record, run the following commands.

git clone https://github.com/KellerJordan/modded-nanogpt.git && cd modded-nanogpt
pip install -r requirements.txt
pip install torch==2.10.0.dev20251210+cu126 --index-url https://download.pytorch.org/whl/nightly/cu126
# downloads only the first 900M training tokens to save time
python data/cached_fineweb10B.py 9
./run.sh

Add torchrun to path if ./run.sh gives error torchrun: command not found.

Note: torch.compile will add around 7 minutes of latency the first time you run the code.

Official records are timed on 8 NVIDIA H100 GPUs from https://app.primeintellect.ai/. PrimeIntellect has generously sponsored recent validation runs.

Alternative: Running with Docker (recommended for precise timing)

For cases where CUDA or NCCL versions aren't compatible with your current system setup, Docker can be a helpful alternative. This approach standardizes versions for CUDA, NCCL, CUDNN, and Python, reducing dependency issues and simplifying setup. Note: an NVIDIA driver must already be installed on the system (useful if only the NVIDIA driver and Docker are available).

git clone https://github.com/KellerJordan/modded-nanogpt.git && cd modded-nanogpt
sudo docker build -t modded-nanogpt .
sudo docker run -it --rm --gpus all -v $(pwd):/modded-nanogpt modded-nanogpt python data/cached_fineweb10B.py 8
sudo docker run -it --rm --gpus all -v $(pwd):/modded-nanogpt modded-nanogpt sh run.sh

To get an interactive docker, you can use

sudo docker run -it --rm --gpus all -v $(pwd):/modded-nanogpt modded-nanogpt bash

---

World record history

The following is the historical progression of world speed records for the following competitive task:

Train a neural network to ≤3.28 validation loss on FineWeb using 8x NVIDIA H100s.

Note: The 3.28 target was selected to match Andrej Karpathy's GPT-2 (small) reproduction.

Rules

New records must:

1. Not modify the train or validation data pipelines. (You can change the batch size, sequence length, attention structure etc.; just don't change the underlying streams of tokens.)
2. Attain ≤3.28 mean val loss. (Due to inter-run variance, submissions must provide enough run logs to attain a statistical significance level of p<0.01 that their mean val loss is ≤3.28. Example code to compute p-value can be found here. For submissions which improve speed by optimizing the systems performance, without touching the ML, this requirement is waived.)
3. Not use any extra torch._inductor.config or torch.compile flags. (These can save a few seconds, but they can also make compilation take >30min. This rule was introduced after the 21st record.)
4. Run faster than the prior record when baselined on the same hardware.

Discretionary reasons why a PR may not be accepted:

1. Disproportionately degrades the readability of the codebase. A 200 line kernel to drop 300ms is considered worthwhile. 500 lines that convolute the optimizer layout for a 50ms gain will likely be rejected.
2. The current record is intentionally kept roughly 0.001-0.002 loss below 3.28 to make validation simpler. If a PR substantially consumes this buffer, it should do so in a way that outperforms a simple step count decrease, when measured at equivalent loss.

Note: torch._inductor.config.coordinate_descent_tuning is allowed for GPT-2 Medium track (a.k.a. 2.92 track).

Other than that, anything and everything is fair game!

further clarifications

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Comment on the target metric

The target metric is cross-entropy loss on the FineWeb val set. To speak mathematically, the goal of the speedrun is *to obtain a probability model of language which assigns a probability of at least math.exp(-3.28 * 10485760) to the first 10,485,760 tokens of the FineWeb valset. Hence, e.g., we allow evaluation at any sequence length, so long as we still have a valid probability model of language.

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Timing change after record 21

After the 21st record, we made two changes to the timing. First, there used to be an initial "grace period" of 10 untimed steps to allow kernel warmup. We replaced this with an explicit kernel-warmup section which is untimed and uses dummy data. This results in an extra runtime of 850ms from the 10 extra timed steps. Second, we banned the use of torch._inductor.config.coordinate_descent_tuning. This saves ~25min of untimed pre-run compilation, but results in an extra runtime of ~3s.

<!--Note: The original llm.c baseline is intended to be closer to a replication of GPT-2 than to an optimized LLM training. So it's no surprise that there is room to improve; as @karpathy has said, 'llm.c still has a lot of pending optimizations.' In addition, many of the techniques used in these records are completely standard, such as rotary embeddings. The goal of this benchmark/speedrun is simply to find out which techniques actually work, and maybe come up with some new ones.--> <!--The goal of this benchmark is simply to find out all the techniques which actually work, because I'm going crazy reading all these LLM training papers which claim a huge benefit but then use their own idiosyncratic non-competitive benchmark and therefore no one in the community has any idea if it's legit for months.--> <!--[LLM](https://arxiv.org/abs/2305.14342) [training](https://arxiv.org/abs/2402.17764) [papers](https://arxiv.org/abs/2410.01131)--> <!--I mean hello??? We're in a completely empirical field; it is insane to not have a benchmark. Ideally everyone uses the same LLM training benchmark, and then reviewing LLM training papers becomes as simple as checking if they beat the benchmark. It's not like this would be unprecedented, that's how things were in the ImageNet days. The only possible 'benefit' I can think of for any empirical field to abandon benchmarks is that it would make it easier to publish false results. Oh, I guess that's why it happened. Hilarious to think about how, in the often-commented-upon and ongoing collapse of the peer review system, people blame the *reviewers* -- yeah, those guys doing free labor who everyone constantly musters all of their intelligence to lie to, it's *their* fault! My bad, you caught me monologuing.-->

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Notable attempts & forks

Notable runs:

• @alexjc's 01/20/2025 2.77-minute TokenMonster-based record. This record is technically outside the rules of the speedrun, since we specified that the train/val tokens must be kept fixed. However, it's very interesting, and worth including. The run is not more data-efficient; rather, the speedup comes from the improved tokenizer allowing the vocabulary size to be reduced (nearly halved!) while preserving the same bytes-per-token, which saves lots of parameters and FLOPs in the head and embeddings.

Notable forks:

• https://github.com/BlinkDL/modded-nanogpt-rwkv
• https://github.com/nikhilvyas/modded-nanogpt-SOAP

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Speedrun track 2: GPT-2 Medium

The target loss for this track is lowered from 3.28 to 2.92, as per Andrej Karpathy's 350M-parameter llm.c baseline. This baseline generates a model with performance similar to the original GPT-2 Medium, whereas the first track's baseline generates a model on par with GPT-2 Small. All other rules remain the same.

Note: torch._inductor.config.coordinate_descent_tuning is turned on after the record 6 (*).

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Q: What is the point of NanoGPT speedrunning?

A: The officially stated goal of NanoGPT speedrunning is as follows: gotta go fast. But for something a little more verbose involving an argument for good benchmarking, here's some kind of manifesto, adorned with a blessing from the master. https://x.com/karpathy/status/1846790537262571739

Q: What makes "NanoGPT speedrunning" not just another idiosyncratic benchmark?

A: Because it is a competitive benchmark. In particular, if you attain a new speed record (using whatever method you want), there is an open invitation for you to post that record (on arXiv or X) and thereby vacuum up all the clout for yourself. I will even help you do it by reposting you as much as I can.

<!--On the contrary, for example, the benchmark used in the [Sophia](https://arxiv.org/abs/2305.14342) paper does *not* have this property. There is no such open invitation for anyone to compete on the benchmark they used. In particular, if, for a random and definitely not weirdly specific example, you happen to find better AdamW hyperparameters for their training setup than the ones they used which significantly close the gap between AdamW and their proposed optimizer, then there is no clear path for you to publish that result in *any* form. You could try posting it on X.com, but then you would be risking being perceived as aggressive/confrontational, which is *not a good look* in this racket. So if you're rational, the result probably just dies with you and no one else learns anything (unless you're in a frontier lab, in which case you can do a nice internal writeup. Boy I'd love to get my hands on those writeups).-->

"Artificial intelligence advances by inventing games and gloating to goad others to play" - Professor Ben Recht

Q: NanoGPT speedrunning is cool and all, but meh it probably won't scale and is just overfitting to val loss

A: This is hard to refute, since "at scale" is an infinite category (what if the methods stop working only for >100T models?), making it impossible to fully prove. Also, I would agree that some of the methods used in the speedrun are unlikely to scale, particularly those which impose additional structure on the network, such as logit softcapping. But if the reader cares about 1.5B models, they might be convinced by this result:

Straightforwardly scaling up the speedrun (10/18/24 version) to 1.5B parameters yields a model with GPT-2 (1.5B)-level HellaSwag performance 2.5x more cheaply than @karpathy's baseline ($233 instead of $576):

[reproducible log]

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Muon optimizer

Muon is defined as follows:

Where NewtonSchulz5 is the following Newton-Schulz iteration [2, 3], which approximately replaces G with U @ V.T where U, S, V = G.svd().

@torch.compile
def zeroth_power_via_newtonschulz5(G, steps=5, eps=1e-7):
    assert len(G.shape) == 2
    a, b, c = (3.4445, -4.7750,  2.0315)
    X = G.bfloat16() / (G.norm() + eps)
    if G.size(0) > G.size(1):
        X = X.T 
    for _ in range(steps):
        A = X @ X.T
        B = b * A + c * A @ A
        X = a * X + B @ X
    if G.size(0) > G.size(1):
        X = X.T 
    return X.to(G.dtype)

For this training scenario, Muon has the following favorable properties:

• Lower memory usage than Adam
• ~1.5x better sample-efficiency
• <2% wallclock overhead

Provenance

Many of the choices made to generate this optimizer were obtained experimentally by our pursuit of CIFAR-10 speedrunning. In particular, we experimentally obtained the following practices:

• Using Nesterov momentum inside the update, with orthogonalization applied after momentum.
• Using a specifically quintic Newton-Schulz iteration as the method of orthogonalization.
• Using non-convergent coefficients for the quintic polynomial in order to maximize slope at zero, and thereby minimize the number of necessary Newton-Schulz iterations. It turns out that the variance doesn't actually matter that much, so we end up with a quintic that rapidly converges to the range 0.68, 1.13 upon repeated application, rather than converging more slowly to 1.
• Running the Newton-Schulz iteration in bfloat16 (whereas Shampoo implementations often depend on inverse-pth-roots run in fp32 or fp64).

Our use of a Newton-Schulz iteration for orthogonalization traces to Bernstein & Newhouse (2024), who suggested it as a way to compute Shampoo [5, 6] preconditioners, and theoretically explored Shampoo without preconditioner accumulation. In particular, Jeremy Bernstein @jxbz sent us the draft, which caused us to experiment with various Newton-Schulz iterations as the orthogonalization method for this optimizer. If we had used SVD instead of a Newton-Schulz iteration, this optimizer would have been too slow to be useful. Bernstein & Newhouse also pointed out that Shampoo without preconditioner accumulation is equivalent to steepest descent in the spectral norm, and therefore Shampoo can be thought of as a way to smooth out spectral steepest descent. The proposed optimizer can be thought of as a second way of smoothing spectral steepest descent, with a different set of memory and runtime tradeoffs compared to Shampoo.

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Running on fewer GPUs

• To run experiments on fewer GPUs, simply modify run.sh to have a different --nproc_per_node. This should not change the behavior of the training.
• If you're running out of memory, you may need to reduce the sequence length for FlexAttention (which does change the training. see here for a guide)

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References

1. Guilherme Penedo et al. "The fineweb datasets: Decanting the web for the finest text data at scale." arXiv preprint arXiv:2406.17557 (2024).
2. Nicholas J. Higham. Functions of Matrices. Society for Industrial and Applied Mathematics (2008). Equation 5.22.
3. Günther Schulz. Iterative Berechnung der reziproken Matrix. Z. Angew. Math. Mech., 13:57–59 (1933).
4. Jeremy Bernstein and Laker Newhouse. "Old Optimizer, New Norm: An Anthology." arxiv preprint arXiv:2409.20325 (2024).
5. Vineet Gupta, Tomer Koren, and Yoram Singer. "Shampoo: Preconditioned stochastic tensor optimization." International Conference on Machine Learning. PMLR, 2018.
6. Rohan Anil et al. "Scalable second order optimization for deep learning." arXiv preprint arXiv:2002.09018 (2020).
7. Alexander Hägele et al. "Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations." arXiv preprint arXiv:2405.18392 (2024).
8. Zhanchao Zhou et al. "Value Residual Learning For Alleviating Attention Concentration In Transformers." arXiv preprint arXiv:2410.17897 (2024).
9. Team, Gemma, et al. "Gemma 2: Improving open language models at a practical size." arXiv preprint arXiv:2408.00118 (2024).
10. Alec Radford et al. "Language models are unsupervised multitask learners." OpenAI blog 1.8 (2019).

Citation

@misc{modded_nanogpt_2024,
  author       = {Keller Jordan and Jeremy Bernstein and Brendan Rappazzo and
                  @fernbear.bsky.social and Boza Vlado and You Jiacheng and
                  Franz Cesista and Braden Koszarsky and @Grad62304977},
  title        = {modded-nanogpt: Speedrunning the NanoGPT baseline},
  year         = {2024},
  url          = {https://github.com/KellerJordan/modded-nanogpt}
}

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