Modded-NanoGPT

This is a modified variant of the PyTorch GPT-2 trainer from Andrej Karpathy's llm.c repo, which attains the same final validation loss in only:

• 0.75B tokens instead of 10B
• 4.4 minutes on 8xH100 instead of 45

It uses the following techniques:

• Modernized architecture: Rotary embeddings, QK-Norm, and ReLU^2.
• New optimizer: Muon - Momentum Orthogonalized by Newton-schulz.
• Untied head from embedding.
• Projection and classification layers initialized to zero (muP-like).
• Architectural shortcuts: value residual and embedding shortcut (partially following https://arxiv.org/abs/2410.17897).
• Momentum warmup.
• Tanh soft logit capping (following Gemma 2).
• FlexAttention with window size warmup.
• Extra embedding layers which are fed into intermediate layers.

The training has attained this speed due to the contributions of meself, @Grad62304977, @jxbz, @bozavlado, @brendanh0gan, @KoszarskyB, & @fernbear.bsky.social.

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Running the current record

To execute the training, run the following three commands. They should all complete within <20min on an 8xH100 with decent internet connection.

pip install -r requirements.txt
pip install --pre torch==2.6.0.dev20241203+cu124 --index-url https://download.pytorch.org/whl/nightly/cu124 --upgrade # install torch 2.6.0
python data/cached_fineweb10B.py 10 # downloads only the first 1.0B training tokens to save time
./run.sh

The result will be a transformer with 124M active parameters trained for 1430 steps on 0.75B tokens of Fineweb [1], achieving ~3.278 mean validation loss (w/ up to 0.005 inter-run stddev). For comparison, the default llm.c PyTorch trainer yields >3.28 validation loss after training for 19560 steps on 10B tokens.

Note: torch.compile will take a long time on the first run.

Running it on fewer GPUs or with less memory

• To run on fewer GPUs, just modify run.sh to have a different --nproc_per_node. (this does not change the expected 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)

Running with Docker

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).

sudo docker build -t modded-nanogpt .
sudo docker run -it --rm --gpus all -v $(pwd):/modded-nanogpt modded-nanogpt python data/cached_fineweb10B.py 18
sudo docker run -it --rm --gpus all -v $(pwd):/modded-nanogpt modded-nanogpt sh run.sh

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World record history

The following is the progression of world records for the task of training a model with 124M active parameters to 3.28 validation loss on FineWeb in the minimal amount of time on an 8xH100 machine.

#	Record time	Description	Date	Log	Contributors
1	45 minutes	llm.c baseline	05/28/24	log	@karpathy, llm.c contributors
2	31.4 minutes	Architectural modernizations & tuned learning rate	06/06/24	log	@kellerjordan0
3	24.9 minutes	Introduced the Muon optimizer	10/04/24	none	@kellerjordan0, @jxbz
4	22.3 minutes	Muon improvements	10/11/24	log	@kellerjordan0, @bozavlado
5	15.2 minutes	Pad embeddings & architectural improvements	10/14/24	log	@Grad62304977, @kellerjordan0
6	13.1 minutes	Distributed the overhead of Muon	10/18/24	log	@kellerjordan0
7	12.0 minutes	Upgraded PyTorch from 2.4.1 to 2.5.0	10/18/24	log	@kellerjordan0
8	10.8 minutes	Untied embed and lm_head	11/03/24	log	@Grad62304977, @kellerjordan0
9	8.2 minutes	Shortcuts & tweaks	11/06/24	log	@Grad62304977, @kellerjordan0
10	7.8 minutes	Bfloat16 activations	11/08/24	log	@kellerjordan0
11	7.2 minutes	U-net & 2x lr	11/10/24	log	@brendanh0gan
12	5.03 minutes	FlexAttention	11/19/24	log	@KoszarskyB
13	4.66 minutes	Attention window warmup	11/24/24	log	@fernbear.bsky.social
14	4.41 minutes	Value Embeddings	12/04/24	log	@KoszarskyB

Speedrun rules

All new record attempts:

1. Must not modify the train or validation data pipelines. (Except to change batch size, seqlen, attention structure etc. I.e., just don't change the underlying tokens.)
2. Must use ≤ 124M active parameters per token. (So MoE is fine; and extra embedding layers can be added since they only contribute hidden_dim active params.)
3. Must attain ≤ 3.28 val loss. Unfortunately, due to high inter-run variance, new record attempts must provide enough run logs to attain a statistical significance level of p<0.01 that their average val loss is lower than 3.28. You see see how to conduct a t-test here.

Other than that, go crazy! Anything is fair game

Notes

• For the llm.c baseline: The 90 minute time is on 8xA100; it's 45 minutes on 8xH100. This baseline is essentially a hardware-optimized GPT-2-small replication using better training data.
• All runs before 11/19/24 can be run with PyTorch 2.5.1 or below. Runs including and after 11/19/24 require PyTorch 2.6.0 (nightly) to use FlexAttention.

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Notable forks

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

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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.

"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. 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 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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Startup script

Here's a good startup script for a fresh 8xH100 instance.

sudo apt-get update
sudo apt-get install vim tmux python3-pip python-is-python3 -y
git clone https://github.com/KellerJordan/modded-nanogpt.git
cd modded-nanogpt
tmux

pip install numpy==1.23.5 huggingface-hub tqdm
pip install --upgrade torch &
python data/cached_fineweb10B.py 18

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References

1. Penedo, Guilherme, 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. Anil, Rohan, et al. "Scalable second order optimization for deep learning." arXiv preprint arXiv:2002.09018 (2020).
7. Hägele, Alexander, et al. "Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations." arXiv preprint arXiv:2405.18392 (2024).