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:
- 1.7B tokens instead of 10B
- 8.2 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).
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
python data/cached_fineweb10B.py 18 # downloads only the first 1.8B training tokens to save time
./run.shThe result will be a transformer with 124M active parameters trained for 4768 steps on 2.4B tokens of Fineweb [1], achieving ~3.275 validation loss. For comparison, the default llm.c PyTorch trainer yields >3.28 validation loss after training for 19560 steps on 10B tokens.
- To run on fewer GPUs, just modify
run.shto have a different--nproc_per_node. - If you're running out of memory, then go into
train_gpt2.pyand scale down thedevice_batch_sizeto either 16 or 32.
Both of these changes will have no effect on the training - you should get the exact same loss curve as the most recent record, because the training code will automatically adjust the gradient accumulation in order to have the same total batch size.
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.
- 45 minutes: llm.c baseline (05/28/24) [training log] (note: the 90 minute time is on 8xA100; it's 45 minutes on 8xH100. This run is essentially a hardware-optimized GPT-2 (small) replication using better training data.)
- 31.4 minutes: Architectural modernizations and learning rate tuning (06/06/24) [training log] (note: this uses half the tokens as the baseline but isn't yet twice as fast since it's slower PyTorch code rather than raw CUDA. also note: most of the improvement here came from simply tripling the learning rate.)
- 24.9 minutes: Introduced the Muon optimizer (10/04/24)
- 22.3 minutes: Muon improvements (10/11/24) [reproducible log]
- 15.2 minutes: Pad embeddings & architectural modernizations (10/14/24) [reproducible log]
- 13.1 minutes: Distributed the overhead of Muon (10/18/24) [reproducible log]
- 12.0 minutes: Upgraded PyTorch from 2.4.1 to 2.5.0 (10/18/24) [reproducible log] (note: this now runs at the same speed per step as the CUDA llm.c trainer!)
- 10.8 minutes: Untied embed and lm_head (11/03/24) [reproducible log]
- 8.2 minutes: Shortcuts & tweaks (11/06/24) [reproducible log]
- 8.05(?) minutes (11/07/24) (this one is a bit difficult to certify since the reproducible log shows a slower time than the 11/06 record, but based on same-hardware tests it does appear to be a new record by 10-15 seconds.)
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
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.
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):
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 = A @ X
X = a * X + b * B + c * A @ B
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
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.
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
- Penedo, Guilherme, et al. "The fineweb datasets: Decanting the web for the finest text data at scale." arXiv preprint arXiv:2406.17557 (2024).
- Nicholas J. Higham. Functions of Matrices. Society for Industrial and Applied Mathematics, 2008. Equation 5.22.
- Günther Schulz. Iterative Berechnung der reziproken Matrix. Z. Angew. Math. Mech., 13:57–59, 1933.
- Jeremy Bernstein and Laker Newhouse. "Old Optimizer, New Norm: An Anthology." arxiv preprint arXiv:2409.20325 (2024).
- Vineet Gupta, Tomer Koren, and Yoram Singer. "Shampoo: Preconditioned stochastic tensor optimization." International Conference on Machine Learning. PMLR, 2018.
- Anil, Rohan, et al. "Scalable second order optimization for deep learning." arXiv preprint arXiv:2002.09018 (2020).
- Hägele, Alexander, et al. "Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations." arXiv preprint arXiv:2405.18392 (2024).
