OpenGNS

An open dataset of Gradient Noise Scale (GNS) measurements: 433 training runs of ResNets, GPTs, and Diffusion Transformers (DiTs), from 11M to 1B parameters, trained under muP over dense batch-size and learning-rate grids. Each run records the GNS, its two components, and the losses throughout training.

Paper: OpenGNS: An Open Dataset of the Gradient Noise Scale across Vision, Language, and Diffusion Models (AutoML 2026)
Code and notebooks: github.com/olympiquemarcel/OpenGNS

What is the GNS?

The GNS, introduced by McCandlish et al. (2018), measures the noise-to-signal ratio of stochastic gradients. This dataset uses its simplified form, which assumes a well-conditioned Hessian:

$$B_{\text{simple}}=\frac{\mathrm{t}\mathrm{r}(\mathrm{\Sigma })}{\parallel G{\parallel }^2}B\_\backslash text\{simple\}\; =\; \backslash frac\{\backslash mathrm\{tr\}(\backslash Sigma)\}\{\backslash lVert\; G\; \backslash rVert^2\}$$

Here $G$ is the true gradient and $\Sigma$ is the per-example gradient covariance. When the noise is high, larger batches give a better gradient estimate. When it is low, extra samples add cost without improving the update. The GNS can therefore approximate the Critical Batch Size, the batch size beyond which scaling efficiency breaks down.

Files

Config	Workload	Runs	Rows	Size
cv	ResNet18 on CIFAR-10	180	~11.2M	343 MB
nlp	GPT on FineWeb	178	~27.5M	1.01 GB
diffusion	DiT on ImageNet	75	~265K	8.22 MB

Usage

from datasets import load_dataset

ds = load_dataset("olympique-marcel/OpenGNS", "diffusion", split="train")

To read one run from the large nlp file:

import pandas as pd
from huggingface_hub import hf_hub_download

path = hf_hub_download("olympique-marcel/OpenGNS", "nlp.parquet", repo_type="dataset")
run = pd.read_parquet(path, filters=[
    ("width", "==", 1024), ("batch_size", "==", 1024),
    ("peak_lr", "==", 2**-7), ("seed", "==", 111),
]).sort_values("samples_seen")

GNS of this run over training. The y-axis shows the stored gns value in sequences of 1,024 tokens.

Columns

All files contain iteration, samples_seen, batch_size (global), and:

• gns: the simplified GNS, tr(Σ) / ‖G‖²
• gns_norm: squared gradient norm ‖G‖²
• gns_var: trace of the per-example gradient covariance tr(Σ)

All three are exponential moving averages.

Config	Columns that identify a run	Other columns
cv	width (1, 2, 4), batch_size, lr	train_loss, train_acc, val_loss, val_acc, test_loss, test_acc (CIFAR-10.1)
nlp	width, batch_size, peak_lr, seed	train/loss, val/loss, lr, lr_schedule
diffusion	heads (2, 4, 8 for widths 144, 288, 576), batch_size, log_lr (log₂)	train/loss, val/loss, coco_val/loss

Notes

• Units: in nlp, gns, batch_size, and samples_seen count sequences of 1,024 tokens. Multiply by 1,024 for tokens.
• Outliers: gns has extreme values and gns_norm can be negative. The paper's plots keep gns < 1e6 for cv and diffusion, and gns < 1e10 for nlp.
• Nulls: not every row holds every metric, so drop nulls on the columns you use.
• Diverged runs: 9 DiT runs and 12 GPT runs are included up to the point of divergence.

Experimental setup

Each configuration was trained once with AdamW.

	ResNet18	GPT	DiT
Training data	10M images	20B tokens	51M images
Widths	1, 2, 4	256, 512, 1024, 2048, 2560	144, 288, 576
Parameters	11M, 45M, 179M	22M, 64M, 203M, 707M, 1B	11M, 43M, 169M
Batch size	2⁵–2¹⁴ images	2¹⁵–2²¹ tokens	2⁶–2¹⁰ images
Learning rate	10⁻⁶–10⁻¹	2⁻¹¹–2⁻⁶	2⁻¹³–2⁻⁹
LR schedule	Cosine (epoch based)	Cosine (step based)	Constant
EMA decay for GNS	0.995	0.95	0.995
Number of GPUs	4	8	8

Citation

@inproceedings{
  aach2026opengns,
  title={Open{GNS}: An Open Dataset of the Gradient Noise Scale across Vision, Language, and Diffusion Models},
  author={Marcel Aach and Jiangtao Wang and Stefan Kesselheim and Andreas Lintermann},
  booktitle={AutoML 2026 ABCD Track},
  year={2026},
  url={https://openreview.net/forum?id=miuqKH543n}
}