a scaling recipe that maps compute budgets to model configurations,
a scaling suite of models trained from that recipe at IsoFLOP budgets from 3 × 10¹⁸ to 1 × 10²³ FLOPs, and
a scaling law which uses the smaller Delphi models to predict the larger ones.

A pre-registered forecast from that scaling law predicted the final loss of the largest Delphi run (1 × 10²³ FLOPs, 25 B parameters, 600 B tokens) within 0.2%, using 300× less compute than the training run itself. The same process forecasts downstream benchmarks — MMLU, HumanEval, and GSM8K — via a two-step regression combining compute and observational scaling laws.

See "Scaling Laws That Extrapolate 300× Past the Fit" for the recipe, fit, and downstream-eval projections. The full set of Delphi checkpoints — IsoFLOP grid points, held-out optima at 1e21/1e22/1e23 with multiple random seeds, and training intermediates — lives on marin-community on the Hub.

This is a research artifact, not a production model.

Model details


Architecture	Qwen 3 (pre-norm decoder, RMSNorm, RoPE, QK-norm with learned scaling, SwiGLU MLPs)
Parameters	156,508,160
Hidden size	512
Layers	6
Attention heads	4
KV heads	4 (no GQA)
Head dim	128
FFN intermediate	2048 (MLP ratio 4)
Vocab size	128,256 (Llama 3 tokenizer)
Max sequence length	4096
Position encoding	RoPE (θ = 500000, Llama 3-style scaling)
Bias terms	None
Tied embeddings	No

Training


Compute	9 × 10¹⁸ FLOPs
Tokens	12,914,786,304
Steps	49,265
Sequence length	4096
Optimizer	AdamH (Adam with Hyperball)
Recipe	Delphi (Complete(d)P-style scaling with `(T₀/T)^0.3` token-horizon LR correction)
LR schedule	WSD: 10% linear warmup, 20% linear decay, 0 floor
Precision	f32 master params, bf16 compute
Parallelism	FSDP
Data mixture	Nemotron-CC + StarCoderData + ProofPile 2
Tokenizer	Llama 3 (vocab 128,256)

AdamH, Adam with Hyperball, constrains every projection weight to stay on the Frobenius- norm sphere it was initialized on, so weight decay has nothing to regularize away and falls out of the recipe. A Complete(d)P-style transfer rule with a (T₀/T)^0.3 correction sets learning rate as token horizon grows. Reference constants: B₀ = 64, T₀ = 2.5 B tokens, η₀ = 0.00630, η₀,Adam = 0.000656, ε₀ = 1.85 × 10⁻⁸. Recipe code: experiments/scaling_law_sweeps/completed_adamh.py.

Companion releases

All Delphi model checkpoints: marin-community on the Hub.
Plot data behind every figure in the blog post: marin-community/delphi-blog-data (one config per figure, with wandb_url on every row).
Pipelines that deterministically reproduce the training mixture from public Nemotron-CC, StarCoderData, and ProofPile 2 sources: see the Marin repo.

Evaluation

This checkpoint is part of the Delphi eval suite (experiments/exp1337_eval_suite.py), which scores every Delphi run alongside reference open-weights baselines (Qwen 3, Llama 2/3, OLMo 2, Marin 8B). Following the blog's two-step forecast, soft metrics (per-choice log-prob for multiple-choice tasks, bits-per-byte for generative tasks) carry the signal the scaling law is fit on, and a sigmoid fit on an external model pool maps soft metric to hard metric (accuracy, pass@1, exact-match). Below ~1e21 FLOPs the hard metrics stay near chance even when the underlying probabilities are improving smoothly; that is expected and is exactly why the soft metrics exist.

Limitations

Trained on an English-heavy web mixture; no multilingual coverage.
Pretrained-only — no instruction tuning, RLHF, or safety alignment.
The Delphi recipe targets compute-optimal training, not inference-cost-aware overtraining; for inference-heavy deployments, an overtrained smaller model may be preferable. The blog's "off-optimal training" section quantifies the penalty.
This is one checkpoint in a much larger Delphi release; pick the one that matches your compute / parameter / token regime, or browse the full set at marin-community.

Citation

bibtex

@misc{held2026delphi,
  title  = {Scaling Laws That Extrapolate 300× Past the Fit},
  author = {Held, Will and {Marin Community}},
  year   = {2026},
  url    = {https://openathena.ai/blog/delphi}
}

marin-community/delphi-9e18-157Mparams-12.9Btokens

delphi-9e18-157Mparams-12.9Btokens

About Delphi