Temperon

Pay for sharpness-aware minimization only where it pays you back.

Tempering is the controlled heat treatment that follows quenching and sets a metal's final toughness. This package governs the training equivalent: what happens during the last anneal.

SAM improves generalization but doubles the cost of every training step, which is why most people skip it. Temperon runs SAM for a contiguous tail aligned to your learning-rate decay instead of the whole run. In our experiments that reaches full-time-SAM quality for roughly a third less wall-clock — and spreading the same SAM budget uniformly across training does worse than either extreme.

Status: pre-release (0.1.0.dev0), published alongside a paper in preparation. The API may still change. Single-GPU, bf16/fp32 tested; DDP and gradient accumulation are not supported yet.

pip install temperon

Usage

import torch
from temperon import Temperon, wsd

base = torch.optim.AdamW(model.parameters(), lr=2e-5)
total = len(loader) * epochs

opt = Temperon(base, total_steps=total, tail_frac=0.3, rho=0.05)
sched = torch.optim.lr_scheduler.LambdaLR(base, wsd(total, 250, decay_frac=0.3))

for batch in loader:
    def closure():
        opt.zero_grad()
        loss = loss_fn(model(batch.x), batch.y)
        loss.backward()
        torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0)
        return loss

    loss = opt.step(closure)   # 1 pass in the cheap phase, 2 in the tail
    sched.step()

The closure follows the torch.optim.LBFGS convention: zero the gradients, compute the loss, call backward(), return the loss. Temperon calls it once per step during the cheap phase and twice during the tail. Nothing else in your training code changes.

The one thing that matters

tail_frac must be aligned to your learning-rate decay, so the tail owns a complete anneal. This is not a detail: in our ablations a SAM tail bolted onto the middle of an ongoing cycle gained nothing at all (flat in tail length, ~1pp below full SAM), while a tail owning a fresh anneal matched full-time SAM. Pass the same fraction to wsd(..., decay_frac=f) and Temperon(tail_frac=f) and the alignment is exact.

Choosing tail_frac

The switch point is a measured quality/cost dial, not a magic number. On CIFAR-100 (5 seeds, same 100-epoch budget, SGD explorer → SAM+Muon tail):

A longer tail buys the expensive method's full ceiling at its full cost; a shorter one gives up a measured slice of that ceiling for a much cheaper run. The default 0.3 is the value that matched full-time SAM quality on GPT-2 pretraining (−29% wall-clock) and GLUE fine-tuning (−36%). Below 0.2 we have no measurements; as tail_frac → 1 you are simply paying for full-time SAM.

Cheap explorer, expensive refiner

You can also switch optimizers at the same boundary — a cheap explorer for most of training, then a stronger optimizer owning the SAM tail:

from temperon import cosine_tail

explorer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
refiner  = Muon(model.parameters(), lr=0.01, weight_decay=0.2)  # any Muon impl.

opt = Temperon(explorer, total_steps=total, tail_frac=0.57,
             tail_optimizer=refiner, transfer="momentum")
sched = torch.optim.lr_scheduler.LambdaLR(explorer, cosine_tail(total, 0.57))

transfer="momentum" carries momentum_buffer across the switch.

When not to use this

Measured limits, stated because they define where the method applies:

• A cheap optimizer wins below its own ceiling. Temperon never accelerates an accuracy target that plain SGD or Adam can already reach; it accelerates targets that only expensive methods reach at all. If your target is modest, use the cheap optimizer.
• Saturated tasks gain nothing. Where the frontier is reached early, the late anneal is not what is limiting you.
• Language-model pretraining is out of scope. In near-single-epoch pretraining there is little overfitting for SAM to prevent, and we measured no useful gain; under heavy data repetition SAM was actively worse. SAM's established language gains are in fine-tuning, which is where this package is aimed for LMs.

Citing

If you use Temperon, please cite the preprint, arXiv:2609.17575:

@article{mastromichalakis2026temperon,
  title   = {Temperon: Full-Time {SAM} Quality at a Third Less Wall-Clock},
  author  = {Mastromichalakis, Stamatis},
  journal = {arXiv preprint arXiv:2609.17575},
  year    = {2026},
  doi     = {10.48550/arXiv.2609.17575}
}

The research code and the full experimental record, including the negative controls this claim rests on, live in the same repository.

License

MIT.