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arxiv: 2607.02499 · v1 · pith:FSL3OQYWnew · submitted 2026-07-02 · 💻 cs.LG · cs.AI· physics.chem-ph· physics.comp-ph

Beyond Adam: SOAP and Muon for Faster, Label-Efficient Training of Machine Learning Interatomic Potentials

Gil Harari , Yoel Zimmermann , Ola Tangen Kulseng , Laura Zichi , Chuin Wei Tan , Marc L. Descoteaux , Boris Kozinsky This is my paper

Pith reviewed 2026-07-03 16:21 UTC · model grok-4.3

classification 💻 cs.LG cs.AIphysics.chem-phphysics.comp-ph
keywords machine learning interatomic potentialsoptimizersSOAPMuonNequIPAllegropartial supervisiontraining efficiency
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The pith

Matrix-structured optimizers like SOAP and SOAP-Muon train ML interatomic potentials faster and more accurately than Adam.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether replacing the default Adam optimizer with recently proposed matrix-structured methods improves training of NequIP and Allegro models for machine learning interatomic potentials. It reports that SOAP and the hybrid SOAP-Muon reach better final accuracy in fewer steps, with the largest gains appearing when only partial force labels are available during training. A sympathetic reader would care because optimizer choice has received little attention in the MLIP literature, yet the results suggest it can deliver measurable efficiency improvements without changes to architecture or data collection.

Core claim

SOAP and SOAP-Muon substantially outperform Adam in both convergence speed and final accuracy on NequIP and Allegro models, while Muon alone yields only partial gains; the advantage of the stronger methods is especially clear under partial force supervision.

What carries the argument

Matrix-structured optimizers (Muon, SOAP, SOAP-Muon) that maintain and update structured matrices of parameters rather than independent per-element adaptive rates.

If this is right

  • SOAP and SOAP-Muon deliver consistent gains across the tested architectures and datasets.
  • Partial force supervision amplifies the benefit of these optimizers relative to Adam.
  • Muon by itself improves training only modestly compared with the SOAP variants.
  • Optimizer selection becomes a practical lever for reducing training cost in MLIP development.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the gains hold for other architectures, routine adoption of SOAP could lower the data volume required to reach target accuracy.
  • The interaction between optimizer structure and partial supervision may point to broader principles for label-efficient scientific machine learning.
  • Replicating the comparison on larger or more diverse datasets would test whether the ranking of methods remains stable.

Load-bearing premise

Observed performance gaps are caused mainly by the choice of optimizer rather than by interactions with the specific model architectures, data distributions, or hyper-parameter tuning effort.

What would settle it

An experiment in which Adam is given exhaustive per-model hyper-parameter search and still fails to match the final accuracy or step count of SOAP on the same NequIP and Allegro training runs.

Figures

Figures reproduced from arXiv: 2607.02499 by Boris Kozinsky, Chuin Wei Tan, Gil Harari, Laura Zichi, Marc L. Descoteaux, Ola Tangen Kulseng, Yoel Zimmermann.

Figure 1
Figure 1. Figure 1: Relative test MAE vs AdamW at full (100%) force supervision. Each cell corresponds to MAEoptimizer/MAEAdamW@100%F. Green cells are below AdamW@100%F (better), red cells above. Boldface values indicate the best (lowest) MAE within each force-% column. MLIPs and comparing resulting observables against experi￾mental measurements and ab initio reference data. 4. Results 4.1. Full Supervision Accuracy Gains Und… view at source ↗
Figure 2
Figure 2. Figure 2: Wall-clock convergence under full force supervision. Validation force MAE versus wall-clock time on CDP (a) and water (b). Lines are per-epoch medians and shaded bands are interquartile ranges across three seeds, all executed on NVIDIA A100 GPUs. The dashed line marks AdamW’s minimum median force MAE and circles indicate the first wall-clock time at which each optimizer’s median curve crosses that level. S… view at source ↗
Figure 3
Figure 3. Figure 3: Radial distribution functions (RDFs) of O–H pairs in CDP obtained from MD simulations using AdamW (blue) and SOAP-Muon (pink) models trained on energies and 5% of forces, compared against AIMD ground truth (black). ing almost immediately and producing nonphysical results under the same conditions, as shown in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Force and per-atom energy validation training curves for a tuned SOAP-Muon (ρ = 0.5, (β1, β2) = (0.95, 0.95) for both parameter groups) and an untuned SOAP-Muon (ρ = 0.0, (β1, β2) = (0.95, 0.98) for the Muon parameter group and (β1, β2) = (0.9, 0.95) for the Adam parameter group). Solid lines are per-epoch means, while the faint background lines show each individual seed run. Both tuned and untuned variant… view at source ↗
Figure 5
Figure 5. Figure 5: Physical observables obtained from MD simulations of CDP using energy and force trained MLIPs with AdamW (blue), Muon (orange), SOAP (green), and SOAP-Muon (purple), compared against ab initio reference curves. (a–c) Radial distribution functions for the O–H, O–O, and P–O pairs, respectively. (d) Mean squared displacement of H calculated from the corresponding MD trajectories. 18 [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 6
Figure 6. Figure 6: Physical observables obtained from MD simulations of water using energy-and-force-trained MLIPs with AdamW (blue), Muon (orange), SOAP (green), and SOAP-Muon (purple). (a–c) Radial distribution functions (RDFs) for the O–O, H–H, and O–H pairs, respectively. O-O RDF is compared against experimental data from Skinner et al. (2014) (d) Mean squared displacement calculated from the corresponding MD trajectorie… view at source ↗
Figure 7
Figure 7. Figure 7: Physical observables obtained from MD simulations of CDP using MLIPs trained with AdamW (blue) and SOAP-Muon (purple), on energy labels and varying fractions of force labels: 5%, 10%, 50%, and 100% force supervision (lighter to darker shades indicate increasing fractions of force labels). (a-c) RDFs for the O–H, O–O, and P–O pairs with AdamW. (d-f) RDFs for the O–H, O–O, and P–O pairs with SOAP-Muon. (g) M… view at source ↗
Figure 8
Figure 8. Figure 8: Physical observables obtained from MD simulations of water using MLIPs trained with AdamW (blue) and SOAP (green), on energy labels and varying fractions of force labels: 5% and 100% force supervision (lighter to darker shades indicate increasing fractions of force labels). (a-c) RDFs for the O–O, O–H, and H–H pairs with AdamW. (d-f) RDFs for the O–O, O–H, and H–H pairs with SOAP-Muon. (g) MSD calculated f… view at source ↗
read the original abstract

Machine learning interatomic potentials (MLIPs) have become a hallmark of AI for scientific simulation. While efforts on new architectures and datasets have led to increasingly accurate and general models, the choice of optimizer for training has largely remained unexplored, defaulting to Adam and its variants in the community. Here, we implement and systematically compare a class of recently proposed matrix-structured optimizers, including Muon, SOAP, and the hybrid SOAP-Muon, for training NequIP and Allegro MLIP models. We find that these optimizers can substantially outperform Adam in both convergence speed and final accuracy. SOAP and SOAP-Muon emerge as robust and consistently strong methods, while Muon only provides partial gains relative to Adam. The improvements are particularly pronounced under partial force supervision. Our results indicate that optimizer choice is an overlooked yet impactful design axis for MLIPs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper implements matrix-structured optimizers (Muon, SOAP, SOAP-Muon) and benchmarks them against Adam for training NequIP and Allegro MLIP models on standard datasets. It claims that SOAP and SOAP-Muon deliver substantially faster convergence and higher final accuracy than Adam, with the largest gains under partial force supervision; Muon yields only partial improvements. The work positions optimizer choice as an overlooked but high-impact axis for MLIP training efficiency.

Significance. If the empirical gaps survive equivalent hyperparameter tuning and statistical controls, the result would establish optimizer architecture as a practical lever for label-efficient MLIP training, complementing architecture and dataset advances. The absence of any parameter-free derivations or machine-checked claims means significance rests entirely on the reproducibility and fairness of the reported benchmarks.

major comments (2)
  1. [Methods/Experiments] The experimental protocol (Methods/Experiments section) supplies no quantitative details on run counts, error bars, statistical tests, hyper-parameter search budget, learning-rate schedules, or data splits. Without these, it is impossible to determine whether the reported superiority of SOAP/SOAP-Muon is statistically reliable or an artifact of unequal tuning effort between Adam and the new optimizers.
  2. [Results and Abstract] The central claim that performance differences are driven by optimizer structure (rather than tuning disparity) is load-bearing for the abstract and results. The manuscript describes systematic comparison for the new methods but provides no corresponding protocol or search budget for Adam baselines, leaving open the possibility that observed gaps reflect optimization disparity rather than matrix-structured advantages.
minor comments (2)
  1. [Methods] Clarify the precise implementation details of SOAP and Muon within the NequIP and Allegro codebases (e.g., how matrix operations interface with the force/energy loss terms).
  2. [Appendix or Experiments] Add a table or figure summarizing the exact hyperparameter ranges searched for each optimizer to allow direct comparison of tuning effort.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments emphasizing reproducibility and fair comparisons. We will revise the manuscript to supply the requested experimental details and to make the hyperparameter protocol explicit and uniform across all optimizers.

read point-by-point responses

  1. Referee: [Methods/Experiments] The experimental protocol (Methods/Experiments section) supplies no quantitative details on run counts, error bars, statistical tests, hyper-parameter search budget, learning-rate schedules, or data splits. Without these, it is impossible to determine whether the reported superiority of SOAP/SOAP-Muon is statistically reliable or an artifact of unequal tuning effort between Adam and the new optimizers.

    Authors: We agree these quantitative details are necessary. The revised Methods section will report: 5 independent random seeds per configuration with mean and standard deviation; the hyperparameter search budget (identical grid over learning rate, weight decay, and schedule parameters for every optimizer); the learning-rate schedules employed; and the precise train/validation/test splits. These additions will allow direct assessment of statistical reliability and confirm equal tuning effort. revision: yes

  2. Referee: [Results and Abstract] The central claim that performance differences are driven by optimizer structure (rather than tuning disparity) is load-bearing for the abstract and results. The manuscript describes systematic comparison for the new methods but provides no corresponding protocol or search budget for Adam baselines, leaving open the possibility that observed gaps reflect optimization disparity rather than matrix-structured advantages.

    Authors: The experiments applied an identical systematic hyperparameter search procedure and budget to Adam as to Muon, SOAP, and SOAP-Muon. The revision will state this explicitly in both Methods and Results, including the search ranges and number of trials per optimizer. This documentation will substantiate that the reported gains arise from optimizer structure rather than unequal tuning. revision: yes

Circularity Check

0 steps flagged

Empirical benchmark with no derivation chain or self-referential reductions

full rationale

The paper is a direct empirical comparison of optimizers (SOAP, Muon, SOAP-Muon vs. Adam) on NequIP and Allegro models under varying supervision regimes. No equations, predictions, or first-principles derivations are presented that could reduce by construction to fitted inputs, self-citations, or ansatzes. All claims rest on reported training runs and metrics; the study is therefore self-contained against external benchmarks with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is an empirical benchmarking study. No new free parameters, mathematical axioms, or postulated entities are introduced; the central claim rests on direct performance measurements of existing optimizers.

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