Recognition: unknown
Benchmarking Optimizers for MLPs in Tabular Deep Learning
Pith reviewed 2026-05-10 12:01 UTC · model grok-4.3
The pith
The Muon optimizer consistently outperforms AdamW when training MLPs on tabular data.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Under a shared experiment protocol, the Muon optimizer consistently outperforms AdamW for training MLP-based models on tabular data. This makes Muon a strong and practical choice for practitioners and researchers provided the associated training efficiency overhead is affordable. Exponential moving average of model weights improves AdamW on vanilla MLPs, although its benefits are less consistent across other model variants.
What carries the argument
Muon optimizer, which replaces AdamW within the standard MLP training pipeline for tabular data and produces superior performance in head-to-head comparisons under fixed experimental conditions.
If this is right
- Practitioners should consider Muon as an alternative to AdamW for tabular deep learning tasks.
- The training efficiency overhead of Muon should be evaluated against its performance benefits in specific use cases.
- Exponential moving average of weights offers a simple way to boost performance of AdamW-trained vanilla MLPs.
- Optimizer selection deserves more systematic study in tabular deep learning similar to architecture design.
Where Pith is reading between the lines
- If Muon generalizes beyond the tested 17 datasets, it could become a new default recommendation in tabular ML toolkits.
- The findings open the door to testing Muon on hybrid architectures that combine MLPs with other components for tabular data.
- Future work might explore whether the advantages stem from Muon's handling of gradient noise common in tabular tasks.
Load-bearing premise
The hyperparameter choices, dataset selection, and MLP variants in the 17-dataset benchmark do not inadvertently favor Muon over AdamW.
What would settle it
An experiment on additional tabular datasets or MLP architectures where AdamW matches or exceeds Muon performance after equivalent tuning would falsify the claim of consistent outperformance.
Figures
read the original abstract
MLP is a heavily used backbone in modern deep learning (DL) architectures for supervised learning on tabular data, and AdamW is the go-to optimizer used to train tabular DL models. Unlike architecture design, however, the choice of optimizer for tabular DL has not been examined systematically, despite new optimizers showing promise in other domains. To fill this gap, we benchmark 15 optimizers on 17 tabular datasets for training MLP-based models in the standard supervised learning setting under a shared experiment protocol. Our main finding is that the Muon optimizer consistently outperforms AdamW, and thus should be considered a strong and practical choice for practitioners and researchers, if the associated training efficiency overhead is affordable. Additionally, we find exponential moving average of model weights to be a simple yet effective technique that improves AdamW on vanilla MLPs, though its effect is less consistent across model variants.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript benchmarks 15 optimizers for training MLPs on 17 tabular datasets under a shared experimental protocol in the standard supervised setting. The central claim is that Muon consistently outperforms the default AdamW optimizer and should be considered a strong practical alternative provided its training efficiency overhead is acceptable; a secondary observation is that exponential moving average of weights improves AdamW on vanilla MLPs, though less consistently across variants.
Significance. If the results prove robust, the work supplies timely, practical guidance for optimizer choice in tabular deep learning, where MLPs remain a common backbone and AdamW is the de-facto standard. A systematic multi-dataset comparison of this kind can shift community practice and motivate further optimizer development tailored to tabular data. The empirical scope (17 datasets, 15 optimizers) is a strength, but the absence of detailed tuning budgets and statistical reporting currently limits the strength of the recommendation.
major comments (3)
- [Abstract / Experiments] Abstract and Experiments section: the assertion of a 'shared experiment protocol' is load-bearing for the headline claim yet provides no information on per-optimizer hyperparameter search effort (number of trials, learning-rate grids, momentum or weight-decay ranges), learning-rate schedules, or early-stopping rules. Without explicit confirmation that every optimizer received equivalent tuning budgets, the observed Muon gains could be an artifact of unequal optimization rather than intrinsic superiority.
- [Results] Results section: the manuscript reports no variance across random seeds, no standard deviations on the performance metrics, and no statistical significance tests (e.g., paired tests across the 17 datasets) for the Muon-vs-AdamW differences. These omissions make it impossible to assess whether the 'consistent outperformance' survives seed variation or is distinguishable from noise.
- [Abstract / Results] Abstract and §5 (or equivalent): the recommendation to adopt Muon 'if the associated training efficiency overhead is affordable' is stated without any quantitative comparison of wall-clock time, iteration cost, or memory footprint versus AdamW, leaving practitioners without the data needed to evaluate the trade-off.
minor comments (2)
- [Tables] Tables should report both mean performance and standard deviation for every optimizer-dataset pair and clearly state the evaluation metric (accuracy, AUC, etc.) used on each dataset.
- [Abstract] The abstract mentions EMA improving AdamW on 'vanilla MLPs' but does not define 'vanilla' or indicate whether the same EMA benefit was tested on the other model variants referenced later.
Simulated Author's Rebuttal
Thank you for the constructive feedback on our manuscript. We address each of the major comments point by point below, proposing specific revisions where appropriate to strengthen the empirical claims and reporting.
read point-by-point responses
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Referee: [Abstract / Experiments] Abstract and Experiments section: the assertion of a 'shared experiment protocol' is load-bearing for the headline claim yet provides no information on per-optimizer hyperparameter search effort (number of trials, learning-rate grids, momentum or weight-decay ranges), learning-rate schedules, or early-stopping rules. Without explicit confirmation that every optimizer received equivalent tuning budgets, the observed Muon gains could be an artifact of unequal optimization rather than intrinsic superiority.
Authors: We agree that explicit details on the tuning procedure are required to fully substantiate the shared protocol. The protocol used identical model architectures, datasets, batch sizes, epoch counts, and evaluation metrics for all 15 optimizers. Learning rates were tuned over a shared logarithmic grid (1e-4 to 1e-1) with the same number of trials per optimizer; other hyperparameters followed each optimizer's standard recommendations. We omitted a full accounting of trial counts and schedules in the original text. In revision we will add a dedicated subsection (or table) in Experiments that lists the exact search spaces, trial budgets, schedules, and early-stopping rules applied uniformly, thereby confirming equivalent effort across optimizers. revision: yes
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Referee: [Results] Results section: the manuscript reports no variance across random seeds, no standard deviations on the performance metrics, and no statistical significance tests (e.g., paired tests across the 17 datasets) for the Muon-vs-AdamW differences. These omissions make it impossible to assess whether the 'consistent outperformance' survives seed variation or is distinguishable from noise.
Authors: This observation correctly identifies a limitation in statistical reporting. The presented results used single runs to emphasize broad trends across 17 datasets and 15 optimizers. We will rerun the key comparisons (Muon vs. AdamW) with at least five random seeds, report means and standard deviations, and add paired statistical tests (Wilcoxon signed-rank test across datasets) to quantify whether the observed differences are significant and robust to seed variation. revision: yes
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Referee: [Abstract / Results] Abstract and §5 (or equivalent): the recommendation to adopt Muon 'if the associated training efficiency overhead is affordable' is stated without any quantitative comparison of wall-clock time, iteration cost, or memory footprint versus AdamW, leaving practitioners without the data needed to evaluate the trade-off.
Authors: We concur that the efficiency trade-off must be quantified for the recommendation to be practical. The original text only notes the overhead qualitatively. In the revised manuscript we will include new measurements of wall-clock training time, per-iteration cost, and peak GPU memory for Muon and AdamW on a representative subset of the datasets, all run on identical hardware. These numbers will be added to the Experiments or Results section to allow readers to assess affordability directly. revision: yes
Circularity Check
Empirical benchmarking study with no derivation chain
full rationale
This paper conducts a direct empirical comparison of 15 optimizers on 17 tabular datasets using MLPs under a shared protocol. No mathematical derivations, first-principles predictions, fitted equations, or ansatzes are presented that could reduce to inputs by construction. The core claim (Muon outperforming AdamW) rests on reported experimental results rather than any self-referential logic, self-citation load-bearing theorem, or renaming of known patterns. External datasets and standard supervised learning settings provide independent falsifiability, so no circularity steps exist.
Axiom & Free-Parameter Ledger
Reference graph
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Table 3: Comparison of Muon with Muon EMA on MLP.∆score is the mean relative unified score (%) with respect to AdamW; the parenthesized value shows the improvement over AdamW
We can see that EMA provides only a marginal gain in relative score and no gain in the overall amount of wins over AdamW. Table 3: Comparison of Muon with Muon EMA on MLP.∆score is the mean relative unified score (%) with respect to AdamW; the parenthesized value shows the improvement over AdamW. W/T/L counts are based on Welch’st-test (α= 0.05) across 17...
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[15]
As such, relevant parts of the text below are copied from (Gorishniy et al., 2025)
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[16]
and tuned jointly (100 iterations). Parameter Distribution / Value Adam W Learning RateLogUniform[3×10 −5,0.001] Weight DecayLogUniform[0.005,5] Adam W EMA EMA decayLogUniform[0.9,0.999] Learning RateLogUniform[3×10 −5,0.001] Weight DecayLogUniform[0.005,5] NAdam W Learning RateLogUniform[3×10 −5,0.001] Weight DecayLogUniform[0.005,5] RAdam Learning RateL...
discussion (0)
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