REVIEW 32 cited by
Fantastic Pretraining Optimizers and Where to Find Them
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Fantastic Pretraining Optimizers and Where to Find Them
read the original abstract
AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered practical adoption: (i) unequal hyperparameter tuning and (ii) limited or misleading evaluation setups. To address these two issues, we conduct a systematic study of ten deep learning optimizers across four model scales (0.1B-1.2B parameters) and data-to-model ratios (1-8x the Chinchilla optimum). We find that fair and informative comparisons require rigorous hyperparameter tuning and evaluations across a range of model scales and data-to-model ratios, performed at the end of training. First, optimal hyperparameters for one optimizer may be suboptimal for another, making blind hyperparameter transfer unfair. Second, the actual speedup of many proposed optimizers over well-tuned baselines is lower than claimed and decreases with model size to only 1.1x for 1.2B parameter models. Thirdly, comparing intermediate checkpoints before reaching the target training budgets can be misleading, as rankings between two optimizers can flip during training due to learning rate decay. Through our thorough investigation, we find that all the fastest optimizers such as Muon and Soap, use matrices as preconditioners -- multiplying gradients with matrices rather than entry-wise scalars. However, the speedup of matrix-based optimizers is inversely proportional to model scale, decreasing from 1.4x over AdamW for 0.1B parameter models to merely 1.1x for 1.2B parameter models.
Forward citations
Cited by 32 Pith papers
-
Autoregressive Learning in Joint KL: Sharp Oracle Bounds and Lower Bounds
Joint KL yields horizon-free approximation but an information-theoretic lower bound of order Omega(H) for estimation error in autoregressive learning, with matching computationally efficient upper bounds.
-
When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds
SignSGD provably beats SGD by a factor of d under sparse noise via matched ℓ1-norm upper and lower bounds, with an equivalent result for Muon on matrices, and this predicts faster GPT-2 pretraining.
-
Why Muon Outperforms Adam: A Curvature Perspective
Muon outperforms Adam by reducing curvature penalty via lower Normalized Directional Sharpness, as shown via Taylor approximation on LLM training and proven on stylized quadratic problems with heterogeneous curvature.
-
Spectral Scaling Laws of Muon
Muon momentum matrices show layer-dependent power-law scaling of stabilized singular value quantiles with model size from 77M to 2.8B parameters.
-
Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds
Intrinsic Muon provides closed-form linear maximization oracles on multiple Riemannian matrix manifolds for unitarily invariant norms, with convergence rates depending only on manifold dimension or rank.
-
MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI
MLS-Bench is a benchmark with 140 tasks that evaluates AI agents on inventing generalizable and scalable ML methods, finding they lag human performance especially in insight-driven invention rather than tuning.
-
MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI
Current AI agents fail to reliably invent transferable ML methods on a controlled 140-task benchmark, and more test-time compute or context does not remove the scientific-judgment bottleneck.
-
Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory
Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing f...
-
ISO: An RLVR-Native Optimization Stack
RLVR can reuse a base model's weight spectra while adapting only singular frames; ISO converts this into a faster optimizer and a data-free expert merger.
-
PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer
A preconditioned, product-aware spectral optimizer for LoRA reaches Adam's final loss in 1.2–1.7x fewer steps on instruction-tuning, with ~3% per-step overhead.
-
OmniOpt: Taxonomy, Geometry, and Benchmarking of Modern Optimizers
A meta-pipeline plus LMO four-axis view yields a dual taxonomy of 108 optimizers, and a multi-objective LLM/vision benchmark shows no single family dominates the quality–cost–memory frontier.
-
Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering
Momentum in Muon functions as a spectral filter on signal-plus-perturbation gradients, enlarging the gap to stabilize singular subspaces before orthogonalization and outperforming the reverse order.
-
Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics
SGD is reformulated via a master equation from discrete updates, producing a discrete Fokker-Planck equation that predicts non-stationary variance growth proportional to learning rate in flat Hessian directions.
-
MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI
MLS-Bench shows that current AI agents fall short of reliably inventing generalizable ML methods, with engineering tuning easier than genuine invention.
-
Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
-
Learning Rate Transfer in Normalized Transformers
νGPT is a modified parameterization of normalized transformers that enables learning rate transfer across width, depth, and token horizon.
-
Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minima
Nexus optimizer improves LLM downstream performance by converging to common minima across data sources despite identical pretraining loss.
-
Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minima
Nexus matches standard pretraining loss while improving downstream and OOD performance by maximizing gradient similarity so task-specific minima stay close.
-
veScale-FSDP: Flexible and High-Performance FSDP at Scale
veScale-FSDP uses RaggedShard and structure-aware planning to support block-wise quantization and non-element-wise optimizers while delivering 5-66% higher throughput and 16-30% lower memory than prior FSDP systems at...
-
Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimization
DeVA_S8 reweights Muon's matrix-sign update in the matrix's eigenbasis with a singular-value signal-to-noise ratio, reaching target LLM validation perplexity with ~6.6% fewer tokens than Muon.
-
Muon in Associative Memory Learning: Training Dynamics and Scaling Laws
In a linear softmax memory model, Muon equalizes learning across frequency tiers and gives exponential (noiseless) or T^{-2} (noisy power-law) convergence, versus polynomial or T^{-(1-1/β)} for gradient descent.
-
Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods
Preconditioned matrix norms unify steepest descent, quasi-Newton, and adaptive optimizers, revealing SGD, Adam, Muon, KL-Shampoo, SOAP, and SPlus as special cases and enabling new methods MuAdam and MuAdam-SANIA that ...
-
Open Problem: Is AdamW Effective Under Heavy-Tailed Noise?
The paper poses whether AdamW converges under heavy-tailed stochastic gradient noise and supplies a weighted-metric benchmark plus a corridor lower-bound showing how denominator memory can obscure large gradients.
-
PC Layer: Polynomial Weight Preconditioning for Improving LLM Pre-Training
A polynomial preconditioning layer controls singular value spectra of transformer weights to stabilize pre-training, shown effective on Llama-1B and supported by convergence theory for deep linear networks.
-
OPTScientist: Multi-Agent Discovery of Typed Optimizer Programs for Transformer Pretraining
A multi-agent typed-DSL search discovers RS-MR, a Muon-like matrix optimizer that beats Muon by 0.57% validation BPB on one 3.15B-token transformer pretraining run, without error bars.
-
Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling
SoftSignum replaces hard sign with soft-sign in optimizers via temperature control and quantile scheduling, extends to SoftMuon, provides a convergence proof for stochastic non-convex settings, and reports better perf...
-
Outer-Momentum Restarting in High-Dimensional Two-Phase Optimization
Periodic outer-momentum restarts in two-phase optimizers exploit phase cancellation in a linearized NTK model to widen stable learning-rate and momentum ranges in language-model pretraining.
-
RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization
RMNP preconditions matrix updates via row-wise L2 normalization instead of Newton-Schulz iteration, reducing complexity to O(mn) while matching Muon's non-convex convergence rate and empirical performance.
-
HTMuon: Improving Muon via Heavy-Tailed Spectral Correction
HTMuon modifies Muon to produce heavier-tailed updates and weight spectra via HT-SR theory, yielding up to 0.98 lower perplexity on LLaMA pretraining and serving as a plug-in for other Muon variants.
-
Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates
AOL column rescaling before Newton-Schulz improves the starting point enough to drop one iteration, making Muon's orthogonalization roughly 2.8x faster at similar final accuracy.
-
Small Experiments, Cheaper Decisions: A Case Study in Staged Promotion for Micro-Pretraining
Case study applies frozen staged budgets and promotion rules to twelve micro-pretraining configurations, identifying a top bridge condition at 12 hours with 169 GPU-hours total versus higher counterfactual costs.
-
Nora: Normalized Orthogonal Row Alignment for Scalable Matrix Optimizer
Nora is a matrix optimizer that stabilizes weight norms and angular velocities through row-wise momentum projection onto the orthogonal complement of the weights while approximating structured preconditioning with O(m...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.