Benchmarking Neural Network Training Algorithms
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Abstract (arXiv)
Training algorithms, broadly construed, are an essential part of every deep learning pipeline. Training algorithm improvements that speed up training across a wide variety of workloads (e.g., better update rules, tuning protocols, learning rate schedules, or data selection schemes) could save time, save computational resources, and lead to better, more accurate, models. Unfortunately, as a community, we are currently unable to reliably identify training algorithm improvements, or even determine the state-of-the-art training algorithm. In this work, using concrete experiments, we argue that real progress in speeding up training requires new benchmarks that resolve three basic challenges faced by empirical comparisons of training algorithms: (1) how to decide when training is complete and precisely measure training time, (2) how to handle the sensitivity of measurements to exact workload details, and (3) how to fairly compare algorithms that require hyperparameter tuning. In order to address these challenges, we introduce a new, competitive, time-to-result benchmark using multiple workloads running on fixed hardware, the AlgoPerf: Training Algorithms benchmark. Our benchmark includes a set of workload variants that make it possible to detect benchmark submissions that are more robust to workload changes than current widely-used methods. Finally, we evaluate baseline submissions constructed using various optimizers that represent current practice, as well as other optimizers that have recently received attention in the literature. These baseline results collectively demonstrate the feasibility of our benchmark, show that non-trivial gaps between methods exist, and set a provisional state-of-the-art for future benchmark submissions to try and surpass.
Key facts. Cited by 52 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Jun 2023.
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Citing papers per year: 2023: 3; 2024: 14; 2025: 17; 2026: 18.
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50 most cited of 52 All 52 (JSON)
- 2026Towards Easier-to-Tune Training Algorithms: New Results from AlgoPerf9 Oct 2026
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- 2026The Best Optimizer Depends on Batch Size6 Oct 2026
- 2026How Bregman Divergences Shape Shampoo6 Oct 2026
- 2026LionMuon: Alternating Spectral and Sign Descent for Efficient Training28 Sep 2026
- 2026Minibatch persistency, eight years later: what batch reuse costs in steps and joules, and what it saves in data12 Sep 2026
- 2026AdamX: Cosine similarity meets gradient descent10 Sep 2026
- 2026The Loss Does Not See the Basis, but Adam Does5 Aug 2026
- 2026Understanding Schedule-Free Methods in Nonconvex Optimization: Rate Guarantees and Escaping Saddles10 Jul 2026
- 2026Beyond a Single Explanation of the Adam--SGD Gap12 Jun 2026
- 2026FOAM: Frequency and Operator Error-Based Adaptive Damping Method for Reducing Staleness-Oriented Error for Shampoo1 Jun 2026
- 2026AMUSE: Anytime Muon with Stable Gradient Evaluation21 May 2026
38 more
- 2026LionMuon: Alternating Spectral and Sign Descent for Efficient Training19 May 2026
- 2026Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers18 May 2026
- 2026Muon Does Not Converge on Convex Lipschitz Functions9 May 2026
- 2026Celo2: Towards Learned Optimization Free Lunch22 Feb 2026
- 2026Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging3 Feb 2026
- 2026DASH: Faster Shampoo via Batched Block Preconditioning and Efficient Inverse-Root Solvers2 Feb 2026
- 2025DyKAF: Dynamical Kronecker Approximation of the Fisher Information Matrix for Gradient Preconditioning9 Nov 2025
- 2025What Really Matters in Matrix-Whitening Optimizers?28 Oct 2025
- 2025Optimization Benchmark for Diffusion Models on Dynamical Systems22 Oct 2025
- 2025NorMuon: Making Muon more efficient and scalable7 Oct 2025
- 2025Per-example gradients: a new frontier for understanding and improving optimizers30 Sep 2025
- 2025FedMuon: Federated Learning with Bias-corrected LMO-based Optimization30 Sep 2025
- 2025Understanding and Improving Shampoo and SOAP via Kullback-Leibler Minimization3 Sep 2025
- 2025Through the River: Understanding the Benefit of Schedule-Free Methods for Language Model Training14 Jul 2025
- 2025Leveraging Coordinate Momentum in SignSGD and Muon: Memory-Optimized Zero-Order4 Jun 2025
- 2025Purifying Shampoo: Investigating Shampoo's Heuristics by Decomposing its Preconditioner4 Jun 2025
- 2025How far away are truly hyperparameter-free learning algorithms?29 May 2025
- 2025Learning by solving differential equations19 May 2025
- 2025Structured Preconditioners in Adaptive Optimization: A Unified Analysis13 Mar 2025
- 2025COSMOS: A Hybrid Adaptive Optimizer for Memory-Efficient Training of LLMs24 Feb 2025
- 2025Training Deep Learning Models with Norm-Constrained LMOs11 Feb 2025
- 2025Implicit Bias of Spectral Descent and Muon on Multiclass Separable Data7 Feb 2025
- 2025Celo: Training Versatile Learned Optimizers on a Compute Diet22 Jan 2025
- 2024Understanding LLM Embeddings for Regression22 Nov 2024
- 2024LASER: Attention with Exponential Transformation5 Nov 2024
- 2024Modular Duality in Deep Learning28 Oct 2024
- 2024Loss Landscape Characterization of Neural Networks without Over-Parametrization16 Oct 2024
- 2024Old Optimizer, New Norm: An Anthology30 Sep 2024
- 2024Fast Optimizer Benchmark26 Jun 2024
- 2024On PI Controllers for Updating Lagrange Multipliers in Constrained Optimization7 Jun 2024
- 2024The Road Less Scheduled24 May 2024
- 2024Position: Why We Must Rethink Empirical Research in Machine Learning3 May 2024
- 2024Expanding the Horizon: Enabling Hybrid Quantum Transfer Learning for Long-Tailed Chest X-Ray Classification30 Apr 2024
- 2024Partial Rankings of Optimizers26 Feb 2024
- 2024Time-, Memory- and Parameter-Efficient Visual Adaptation5 Feb 2024
- 2024MetaOptimize: A Framework for Optimizing Step Sizes and Other Meta-parameters4 Feb 2024
- 2024Stabilizing Sharpness-aware Minimization Through A Simple Renormalization Strategy14 Jan 2024
- 2023Kronecker-Factored Approximate Curvature for Modern Neural Network Architectures1 Nov 2023
50 newest of 52 All 52 (JSON)
- 2024Old Optimizer, New Norm: An Anthologycited by 193
- 2025Training Deep Learning Models with Norm-Constrained LMOscited by 192
- 2024The Road Less Scheduledcited by 163
- 2025NorMuon: Making Muon more efficient and scalablecited by 84
- 2024Modular Duality in Deep Learningcited by 77
- 2023Kronecker-Factored Approximate Curvature for Modern Neural Network Architecturescited by 49
- 2023No Train No Gain: Revisiting Efficient Training Algorithms For Transformer-based Language Modelscited by 41
- 2025Implicit Bias of Spectral Descent and Muon on Multiclass Separable Datacited by 41
- 2025Structured Preconditioners in Adaptive Optimization: A Unified Analysiscited by 33
- 2025COSMOS: A Hybrid Adaptive Optimizer for Memory-Efficient Training of LLMscited by 30
- 2024Time-, Memory- and Parameter-Efficient Visual Adaptationcited by 28
- 2025Purifying Shampoo: Investigating Shampoo's Heuristics by Decomposing its Preconditionercited by 23
12 most cited of 50 All 50 (JSON)
- 2026Towards Easier-to-Tune Training Algorithms: New Results from AlgoPerf9 Oct 2026
- 2026What a Reporting Convention Hides: A Matched-Budget Audit of Quantum Natural Gradient with an Exactly Computed Metric7 Oct 2026
- 2026The Best Optimizer Depends on Batch Size6 Oct 2026
- 2026How Bregman Divergences Shape Shampoo6 Oct 2026
- 2026LionMuon: Alternating Spectral and Sign Descent for Efficient Training28 Sep 2026
- 2026Minibatch persistency, eight years later: what batch reuse costs in steps and joules, and what it saves in data12 Sep 2026
- 2026AdamX: Cosine similarity meets gradient descent10 Sep 2026
- 2026The Loss Does Not See the Basis, but Adam Does5 Aug 2026
- 2026Understanding Schedule-Free Methods in Nonconvex Optimization: Rate Guarantees and Escaping Saddles10 Jul 2026
- 2026Beyond a Single Explanation of the Adam--SGD Gap12 Jun 2026
- 2026FOAM: Frequency and Operator Error-Based Adaptive Damping Method for Reducing Staleness-Oriented Error for Shampoo1 Jun 2026
- 2026AMUSE: Anytime Muon with Stable Gradient Evaluation21 May 2026
12 newest of 50 All 50 (JSON)