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Adafactor

733 papers tagged archive 2025-07-28

Introduced by Noam Shazeer et al. in Adafactor: Adaptive Learning Rates with Sublinear Memory Cost

archive 2025-07-28 Description, source and code snippet are the archive's method entry.

Adafactor is a stochastic optimization method based on Adam that reduces memory usage while retaining the empirical benefits of adaptivity. This is achieved through maintaining a factored representation of the squared gradient accumulator across training steps. Specifically, by tracking moving averages of the row and column sums of the squared gradients for matrix-valued variables, we are able to reconstruct a low-rank approximation of the exponentially smoothed accumulator at each training step that is optimal with respect to the generalized Kullback-Leibler divergence. For an n ×m matrix, this reduces the memory requirements from O(n m) to O(n + m).

Instead of defining the optimization algorithm in terms of absolute step sizes {αₜ}ₜ₌₁ᵀ, the authors define the optimization algorithm in terms of relative step sizes {ρₜ}ₜ₌₁ᵀ, which get multiplied by the scale of the parameters. The scale of a parameter vector or matrix is defined as the root-mean-square of its components, lower-bounded by a small constant ϵ₂. The reason for this lower bound is to allow zero-initialized parameters to escape 0.

Proposed hyperparameters are: ϵ₁ = 10⁻³⁰, ϵ₂ = 10⁻³, d=1, pₜ = min(10⁻², 1/(√(t))), β̂_(2ₜ) = 1 - t^(-0.8).

PaperSourceSee Code · DeadAt0m/adafactor-pytorch

Papers archive 2025-07-28

30 shown of 733, newest first. Repository counts are the archive's code-links table. A Syntology line states what Syntology ran from that paper's harvested code; it is per sample and not a correctness claim.

Tasks archive 2025-07-28

20 shown of 492 tasks the archive attaches to papers tagged with this method, by distinct papers. A task without a page in the catalog is plain text.

TaskPapers
Language Modelling128
Language Modeling100
Question Answering86
Decoder79
Text Generation65
Sentence58
Translation47
Machine Translation41
Retrieval40
Transfer Learning40
Natural Language Understanding29
Abstractive Text Summarization23
Semantic Parsing23
Sentiment Analysis22
Natural Language Inference21
Code Generation20
Data Augmentation20
Text Summarization19
Diversity18
Knowledge Graphs17

Usage over time archive 2025-07-28

Papers per year tagged with Adafactor: 2018 to 2025, peak 202 202 0 2018: 1 paper 2018 2019: 2 papers 2019 2020: 37 papers 2020 2021: 112 papers 2021 2022: 168 papers 2022 2023: 202 papers 2023 2024: 158 papers 2024 2025: 53 papers 2025
Papers per year the archive tags with this method, by the paper's archive date (733 dated). Bars are counts, not a trend claim.

Components: the archive holds no method-to-method composition, so PwC's Components table cannot be rebuilt; the Papers list carries no Results column for the same reason (the archive does not join its leaderboard rows to method tags).

Categories archive 2025-07-28

Large Batch OptimizationStochastic Optimization

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