Methods › General › Regularization › Weight Decay

Weight Decay

introduced 1943 10,713 papers tagged archive 2025-07-28

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

Weight Decay, or L₂ Regularization, is a regularization technique applied to the weights of a neural network. We minimize a loss function compromising both the primary loss function and a penalty on the L₂ Norm of the weights:

L_(new)(w) = L_(original)(w) + λwᵀw

where λ is a value determining the strength of the penalty (encouraging smaller weights).

Weight decay can be incorporated directly into the weight update rule, rather than just implicitly by defining it through to objective function. Often weight decay refers to the implementation where we specify it directly in the weight update rule (whereas L2 regularization is usually the implementation which is specified in the objective function).

Image Source: Deep Learning, Goodfellow et al

Papers archive 2025-07-28

30 shown of 10,713, 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 1,523 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 Modelling1,799
Language Modeling1,406
Retrieval1,368
RAG1,244
Retrieval-augmented Generation1,068
Question Answering996
Sentence866
Large Language Model480
Sentiment Analysis458
Text Classification448
Text Generation417
text-classification397
Transfer Learning369
Classification300
Information Retrieval291
Natural Language Understanding285
Word Embeddings274
Named Entity Recognition264
Articles255
named-entity-recognition254

Usage over time archive 2025-07-28

Papers per year tagged with Weight Decay: 2012 to 2025, peak 2,658 2,658 0 2012: 1 paper 2012 2013: 3 papers 2013 2014: 5 papers 2014 2015: 6 papers 2015 2016: 21 papers 2016 2017: 21 papers 2017 2018: 61 papers 2018 2019: 678 papers 2019 2020: 1425 papers 2020 2021: 1580 papers 2021 2022: 1211 papers 2022 2023: 1986 papers 2023 2024: 2658 papers 2024 2025: 1057 papers 2025
Papers per year the archive tags with this method, by the paper's archive date (10,713 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

Regularization

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections