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=== Adaptive ===
'''Adaptive layer norm''' ('''adaLN''') computes the <math>\gamma, \beta</math> in a LayerNorm not from the layer activation itself, but from other data. It was first proposed for CNN,<ref>{{Cite journal |last1=Perez |first1=Ethan |last2=Strub |first2=Florian |last3=De Vries |first3=Harm |last4=Dumoulin |first4=Vincent |last5=Courville |first5=Aaron |date=2018-04-29 |title=FiLM: Visual Reasoning with a General Conditioning Layer |url=https://ojs.aaai.org/index.php/AAAI/article/view/11671 |journal=Proceedings of the AAAI Conference on Artificial Intelligence |volume=32 |issue=1 |doi=10.1609/aaai.v32i1.11671 |issn=2374-3468|arxiv=1709.07871 }}</ref> and has been used effectively in [[diffusion Transformer]] (DiT).<ref>{{Cite journal |last1=Peebles |first1=William |last2=Xie |first2=Saining |date=2023 |title=Scalable Diffusion Models with Transformers |url=https://openaccess.thecvf.com/content/ICCV2023/html/Peebles_Scalable_Diffusion_Models_with_Transformers_ICCV_2023_paper.html |language=en |pages=4195–4205 |arxiv=2212.09748}}</ref> For example, in DiT, the conditioning information (such as text encoding vector) is processed by an MLP into <math>\gamma, \beta</math>, which is then applied in the LayerNorm module in a Transformer.
== Weight normalization ==
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The original 2017 Transformer used the "post-LN" configuration for its LayerNorms. It was difficult to train and required careful hyperparameter tuning and a "warm-up" in learning rate, where it starts small and gradually increases. The pre-LN convention, proposed several times in 2018,<ref>{{Citation |last1=Wang |first1=Qiang |title=Learning Deep Transformer Models for Machine Translation |date=2019-06-04 |url=https://arxiv.org/abs/1906.01787 |access-date=2024-10-18 |arxiv=1906.01787 |last2=Li |first2=Bei |last3=Xiao |first3=Tong |last4=Zhu |first4=Jingbo |last5=Li |first5=Changliang |last6=Wong |first6=Derek F. |last7=Chao |first7=Lidia S.}}</ref> was found to be easier to train, requiring no warm-up, leading to faster convergence.<ref name="auto1">{{cite arXiv |eprint=2002.04745 |class=cs.LG |first1=Ruibin |last1=Xiong |first2=Yunchang |last2=Yang |title=On Layer Normalization in the Transformer Architecture |date=2020-06-29 |last3=He |first3=Di |last4=Zheng |first4=Kai |last5=Zheng |first5=Shuxin |last6=Xing |first6=Chen |last7=Zhang |first7=Huishuai |last8=Lan |first8=Yanyan |last9=Wang |first9=Liwei |last10=Liu |first10=Tie-Yan}}</ref>
'''FixNorm'''<ref>{{Citation |last1=Nguyen |first1=Toan Q. |title=Improving Lexical Choice in Neural Machine Translation |date=2018-04-17 |url=https://arxiv.org/abs/1710.01329 |access-date=2024-10-18 |arxiv=1710.01329 |last2=Chiang |first2=David}}</ref> and '''ScaleNorm<ref>{{Cite journal |last1=Nguyen |first1=Toan Q. |last2=Salazar |first2=Julian |date=2019-11-02 |title=Transformers without Tears: Improving the Normalization of Self-Attention |doi=10.5281/zenodo.3525484|arxiv=1910.05895 }}</ref>''' both normalize activation vectors in a Transformer. The FixNorm method divides the ''output'' vectors from a Transformer by their L2 norms, then multiply by a learned parameter <math>g</math>. The ScaleNorm replaces all LayerNorms inside a Transformer by division with L2 norm, then multiplying by a learned parameter <math>g'</math> (shared by all ScaleNorm modules of a Transformer). '''Query-Key normalization''' ('''QKNorm''')<ref>{{Cite journal |last1=Henry |first1=Alex |last2=Dachapally |first2=Prudhvi Raj |last3=Pawar |first3=Shubham Shantaram |last4=Chen |first4=Yuxuan |date=November 2020 |editor-last=Cohn |editor-first=Trevor |editor2-last=He |editor2-first=Yulan |editor3-last=Liu |editor3-first=Yang |title=Query-Key Normalization for Transformers |url=https://aclanthology.org/2020.findings-emnlp.379/ |journal=Findings of the Association for Computational Linguistics: EMNLP 2020 |___location=Online |publisher=Association for Computational Linguistics |pages=4246–4253 |doi=10.18653/v1/2020.findings-emnlp.379|arxiv=2010.04245 }}</ref> normalizes query and key vectors to have unit L2 norm.
In '''nGPT''', many vectors are normalized to have unit L2 norm:<ref>{{Citation |last1=Loshchilov |first1=Ilya |title=nGPT: Normalized Transformer with Representation Learning on the Hypersphere |date=2024-10-01 |url=https://arxiv.org/abs/2410.01131 |access-date=2024-10-18 |arxiv=2410.01131 |last2=Hsieh |first2=Cheng-Ping |last3=Sun |first3=Simeng |last4=Ginsburg |first4=Boris}}</ref> hidden state vectors, input and output embedding vectors, weight matrix columns, query and key vectors.
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