mlsanityData to 7 Oct 2026

Of Non-Linearity and Commutativity in BERT

arXiv 2101.04547 ↗First posted 12 Jan 2021cs.CL cs.AIcited by 16

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Abstract (arXiv)

In this work we provide new insights into the transformer architecture, and in particular, its best-known variant, BERT. First, we propose a method to measure the degree of non-linearity of different elements of transformers. Next, we focus our investigation on the feed-forward networks (FFN) inside transformers, which contain 2/3 of the model parameters and have so far not received much attention. We find that FFNs are an inefficient yet important architectural element and that they cannot simply be replaced by attention blocks without a degradation in performance. Moreover, we study the interactions between layers in BERT and show that, while the layers exhibit some hierarchical structure, they extract features in a fuzzy manner. Our results suggest that BERT has an inductive bias towards layer commutativity, which we find is mainly due to the skip connections. This provides a justification for the strong performance of recurrent and weight-shared transformer models.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 33 of its 41 references that are in the map. First posted on arXiv 12 Jan 2021.

Builds on

33 of 41 references.

References · 33

  1. 2017Attention Is All You Needcited by 59,932
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  3. 2020Language Models are Few-Shot Learnerscited by 32,199
  4. 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,491
  5. 2019RoBERTa: A Robustly Optimized BERT Pretraining Approachcited by 13,266
  6. 2018GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understandingcited by 4,854
  7. 2019DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lightercited by 4,243
  8. 2016Gaussian Error Linear Units (GELUs)cited by 3,431
  9. 2019XLNet: Generalized Autoregressive Pretraining for Language Understandingcited by 2,801
  10. 2019ALBERT: A Lite BERT for Self-supervised Learning of Language Representationscited by 2,772
  11. 2020Reformer: The Efficient Transformercited by 1,658
  12. 2019BERT Rediscovers the Classical NLP Pipelinecited by 1,046
21 more
  1. 2015Aligning Books and Movies: Towards Story-like Visual Explanations by Watching Movies and Reading Bookscited by 1,041
  2. 2019What Does BERT Look At? An Analysis of BERT's Attentioncited by 994
  3. 2019Attention is not Explanationcited by 916
  4. 2019Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Prunedcited by 844
  5. 2020A Primer in BERTology: What we know about how BERT workscited by 807
  6. 2019Are Sixteen Heads Really Better than One?cited by 803
  7. 2019How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddingscited by 770
  8. 2018Universal Transformerscited by 613
  9. 2019Deep Equilibrium Modelscited by 603
  10. 2019What do you learn from context? Probing for sentence structure in contextualized word representationscited by 436
  11. 2019Revealing the Dark Secrets of BERTcited by 300
  12. 2019Cross-Lingual Ability of Multilingual BERT: An Empirical Studycited by 182
  13. 2020Lite Transformer with Long-Short Range Attentioncited by 127
  14. 2019Open Sesame: Getting Inside BERT's Linguistic Knowledgecited by 119
  15. 2019On Identifiability in Transformerscited by 115
  16. 2019Learning to Deceive with Attention-Based Explanationscited by 111
  17. 2020Analyzing Individual Neurons in Pre-trained Language Modelscited by 97
  18. 2019Do Attention Heads in BERT Track Syntactic Dependencies?cited by 87
  19. 2020Similarity Analysis of Contextual Word Representation Modelscited by 54
  20. 2019Improving Transformer Models by Reordering their Sublayerscited by 52
  21. 2020Telling BERT's full story: from Local Attention to Global Aggregationcited by 15

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Citing papers per year: 2021: 1; 2022: 3; 2023: 7; 2024: 2; 2025: 3.

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  1. 2022Locating and Editing Factual Associations in GPTcited by 2,609
  2. 2023Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Modelscited by 237
  3. 2022A Review on Language Models as Knowledge Basescited by 156
  4. 2023The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reductioncited by 120
  5. 2023Jump to Conclusions: Short-Cutting Transformers With Linear Transformationscited by 89
  6. 2023Neurons in Large Language Models: Dead, N-gram, Positionalcited by 88
  7. 2025To Steer or Not to Steer? Mechanistic Error Reduction with Abstention for Language Modelscited by 26
  8. 2022How to Dissect a Muppet: The Structure of Transformer Embedding Spacescited by 19
  9. 2024A Survey on Symbolic Knowledge Distillation of Large Language Modelscited by 9
  10. 2023Interpretability in Activation Space Analysis of Transformers: A Focused Surveycited by 3
  11. 2023Why bother with geometry? On the relevance of linear decompositions of Transformer embeddingscited by 2
  12. 2025Decoding Vision Transformers: the Diffusion Steering Lenscited by 1
4 more
  1. 2025Compress to Impress: Efficient LLM Adaptation Using a Single Gradient Step on 100 Samplescited by 1
  2. 2021On Isotropy Calibration of Transformerscited by 0
  3. 2023Beyond Universal Transformer: block reusing with adaptor in Transformer for automatic speech recognitioncited by 0
  4. 2024Beyond Individual Facts: Investigating Categorical Knowledge Locality of Taxonomy and Meronomy Concepts in GPT Modelscited by 0