mlsanityData to 14 Oct 2026

Low-Rank Softmax Can Have Unargmaxable Classes in Theory but Rarely in Practice

arXiv 2203.06462 ↗First posted 12 Mar 2022cs.LG cs.CLcited by 15

Not on the map. Why?

Abstract (arXiv)

Classifiers in natural language processing (NLP) often have a large number of output classes. For example, neural language models (LMs) and machine translation (MT) models both predict tokens from a vocabulary of thousands. The Softmax output layer of these models typically receives as input a dense feature representation, which has much lower dimensionality than the output. In theory, the result is some words may be impossible to be predicted via argmax, irrespective of input features, and empirically, there is evidence this happens in small language models. In this paper we ask whether it can happen in practical large language models and translation models. To do so, we develop algorithms to detect such unargmaxable tokens in public models. We find that 13 out of 150 models do indeed have such tokens; however, they are very infrequent and unlikely to impact model quality. We release our code so that others can inspect their models.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 32 of its 66 references that are in the map. First posted on arXiv 12 Mar 2022.

Builds on

32 of 66 references.

References · 32

  1. 2017Attention Is All You Needcited by 60,361
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  4. 2019RoBERTa: A Robustly Optimized BERT Pretraining Approachcited by 13,372
  5. 2019Unsupervised Cross-lingual Representation Learning at Scalecited by 3,935
  6. 2015Neural Machine Translation of Rare Words with Subword Unitscited by 2,918
  7. 2021Convex optimizationcited by 2,515
  8. 2021Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processingcited by 2,234
  9. 2020Multilingual Denoising Pre-training for Neural Machine Translationcited by 1,035
  10. 2019Decoupling Representation and Classifier for Long-Tailed Recognitioncited by 809
  11. 2016Sequence-Level Knowledge Distillationcited by 801
  12. 2018Poison Frogs! Targeted Clean-Label Poisoning Attacks on Neural Networkscited by 519
20 more
  1. 2016On the Expressive Power of Deep Neural Networkscited by 306
  2. 2017Regularizing and Optimizing LSTM Language Modelscited by 205
  3. 2018Marian: Fast Neural Machine Translation in C++cited by 203
  4. 2020Dataset Security for Machine Learning: Data Poisoning, Backdoor Attacks, and Defensescited by 180
  5. 2019Facebook FAIR's WMT19 News Translation Task Submissioncited by 179
  6. 2017Breaking the Softmax Bottleneck: A High-Rank RNN Language Modelcited by 152
  7. 2019Transferable Clean-Label Poisoning Attacks on Deep Neural Netscited by 131
  8. 2020The Tatoeba Translation Challenge -- Realistic Data Sets for Low Resource and Multilingual MTcited by 128
  9. 2020Low-Rank Bottleneck in Multi-head Attention Modelscited by 89
  10. 2020O(n) Connections are Expressive Enough: Universal Approximability of Sparse Transformerscited by 83
  11. 2020Bullseye Polytope: A Scalable Clean-Label Poisoning Attack with Improved Transferabilitycited by 66
  12. 2018Model-Reuse Attacks on Deep Learning Systemscited by 49
  13. 2020Stolen Probability: A Structural Weakness of Neural Language Modelscited by 22
  14. 2018Sigsoftmax: Reanalysis of the Softmax Bottleneckcited by 20
  15. 2020On Long-Tailed Phenomena in Neural Machine Translationcited by 20
  16. 2017Improving Lexical Choice in Neural Machine Translationcited by 17
  17. 2017The University of Edinburgh's Neural MT Systems for WMT17cited by 16
  18. 2015Strategies for Training Large Vocabulary Neural Language Modelscited by 14
  19. 2019Breaking the Softmax Bottleneck via Learnable Monotonic Pointwise Non-linearitiescited by 14
  20. 2021Data-Driven Low-Rank Neural Network Compressioncited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 1; 2025: 3; 2026: 5.

15 papers.

Sort:

By area:

  1. 2024Logits of API-Protected LLMs Leak Proprietary Informationcited by 40
  2. 2025The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?cited by 37
  3. 2023On the Expressivity Role of LayerNorm in Transformers' Attentioncited by 33
  4. 2023Closing the Curious Case of Neural Text Degenerationcited by 32
  5. 2023Why do Nearest Neighbor Language Models Work?cited by 29
  6. 2023Generative Models as a Complex Systems Science: How can we make sense of large language model behavior?cited by 19
  7. 2023Taming the Sigmoid Bottleneck: Provably Argmaxable Sparse Multi-Label Classificationcited by 11
  8. 2025Better Language Model Inversion by Compactly Representing Next-Token Distributionscited by 9
  9. 2026Lost in Backpropagation: The LM Head is a Gradient Bottleneckcited by 9
  10. 2023The Unreasonable Effectiveness of Random Target Embeddings for Continuous-Output Neural Machine Translationcited by 2
  11. 2025On the Theoretical Limitations of Embedding-based Link Predictioncited by 1
  12. 2026What Cosine Similarity of Label Representations Can and Cannot Tell uscited by 1
3 more
  1. 2026MIXAR: Scaling Autoregressive Pixel-based Language Models to Multiple Languages and Scriptscited by 1
  2. 2026How Much Rank Does LoRA Need? Rank-Error Bounds for Transformer Attentioncited by 0
  3. 2026Copy-Paste Language Modelscited by 0