Transformers Learn Low Sensitivity Functions: Investigations and Implications
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Abstract (arXiv)
Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of their inductive biases and how those biases differ from other neural network architectures remains elusive. In this work, we identify the sensitivity of the model to token-wise random perturbations in the input as a unified metric which explains the inductive bias of transformers across different data modalities and distinguishes them from other architectures. We show that transformers have lower sensitivity than MLPs, CNNs, ConvMixers and LSTMs, across both vision and language tasks. We also show that this low-sensitivity bias has important implications: i) lower sensitivity correlates with improved robustness; it can also be used as an efficient intervention to further improve the robustness of transformers; ii) it corresponds to flatter minima in the loss landscape; and iii) it can serve as a progress measure for grokking. We support these findings with theoretical results showing (weak) spectral bias of transformers in the NTK regime, and improved robustness due to the lower sensitivity. The code is available at https://github.com/estija/sensitivity.
Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 94 of its 118 references that are in the map. First posted on arXiv 11 Mar 2024.
Builds on
94 of 118 references.
References · 94
- 2017Attention Is All You Needcited by 59,932
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
- 2019RoBERTa: A Robustly Optimized BERT Pretraining Approachcited by 13,266
- 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
- 2016Densely Connected Convolutional Networkscited by 6,691
- 2017mixup: Beyond Empirical Risk Minimizationcited by 5,155
- 2022A ConvNet for the 2020scited by 3,545
- 2019Benchmarking Neural Network Robustness to Common Corruptions and Perturbationscited by 2,857
- 2022Locating and Editing Factual Associations in GPTcited by 2,609
- 2020Shortcut Learning in Deep Neural Networkscited by 1,928
- 2018ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustnesscited by 1,430
38 more
- 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,337
- 2018On the Spectral Bias of Neural Networkscited by 1,321
- 2017A Closer Look at Memorization in Deep Networkscited by 936
- 2023Progress measures for grokking via mechanistic interpretabilitycited by 822
- 2022Transformers learn in-context by gradient descentcited by 714
- 2022What Can Transformers Learn In-Context? A Case Study of Simple Function Classescited by 700
- 2023Towards Automated Circuit Discovery for Mechanistic Interpretabilitycited by 700
- 2021Do Vision Transformers See Like Convolutional Neural Networks?cited by 671
- 2022What learning algorithm is in-context learning? Investigations with linear modelscited by 671
- 2018Annotation Artifacts in Natural Language Inference Datacited by 656
- 2017The Implicit Bias of Gradient Descent on Separable Datacited by 649
- 2017Deep Neural Networks as Gaussian Processescited by 617
- 2022Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasetscited by 599
- 2017Exploring Generalization in Deep Learningcited by 595
- 2021Intriguing Properties of Vision Transformerscited by 446
- 2019Implicit Regularization in Deep Matrix Factorizationcited by 402
- 2022Last Layer Re-Training is Sufficient for Robustness to Spurious Correlationscited by 379
- 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 360
- 2020The Pitfalls of Simplicity Bias in Neural Networkscited by 349
- 2014In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learningcited by 339
- 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 314
- 2019Gradient Descent Maximizes the Margin of Homogeneous Neural Networkscited by 308
- 2019Revealing the Dark Secrets of BERTcited by 300
- 2023Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selectioncited by 291
- 2020Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Losscited by 267
- 2020Gradient Starvation: A Learning Proclivity in Neural Networkscited by 262
- 2021Understanding Robustness of Transformers for Image Classificationcited by 250
- 2019Fast AutoAugmentcited by 243
- 2021Vision Transformers are Robust Learnerscited by 208
- 2019SGD on Neural Networks Learns Functions of Increasing Complexitycited by 203
- 2022Patches Are All You Need?cited by 201
- 2023How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language modelcited by 199
- 2021Data Augmentation Can Improve Robustnesscited by 193
- 2018Sensitivity and Generalization in Neural Networks: an Empirical Studycited by 187
- 2022Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limitcited by 184
- 2018Deep learning generalizes because the parameter-function map is biased towards simple functionscited by 180
- 2019On the Inductive Bias of Neural Tangent Kernelscited by 177
- 2019Towards Understanding the Spectral Bias of Deep Learningcited by 173
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