# Sequence Length Independent Norm-Based Generalization Bounds for Transformers

arXiv: https://arxiv.org/abs/2310.13088 · HTML: https://mlsanity.com/paper/2310.13088/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Learning Deep Transformer Models for Machine Translation](https://mlsanity.com/paper/1906.01787/) (2019)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [Understanding and Improving Layer Normalization](https://mlsanity.com/paper/1911.07013/) (2019)
- [Inductive Biases and Variable Creation in Self-Attention Mechanisms](https://mlsanity.com/paper/2110.10090/) (2021)
- [Statistically Meaningful Approximation: a Case Study on Approximating Turing Machines with Transformers](https://mlsanity.com/paper/2107.13163/) (2021)
- [Mitigating Memorization of Noisy Labels by Clipping the Model Prediction](https://mlsanity.com/paper/2212.04055/) (2022)
- [What can a Single Attention Layer Learn? A Study Through the Random Features Lens](https://mlsanity.com/paper/2307.11353/) (2023)
- [Generalization Bounds for Convolutional Neural Networks](https://mlsanity.com/paper/1910.01487/) (2019)
- [On Rademacher Complexity-based Generalization Bounds for Deep Learning](https://mlsanity.com/paper/2208.04284/) (2022)
- [An Analysis of Attention via the Lens of Exchangeability and Latent Variable Models](https://mlsanity.com/paper/2212.14852/) (2022)

## Built on by (most cited first, 29 of 29)

- [Provably learning a multi-head attention layer](https://mlsanity.com/paper/2402.04084/) (2024)
- [Superiority of Multi-Head Attention in In-Context Linear Regression](https://mlsanity.com/paper/2401.17426/) (2024)
- [LENSLLM: Unveiling Fine-Tuning Dynamics for LLM Selection](https://mlsanity.com/paper/2505.03793/) (2025)
- [On the Optimal Memorization Capacity of Transformers](https://mlsanity.com/paper/2409.17677/) (2024)
- [Towards Understanding the Word Sensitivity of Attention Layers: A Study via Random Features](https://mlsanity.com/paper/2402.02969/) (2024)
- [Learning Linear Attention in Polynomial Time](https://mlsanity.com/paper/2410.10101/) (2024)
- [Generalization Error Analysis for Selective State-Space Models Through the Lens of Attention](https://mlsanity.com/paper/2502.01473/) (2025)
- [Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective](https://mlsanity.com/paper/2504.13558/) (2025)
- [On Generalisation Error Bounds for Transformers](https://mlsanity.com/paper/2410.11500/) (2024)
- [When Do Transformers Outperform Feedforward and Recurrent Networks? A Statistical Perspective](https://mlsanity.com/paper/2503.11272/) (2025)
- [Sharper Generalization Bounds for Transformer](https://mlsanity.com/paper/2603.21541/) (2026)
- [Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity](https://mlsanity.com/paper/2605.07097/) (2026)
- [Length independent generalization bounds for deep SSM architectures via Rademacher contraction and stability constraints](https://mlsanity.com/paper/2405.20278/) (2024)
- [Impact of Positional Encoding: Clean and Adversarial Rademacher Complexity for Transformers under In-Context Regression](https://mlsanity.com/paper/2512.09275/) (2025)
- [Generalization Bounds for Transformer Channel Decoders](https://mlsanity.com/paper/2601.06969/) (2026)
- [Tight Sample Complexity of Transformers](https://mlsanity.com/paper/2606.09731/) (2026)
- [A Theory for Conditional Generative Modeling on Multiple Data Sources](https://mlsanity.com/paper/2502.14583/) (2025)
- [From Small to Large: Generalization Bounds for Transformers on Variable-Size Inputs](https://mlsanity.com/paper/2512.12805/) (2025)
- [SPA-Cache: Singular Proxies for Adaptive Caching in Diffusion Language Models](https://mlsanity.com/paper/2602.02544/) (2026)
- [Lossless Anti-Distillation Sampling](https://mlsanity.com/paper/2605.18829/) (2026)
- [Generalizability of Neural Networks Minimizing Empirical Risk Based on Expressive Ability](https://mlsanity.com/paper/2503.04111/) (2025)
- [Forecasting Geopolitical Events with a Sparse Temporal Fusion Transformer and Gaussian Process Hybrid: A Case Study in Middle Eastern and U.S. Conflict Dynamics](https://mlsanity.com/paper/2506.20935/) (2025)
- [Effective Sample Size and Generalization Bounds for Temporal Networks](https://mlsanity.com/paper/2508.06066/) (2025)
- [Dynamical Implicit Neural Representations](https://mlsanity.com/paper/2511.21787/) (2025)
- [ARMOR: Adaptive Retriever Optimization for Low-Resource Telecom Question Answering](https://mlsanity.com/paper/2606.29706/) (2026)
- [Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation](https://mlsanity.com/paper/2606.31184/) (2026)
- [Generalization Bounds on Optimal Control for Transformer Training and Wasserstein Distributional Robustness](https://mlsanity.com/paper/2607.27975/) (2026)
- [VC Dimension and Expressivity of Real-Valued Transformers](https://mlsanity.com/paper/2609.31999/) (2026)
- [On the Trade-off Between Information Loss and Generalization in Sparse Attention](https://mlsanity.com/paper/2610.04424/) (2026)

## Abstract (arXiv)

This paper provides norm-based generalization bounds for the Transformer architecture that do not depend on the input sequence length. We employ a covering number based approach to prove our bounds. We use three novel covering number bounds for the function class of bounded linear transformations to upper bound the Rademacher complexity of the Transformer. Furthermore, we show this generalization bound applies to the common Transformer training technique of masking and then predicting the masked word. We also run a simulated study on a sparse majority data set that empirically validates our theoretical findings.