# Trained Transformer Classifiers Generalize and Exhibit Benign Overfitting In-Context

arXiv: https://arxiv.org/abs/2410.01774 · HTML: https://mlsanity.com/paper/2410.01774/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 34 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [Gradient Descent Maximizes the Margin of Homogeneous Neural Networks](https://mlsanity.com/paper/1906.05890/) (2019)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Directional convergence and alignment in deep learning](https://mlsanity.com/paper/2006.06657/) (2020)
- [One Step of Gradient Descent is Provably the Optimal In-Context Learner with One Layer of Linear Self-Attention](https://mlsanity.com/paper/2307.03576/) (2023)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [The Evolution of Statistical Induction Heads: In-Context Learning Markov Chains](https://mlsanity.com/paper/2402.11004/) (2024)
- [How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?](https://mlsanity.com/paper/2310.08391/) (2023)
- [Does data interpolation contradict statistical optimality?](https://mlsanity.com/paper/1806.09471/) (2018)
- [On the Implicit Bias in Deep-Learning Algorithms](https://mlsanity.com/paper/2208.12591/) (2022)
- [Finite-sample Analysis of Interpolating Linear Classifiers in the Overparameterized Regime](https://mlsanity.com/paper/2004.12019/) (2020)
- [Benign Overfitting without Linearity: Neural Network Classifiers Trained by Gradient Descent for Noisy Linear Data](https://mlsanity.com/paper/2202.05928/) (2022)
- [Max-Margin Token Selection in Attention Mechanism](https://mlsanity.com/paper/2306.13596/) (2023)
- [Implicit Bias in Leaky ReLU Networks Trained on High-Dimensional Data](https://mlsanity.com/paper/2210.07082/) (2022)
- [Transformers are Minimax Optimal Nonparametric In-Context Learners](https://mlsanity.com/paper/2408.12186/) (2024)
- [Implicit Bias and Fast Convergence Rates for Self-attention](https://mlsanity.com/paper/2402.05738/) (2024)
- [Benign Overfitting in Linear Classifiers and Leaky ReLU Networks from KKT Conditions for Margin Maximization](https://mlsanity.com/paper/2303.01462/) (2023)
- [The Double-Edged Sword of Implicit Bias: Generalization vs. Robustness in ReLU Networks](https://mlsanity.com/paper/2303.01456/) (2023)
- [On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Bias](https://mlsanity.com/paper/2205.09072/) (2022)
- [Implicit Optimization Bias of Next-Token Prediction in Linear Models](https://mlsanity.com/paper/2402.18551/) (2024)

## Built on by (most cited first, 15 of 15)

- [Training Dynamics of In-Context Learning in Linear Attention](https://mlsanity.com/paper/2501.16265/) (2025)
- [The broader spectrum of in-context learning](https://mlsanity.com/paper/2412.03782/) (2024)
- [On the Training Convergence of Transformers for In-Context Classification of Gaussian Mixtures](https://mlsanity.com/paper/2410.11778/) (2024)
- [Short-length Adversarial Training Helps LLMs Defend Long-length Jailbreak Attacks: Theoretical and Empirical Evidence](https://mlsanity.com/paper/2502.04204/) (2025)
- [On the Robustness of Transformers against Context Hijacking for Linear Classification](https://mlsanity.com/paper/2502.15609/) (2025)
- [Adversarially Pretrained Transformers May Be Universally Robust In-Context Learners](https://mlsanity.com/paper/2505.14042/) (2025)
- [Understanding Generalization in Transformers: Error Bounds and Training Dynamics Under Benign and Harmful Overfitting](https://mlsanity.com/paper/2502.12508/) (2025)
- [Stability of In-Context Learning: A Spectral Coverage Perspective](https://mlsanity.com/paper/2509.20677/) (2025)
- [Learning Linear Regression with Low-Rank Tasks in-Context](https://mlsanity.com/paper/2510.04548/) (2025)
- [Transformers are almost optimal metalearners for linear classification](https://mlsanity.com/paper/2510.19797/) (2025)
- [Understanding and Improving Continuous Adversarial Training for LLMs via In-context Learning Theory](https://mlsanity.com/paper/2604.12817/) (2026)
- [Benign Overfitting in Adversarial Training for Vision Transformers](https://mlsanity.com/paper/2604.19724/) (2026)
- [When Does ℓ2-Boosting Overfit Benignly? High-Dimensional Risk Asymptotics and the ℓ1 Implicit Bias](https://mlsanity.com/paper/2605.06314/) (2026)
- [Data Distribution as a Lever for Guiding Optimizers Toward Superior Generalization in LLMs](https://mlsanity.com/paper/2602.00576/) (2026)
- [Theory on Attention Dynamics for Out-of-Distribution In-Context Learning](https://mlsanity.com/paper/2609.36448/) (2026)

## Abstract (arXiv)

Transformers have the capacity to act as supervised learning algorithms: by properly encoding a set of labeled training ("in-context") examples and an unlabeled test example into an input sequence of vectors of the same dimension, the forward pass of the transformer can produce predictions for that unlabeled test example. A line of recent work has shown that when linear transformers are pre-trained on random instances for linear regression tasks, these trained transformers make predictions using an algorithm similar to that of ordinary least squares. In this work, we investigate the behavior of linear transformers trained on random linear classification tasks. Via an analysis of the implicit regularization of gradient descent, we characterize how many pre-training tasks and in-context examples are needed for the trained transformer to generalize well at test-time. We further show that in some settings, these trained transformers can exhibit "benign overfitting in-context": when in-context examples are corrupted by label flipping noise, the transformer memorizes all of its in-context examples (including those with noisy labels) yet still generalizes near-optimally for clean test examples.