# Transformers Don't In-Context Learn Least Squares Regression

arXiv: https://arxiv.org/abs/2507.09440 · HTML: https://mlsanity.com/paper/2507.09440/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 13 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [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)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [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)
- [Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve](https://mlsanity.com/paper/2309.13638/) (2023)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Pretraining task diversity and the emergence of non-Bayesian in-context learning for regression](https://mlsanity.com/paper/2306.15063/) (2023)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)
- [More Data Can Hurt for Linear Regression: Sample-wise Double Descent](https://mlsanity.com/paper/1912.07242/) (2019)
- [Bayesian scaling laws for in-context learning](https://mlsanity.com/paper/2410.16531/) (2024)

## Built on by (most cited first, 3 of 3)

- [Transformers Learn Robust In-Context Regression under Distributional Uncertainty](https://mlsanity.com/paper/2603.18564/) (2026)
- [The Illusion of Replacement: Rethinking Specialized Machine Learning Models in the Foundation Model Era](https://mlsanity.com/paper/2608.28980/) (2026)
- [Fisher information and the geometry of memorization in neural networks](https://mlsanity.com/paper/2610.16161/) (2026)

## Abstract (arXiv)

In-context learning (ICL) has emerged as a powerful capability of large pretrained transformers, enabling them to solve new tasks implicit in example input-output pairs without any gradient updates. Despite its practical success, the mechanisms underlying ICL remain largely mysterious. In this work we study synthetic linear regression to probe how transformers implement learning at inference time. Previous works have demonstrated that transformers match the performance of learning rules such as Ordinary Least Squares (OLS) regression or gradient descent and have suggested ICL is facilitated in transformers through the learned implementation of one of these techniques. In this work, we demonstrate through a suite of out-of-distribution generalization experiments that transformers trained for ICL fail to generalize after shifts in the prompt distribution, a behaviour that is inconsistent with the notion of transformers implementing algorithms such as OLS. Finally, we highlight the role of the pretraining corpus in shaping ICL behaviour through a spectral analysis of the learned representations in the residual stream. Inputs from the same distribution as the training data produce representations with a unique spectral signature: inputs from this distribution tend to have the same top two singular vectors. This spectral signature is not shared by out-of-distribution inputs, and a metric characterizing the presence of this signature is highly correlated with low loss.