# In-context classification: Calibration and noise in linear attention with softmax readout

arXiv: https://arxiv.org/abs/2610.17061 · HTML: https://mlsanity.com/paper/2610.17061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 29 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 23 of 23)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Generalisation error in learning with random features and the hidden manifold model](https://mlsanity.com/paper/2002.09339/) (2020)
- [What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization](https://mlsanity.com/paper/2305.19420/) (2023)
- [Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models](https://mlsanity.com/paper/1708.03395/) (2017)
- [Linear attention is (maybe) all you need (to understand transformer optimization)](https://mlsanity.com/paper/2310.01082/) (2023)
- [How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?](https://mlsanity.com/paper/2310.08391/) (2023)
- [A modern maximum-likelihood theory for high-dimensional logistic regression](https://mlsanity.com/paper/1803.06964/) (2018)
- [Asymptotic theory of in-context learning by linear attention](https://mlsanity.com/paper/2405.11751/) (2024)
- [The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression](https://mlsanity.com/paper/1804.09753/) (2018)
- [Pretrained transformer efficiently learns low-dimensional target functions in-context](https://mlsanity.com/paper/2411.02544/) (2024)
- [Are Gaussian data all you need? Extents and limits of universality in high-dimensional generalized linear estimation](https://mlsanity.com/paper/2302.08923/) (2023)
- [Theory of Scaling Laws for In-Context Regression: Depth, Width, Context and Time](https://mlsanity.com/paper/2510.01098/) (2025)
- [Transformers Learn Low Sensitivity Functions: Investigations and Implications](https://mlsanity.com/paper/2403.06925/) (2024)
- [Pretrain-Test Task Alignment Governs Generalization in In-Context Learning](https://mlsanity.com/paper/2509.26551/) (2025)
- [Transformers Efficiently Perform In-Context Logistic Regression via Normalized Gradient Descent](https://mlsanity.com/paper/2605.06609/) (2026)
- [Sequential Correlations Change In-Context Learning: Effective Context Length and Architectural Mismatch](https://mlsanity.com/paper/2607.03660/) (2026)

## Abstract (arXiv)

We study in-context binary classification in a simple attention model trained to minimise a logistic loss. Each prompt has a latent logistic teacher, and the learner must infer its direction from Bernoulli-labeled context examples. We derive an asymptotic prediction for the test logit in a high-dimensional regime with context length proportional to token dimension, and total training prompts proportional to dimension squared. Our formula cleanly separates calibration, test-time context noise, and non-isotropic parameter-estimation noise as interpretable effects on in-context performance. Our analysis also identifies the ridgeless separability regime and addresses the effects of context length, pretraining-set size, regularisation, and sampling temperature on in-context classification performance. The theory's predictions closely agree with finite-dimensional simulations and fully trained linear-attention models, while experiments with standard softmax attention show qualitatively related behaviour beyond the regime assumed by our analysis.