# In-Context Function Learning in Large Language Models

arXiv: https://arxiv.org/abs/2602.11863 · HTML: https://mlsanity.com/paper/2602.11863/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 28 of 28)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (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)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [Larger language models do in-context learning differently](https://mlsanity.com/paper/2303.03846/) (2023)
- [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)
- [What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization](https://mlsanity.com/paper/2305.19420/) (2023)
- [A Theory of Emergent In-Context Learning as Implicit Structure Induction](https://mlsanity.com/paper/2303.07971/) (2023)
- [Understanding In-Context Learning in Transformers and LLMs by Learning to Learn Discrete Functions](https://mlsanity.com/paper/2310.03016/) (2023)
- [Meta-in-context learning in large language models](https://mlsanity.com/paper/2305.12907/) (2023)
- [From Words to Numbers: Your Large Language Model Is Secretly A Capable Regressor When Given In-Context Examples](https://mlsanity.com/paper/2404.07544/) (2024)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)
- [LLM Processes: Numerical Predictive Distributions Conditioned on Natural Language](https://mlsanity.com/paper/2405.12856/) (2024)
- [Measuring Inductive Biases of In-Context Learning with Underspecified Demonstrations](https://mlsanity.com/paper/2305.13299/) (2023)
- [Calibrating Transformers via Sparse Gaussian Processes](https://mlsanity.com/paper/2303.02444/) (2023)
- [Estimating the Hallucination Rate of Generative AI](https://mlsanity.com/paper/2406.07457/) (2024)
- [The Human Kernel](https://mlsanity.com/paper/1510.07389/) (2015)
- [Reinforcement Learning Fine-tuning of Language Models is Biased Towards More Extractable Features](https://mlsanity.com/paper/2311.04046/) (2023)

## Abstract (arXiv)

Large language models (LLMs) can learn from a few demonstrations provided at inference time. We study this in-context learning phenomenon through the lens of Gaussian Processes (GPs). We build controlled experiments where models observe sequences of multivariate scalar-valued function samples drawn from known GP priors. We evaluate prediction error in relation to the number of demonstrations and compare against two principled references: (i) an empirical GP-regression learner that gives a lower bound on achievable error, and (ii) the expected error of a 1-nearest-neighbor (1-NN) rule, which gives a data-driven upper bound. Across model sizes, we find that LLM learning curves are strongly influenced by the function-generating kernels and approach the GP lower bound as the number of demonstrations increases. We then study the inductive biases of these models using a likelihood-based analysis. We find that LLM predictions are most likely under less smooth GP kernels. Finally, we explore whether post-training can shift these inductive biases and improve sample-efficiency on functions sampled from GPs with smoother kernels. We find that both reinforcement learning and supervised fine-tuning can effectively shift inductive biases in the direction of the training data. Together, our framework quantifies the extent to which LLMs behave like GP learners and provides tools for steering their inductive biases for continuous function learning tasks.