# Capturing In-Context Learning Dynamics with Task Operators

arXiv: https://arxiv.org/abs/2610.01054 · HTML: https://mlsanity.com/paper/2610.01054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [In-context Vectors: Making In Context Learning More Effective and Controllable Through Latent Space Steering](https://mlsanity.com/paper/2311.06668/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [Representation Surgery: Theory and Practice of Affine Steering](https://mlsanity.com/paper/2402.09631/) (2024)
- [Multimodal Task Vectors Enable Many-Shot Multimodal In-Context Learning](https://mlsanity.com/paper/2406.15334/) (2024)
- [Steering Large Language Models using Conceptors: Improving Addition-Based Activation Engineering](https://mlsanity.com/paper/2410.16314/) (2024)
- [Activation Scaling for Steering and Interpreting Language Models](https://mlsanity.com/paper/2410.04962/) (2024)
- [Refusal in LLMs is an Affine Function](https://mlsanity.com/paper/2411.09003/) (2024)
- [In-Context Learning State Vector with Inner and Momentum Optimization](https://mlsanity.com/paper/2404.11225/) (2024)
- [Learning Task Representations from In-Context Learning](https://mlsanity.com/paper/2502.05390/) (2025)
- [Emergence and Effectiveness of Task Vectors in In-Context Learning: An Encoder Decoder Perspective](https://mlsanity.com/paper/2412.12276/) (2024)
- [Understanding Task Vectors in In-Context Learning: Emergence, Functionality, and Limitations](https://mlsanity.com/paper/2506.09048/) (2025)
- [Adaptive Task Vectors for Large Language Models](https://mlsanity.com/paper/2506.03426/) (2025)
- [Beyond Demonstrations: Dynamic Vector Construction from Latent Representations](https://mlsanity.com/paper/2505.20318/) (2025)

## Abstract (arXiv)

In-context learning (ICL) enables language models to perform new tasks from demonstrations without weight updates. However, every ICL inference requires processing the full set of examples, resulting in inefficient deployments, and how ICL works mechanistically is not fully understood. Prior work compresses ICL into fixed activation vectors extracted from specific layers or positions, but these input-independent interventions fail on complex tasks where the output depends on fine-grained interactions with the input. By analyzing the ICL forward pass, we show that each attention head's output is an affine transformation of its context-masked counterpart, and that the parameters of this transformation are empirically stable across samples for a given task. Building on this, we introduce Task Operator (TO), which replays this transformation as an analytically derived update to the attention output projection. Across lexical, algorithmic, and reasoning tasks, TO achieves the best overall performance among prior methods and substantially narrows the gap between zero-shot inference and ICL. We further show that the extracted knowledge concentrates in a task-specific sparse circuit across layers and positions, and that averaging operators from disjoint demonstration batches enables effective many-shot scaling without expanding the context window. Our code is available at https://github.com/gzxiong/task_operator.