Provable In-Context Learning of Nonlinear Regression with Transformers

• URL: http://arxiv.org/abs/2507.20443v1
• Date: Mon, 28 Jul 2025 00:09:28 GMT
• Title: Provable In-Context Learning of Nonlinear Regression with Transformers
• Authors: Hongbo Li, Lingjie Duan, Yingbin Liang,
• Abstract summary: In-context learning (ICL) is the ability to perform unseen tasks using task-specific prompts without updating parameters.<n>Recent research has actively explored the training dynamics behind ICL.<n>This paper investigates more complex nonlinear regression tasks, aiming to uncover how transformers acquire in-context learning capabilities.
• Score: 58.018629320233174
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The transformer architecture, which processes sequences of input tokens to produce outputs for query tokens, has revolutionized numerous areas of machine learning. A defining feature of transformers is their ability to perform previously unseen tasks using task-specific prompts without updating parameters, a phenomenon known as in-context learning (ICL). Recent research has actively explored the training dynamics behind ICL, with much of the focus on relatively simple tasks such as linear regression and binary classification. To advance the theoretical understanding of ICL, this paper investigates more complex nonlinear regression tasks, aiming to uncover how transformers acquire in-context learning capabilities in these settings. We analyze the stage-wise dynamics of attention during training: attention scores between a query token and its target features grow rapidly in the early phase, then gradually converge to one, while attention to irrelevant features decays more slowly and exhibits oscillatory behavior. Our analysis introduces new proof techniques that explicitly characterize how the nature of general non-degenerate L-Lipschitz task functions affects attention weights. Specifically, we identify that the Lipschitz constant L of nonlinear function classes as a key factor governing the convergence dynamics of transformers in ICL. Leveraging these insights, for two distinct regimes depending on whether L is below or above a threshold, we derive different time bounds to guarantee near-zero prediction error. Notably, despite the convergence time depending on the underlying task functions, we prove that query tokens consistently attend to prompt tokens with highly relevant features at convergence, demonstrating the ICL capability of transformers for unseen functions.

Related papers

• Transformers Don't In-Context Learn Least Squares Regression [5.648229654902264]
  In-context learning (ICL) has emerged as a powerful capability of large pretrained transformers.<n>We study how transformers implement learning at inference time.<n>We highlight the role of the pretraining corpus in shaping ICL behaviour.
  arXiv  Detail & Related papers  (2025-07-13T01:09:26Z)
• How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias [48.9399496805422]
  We focus on two representative tasks in the category of regular language recognition, known as even pairs' and parity check'<n>Our goal is to explore how a one-layer transformer, consisting of an attention layer followed by a linear layer, learns to solve these tasks.
  arXiv  Detail & Related papers  (2025-05-02T00:07:35Z)
• Sequence Complementor: Complementing Transformers For Time Series Forecasting with Learnable Sequences [5.244482076690776]
  We find that expressive capability of sequence representation is a key factor influencing Transformer performance in time forecasting.<n>We propose a novel attention mechanism with Sequence Complementors and prove feasible from an information theory perspective.
  arXiv  Detail & Related papers  (2025-01-06T03:08:39Z)
• Interpreting Affine Recurrence Learning in GPT-style Transformers [54.01174470722201]
  In-context learning allows GPT-style transformers to generalize during inference without modifying their weights. This paper focuses specifically on their ability to learn and predict affine recurrences as an ICL task. We analyze the model's internal operations using both empirical and theoretical approaches.
  arXiv  Detail & Related papers  (2024-10-22T21:30:01Z)
• Asymptotic theory of in-context learning by linear attention [33.53106537972063]
  In-context learning is a cornerstone of Transformers' success.<n>Questions about the necessary sample complexity, pretraining task diversity, and context length for successful ICL remain unresolved.
  arXiv  Detail & Related papers  (2024-05-20T03:24:24Z)
• How Do Nonlinear Transformers Learn and Generalize in In-Context Learning? [82.51626700527837]
  Transformer-based large language models displayed impressive in-context learning capabilities, where a pre-trained model can handle new tasks without fine-tuning. We analyze how the mechanics of how Transformer to achieve ICL contribute to the technical challenges of the training problems in Transformers.
  arXiv  Detail & Related papers  (2024-02-23T21:07:20Z)
• How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations [98.7450564309923]
  This paper takes initial steps on understanding in-context learning (ICL) in more complex scenarios, by studying learning with representations. We construct synthetic in-context learning problems with a compositional structure, where the label depends on the input through a possibly complex but fixed representation function. We show theoretically the existence of transformers that approximately implement such algorithms with mild depth and size.
  arXiv  Detail & Related papers  (2023-10-16T17:40:49Z)
• In-Context Convergence of Transformers [63.04956160537308]
  We study the learning dynamics of a one-layer transformer with softmax attention trained via gradient descent. For data with imbalanced features, we show that the learning dynamics take a stage-wise convergence process.
  arXiv  Detail & Related papers  (2023-10-08T17:55:33Z)
• Trained Transformers Learn Linear Models In-Context [39.56636898650966]
  Attention-based neural networks as transformers have demonstrated a remarkable ability to exhibit inattention learning (ICL) We show that when transformer training over random instances of linear regression problems, these models' predictions mimic nonlinear of ordinary squares.
  arXiv  Detail & Related papers  (2023-06-16T15:50:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.