What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization

• URL: http://arxiv.org/abs/2305.19420v2
• Date: Tue, 10 Oct 2023 04:47:47 GMT
• Title: What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization
• Authors: Yufeng Zhang, Fengzhuo Zhang, Zhuoran Yang, Zhaoran Wang
• Abstract summary: We study In-Context Learning (ICL) by addressing several open questions. We show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm. We prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error.
• Score: 111.55277952086155
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we conduct a comprehensive study of In-Context Learning (ICL) by addressing several open questions: (a) What type of ICL estimator is learned by large language models? (b) What is a proper performance metric for ICL and what is the error rate? (c) How does the transformer architecture enable ICL? To answer these questions, we adopt a Bayesian view and formulate ICL as a problem of predicting the response corresponding to the current covariate, given a number of examples drawn from a latent variable model. To answer (a), we show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm, which is proven to be approximately parameterized by the attention mechanism. For (b), we analyze the ICL performance from an online learning perspective and establish a $\mathcal{O}(1/T)$ regret bound for perfectly pretrained ICL, where $T$ is the number of examples in the prompt. To answer (c), we show that, in addition to encoding Bayesian model averaging via attention, the transformer architecture also enables a fine-grained statistical analysis of pretraining under realistic assumptions. In particular, we prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error, where the former decays to zero exponentially as the depth grows, and the latter decays to zero sublinearly with the number of tokens in the pretraining dataset. Our results provide a unified understanding of the transformer and its ICL ability with bounds on ICL regret, approximation, and generalization, which deepens our knowledge of these essential aspects of modern language models.

Related papers

• An In-depth Investigation of Sparse Rate Reduction in Transformer-like Models [32.04194224236952]
  We propose an information-theoretic objective function called Sparse Rate Reduction (SRR) We show that SRR has a positive correlation coefficient and outperforms other baseline measures, such as path-norm and sharpness-based ones. We show that generalization can be improved using SRR as regularization on benchmark image classification datasets.
  arXiv  Detail & Related papers  (2024-11-26T07:44:57Z)
• Deeper Insights Without Updates: The Power of In-Context Learning Over Fine-Tuning [22.341935761925892]
  Fine-tuning and in-context learning (ICL) are two prevalent methods in imbuing large language models with task-specific knowledge. This paper presents a counterintuitive finding: For tasks with implicit patterns, ICL captures these patterns significantly better than fine-tuning.
  arXiv  Detail & Related papers  (2024-10-07T02:12:22Z)
• Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods [59.779795063072655]
  Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems. We analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity.
  arXiv  Detail & Related papers  (2024-08-25T04:07:18Z)
• Transformers are Minimax Optimal Nonparametric In-Context Learners [36.291980654891496]
  In-context learning of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. We develop approximation and generalization error bounds for a transformer composed of a deep neural network and one linear attention layer. We show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context.
  arXiv  Detail & Related papers  (2024-08-22T08:02:10Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  This paper presents a succinct derivation of the training and generalization performance of a variety of high-dimensional ridge regression models. We provide an introduction and review of recent results on these topics, aimed at readers with backgrounds in physics and deep learning.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• In-Context Language Learning: Architectures and Algorithms [73.93205821154605]
  We study ICL through the lens of a new family of model problems we term in context language learning (ICLL) We evaluate a diverse set of neural sequence models on regular ICLL tasks.
  arXiv  Detail & Related papers  (2024-01-23T18:59:21Z)
• Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection [88.23337313766353]
  This work first provides a comprehensive statistical theory for transformers to perform ICL. We show that transformers can implement a broad class of standard machine learning algorithms in context. A emphsingle transformer can adaptively select different base ICL algorithms.
  arXiv  Detail & Related papers  (2023-06-07T17:59:31Z)
• Explaining Emergent In-Context Learning as Kernel Regression [61.57151500616111]
  Large language models (LLMs) have initiated a paradigm shift in transfer learning. In this paper, we investigate the reason why a transformer-based language model can accomplish in-context learning after pre-training. We find that during ICL, the attention and hidden features in LLMs match the behaviors of a kernel regression.
  arXiv  Detail & Related papers  (2023-05-22T06:45:02Z)

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.