Bypassing the Exponential Dependency: Looped Transformers Efficiently Learn In-context by Multi-step Gradient Descent

• URL: http://arxiv.org/abs/2410.11268v1
• Date: Tue, 15 Oct 2024 04:44:23 GMT
• Title: Bypassing the Exponential Dependency: Looped Transformers Efficiently Learn In-context by Multi-step Gradient Descent
• Authors: Bo Chen, Xiaoyu Li, Yingyu Liang, Zhenmei Shi, Zhao Song,
• Abstract summary: We show that linear looped Transformers can implement multi-step gradient descent efficiently for in-context learning. Our results demonstrate that as long as the input data has a constant condition number, $n = O(d)$, the linear looped Transformers can achieve a small error.
• Score: 26.764893400499354
• License:
• Abstract: In-context learning has been recognized as a key factor in the success of Large Language Models (LLMs). It refers to the model's ability to learn patterns on the fly from provided in-context examples in the prompt during inference. Previous studies have demonstrated that the Transformer architecture used in LLMs can implement a single-step gradient descent update by processing in-context examples in a single forward pass. Recent work has further shown that, during in-context learning, a looped Transformer can implement multi-step gradient descent updates in forward passes. However, their theoretical results require an exponential number of in-context examples, $n = \exp(\Omega(T))$, where $T$ is the number of loops or passes, to achieve a reasonably low error. In this paper, we study linear looped Transformers in-context learning on linear vector generation tasks. We show that linear looped Transformers can implement multi-step gradient descent efficiently for in-context learning. Our results demonstrate that as long as the input data has a constant condition number, e.g., $n = O(d)$, the linear looped Transformers can achieve a small error by multi-step gradient descent during in-context learning. Furthermore, our preliminary experiments validate our theoretical analysis. Our findings reveal that the Transformer architecture possesses a stronger in-context learning capability than previously understood, offering new insights into the mechanisms behind LLMs and potentially guiding the better design of efficient inference algorithms for LLMs.

Related papers

• On the Role of Depth and Looping for In-Context Learning with Task Diversity [69.4145579827826]
  We study in-context learning for linear regression with diverse tasks. We show that multilayer Transformers are not robust to even distributional shifts as small as $O(e-L)$ in Wasserstein distance.
  arXiv  Detail & Related papers  (2024-10-29T03:27:56Z)
• Can Looped Transformers Learn to Implement Multi-step Gradient Descent for In-context Learning? [69.4145579827826]
  We show a fast flow on the regression loss despite the gradient non-ity algorithms for our convergence landscape. This is the first theoretical analysis for multi-layer Transformer in this setting.
  arXiv  Detail & Related papers  (2024-10-10T18:29:05Z)
• On Mesa-Optimization in Autoregressively Trained Transformers: Emergence and Capability [34.43255978863601]
  Several suggest that transformers learn a mesa-optimizer during autorere training. We show that a stronger assumption related to the moments of data is the sufficient necessary condition that the learned mesa-optimizer can perform.
  arXiv  Detail & Related papers  (2024-05-27T05:41:06Z)
• Supervised Pretraining Can Learn In-Context Reinforcement Learning [96.62869749926415]
  In this paper, we study the in-context learning capabilities of transformers in decision-making problems. We introduce and study Decision-Pretrained Transformer (DPT), a supervised pretraining method where the transformer predicts an optimal action. We find that the pretrained transformer can be used to solve a range of RL problems in-context, exhibiting both exploration online and conservatism offline.
  arXiv  Detail & Related papers  (2023-06-26T17:58:50Z)
• 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)
• Transformers learn in-context by gradient descent [58.24152335931036]
  Training Transformers on auto-regressive objectives is closely related to gradient-based meta-learning formulations. We show how trained Transformers become mesa-optimizers i.e. learn models by gradient descent in their forward pass.
  arXiv  Detail & Related papers  (2022-12-15T09:21:21Z)
• What learning algorithm is in-context learning? Investigations with linear models [87.91612418166464]
  We investigate the hypothesis that transformer-based in-context learners implement standard learning algorithms implicitly. We show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression. Preliminary evidence that in-context learners share algorithmic features with these predictors.
  arXiv  Detail & Related papers  (2022-11-28T18:59:51Z)

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.