Transformers as Statisticians: Provable In-Context Learning with
In-Context Algorithm Selection
- URL: http://arxiv.org/abs/2306.04637v2
- Date: Thu, 6 Jul 2023 16:55:36 GMT
- Title: Transformers as Statisticians: Provable In-Context Learning with
In-Context Algorithm Selection
- Authors: Yu Bai, Fan Chen, Huan Wang, Caiming Xiong, Song Mei
- Abstract summary: 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.
- Score: 88.23337313766353
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Neural sequence models based on the transformer architecture have
demonstrated remarkable \emph{in-context learning} (ICL) abilities, where they
can perform new tasks when prompted with training and test examples, without
any parameter update to the model. This work first provides a comprehensive
statistical theory for transformers to perform ICL. Concretely, we show that
transformers can implement a broad class of standard machine learning
algorithms in context, such as least squares, ridge regression, Lasso, learning
generalized linear models, and gradient descent on two-layer neural networks,
with near-optimal predictive power on various in-context data distributions.
Using an efficient implementation of in-context gradient descent as the
underlying mechanism, our transformer constructions admit mild size bounds, and
can be learned with polynomially many pretraining sequences.
Building on these ``base'' ICL algorithms, intriguingly, we show that
transformers can implement more complex ICL procedures involving
\emph{in-context algorithm selection}, akin to what a statistician can do in
real life -- A \emph{single} transformer can adaptively select different base
ICL algorithms -- or even perform qualitatively different tasks -- on different
input sequences, without any explicit prompting of the right algorithm or task.
We both establish this in theory by explicit constructions, and also observe
this phenomenon experimentally. In theory, we construct two general mechanisms
for algorithm selection with concrete examples: pre-ICL testing, and post-ICL
validation. As an example, we use the post-ICL validation mechanism to
construct a transformer that can perform nearly Bayes-optimal ICL on a
challenging task -- noisy linear models with mixed noise levels.
Experimentally, we demonstrate the strong in-context algorithm selection
capabilities of standard transformer architectures.
Related papers
- On the Learn-to-Optimize Capabilities of Transformers in In-Context Sparse Recovery [15.164710897163099]
We show that a K-layer Transformer can perform an L2O algorithm with a provable convergence rate linear in K.
Unlike the conventional L2O algorithms that require the measurement matrix involved in training to match that in testing, the trained Transformer is able to solve sparse recovery problems generated with different measurement matrices.
arXiv Detail & Related papers (2024-10-17T19:18:28Z) - Learning Linear Attention in Polynomial Time [115.68795790532289]
We provide the first results on learnability of single-layer Transformers with linear attention.
We show that linear attention may be viewed as a linear predictor in a suitably defined RKHS.
We show how to efficiently identify training datasets for which every empirical riskr is equivalent to the linear Transformer.
arXiv Detail & Related papers (2024-10-14T02:41:01Z) - 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) - In-Context Learning for MIMO Equalization Using Transformer-Based
Sequence Models [44.161789477821536]
Large pre-trained sequence models have the capacity to carry out in-context learning (ICL)
In ICL, a decision on a new input is made via a direct mapping of the input and of a few examples from the given task.
We demonstrate via numerical results that transformer-based ICL has a threshold behavior.
arXiv Detail & Related papers (2023-11-10T15:09:04Z) - 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) - Transformers as Decision Makers: Provable In-Context Reinforcement Learning via Supervised Pretraining [25.669038513039357]
This paper provides a theoretical framework that analyzes supervised pretraining for in-context reinforcement learning.
We show transformers with ReLU attention can efficiently approximate near-optimal online reinforcement learning algorithms.
arXiv Detail & Related papers (2023-10-12T17:55:02Z) - Uncovering mesa-optimization algorithms in Transformers [61.06055590704677]
Some autoregressive models can learn as an input sequence is processed, without undergoing any parameter changes, and without being explicitly trained to do so.
We show that standard next-token prediction error minimization gives rise to a subsidiary learning algorithm that adjusts the model as new inputs are revealed.
Our findings explain in-context learning as a product of autoregressive loss minimization and inform the design of new optimization-based Transformer layers.
arXiv Detail & Related papers (2023-09-11T22:42:50Z) - 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 Algorithms: Generalization and Implicit Model Selection
in In-context Learning [23.677503557659705]
In-context learning (ICL) is a type of prompting where a transformer model operates on a sequence of examples and performs inference on-the-fly.
We treat the transformer model as a learning algorithm that can be specialized via training to implement-at inference-time-another target algorithm.
We show that transformers can act as an adaptive learning algorithm and perform model selection across different hypothesis classes.
arXiv Detail & Related papers (2023-01-17T18:31:12Z)
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.