An official website of the United States government
Transformers have a remarkable ability to learn and execute tasks based on examples provided within the input itself, without explicit prior training. It has been argued that this capability, known as in-context learning (ICL), is a cornerstone of Transformers’ success, yet questions about the necessary sample complexity, pretraining task diversity, and context length for successful ICL remain unresolved. Here, we provide a precise answer to these questions in an exactly solvable model of ICL of a linear regression task by linear attention. We derive sharp asymptotics for the learning curve in a phenomenologically rich scaling regime where the token dimension is taken to infinity; the context length and pretraining task diversity scale proportionally with the token dimension; and the number of pretraining examples scales quadratically. We demonstrate a double-descent learning curve with increasing pretraining examples, and uncover a phase transition in the model’s behavior between low and high task diversity regimes: in the low diversity regime, the model tends toward memorization of training tasks, whereas in the high diversity regime, it achieves genuine ICL and generalization beyond the scope of pretrained tasks. These theoretical insights are empirically validated through experiments with both linear attention and full nonlinear Transformer architectures.
more »
« less
In-Context Learning with Transformers: Softmax Attention Adapts to Function Lipschitzness
A striking property of transformers is their ability to perform in-context learning (ICL), a machine learning framework in which the learner is presented with a novel context during inference implicitly through some data, and tasked with making a prediction in that context. As such, that learner must adapt to the context without additional training. We explore the role of softmax attention in an ICL setting where each context encodes a regression task. We show that an attention unit learns a window that it uses to implement a nearest-neighbors predictor adapted to the landscape of the pretraining tasks. Specifically, we show that this window widens with decreasing Lipschitzness and increasing label noise in the pretraining tasks. We also show that on low-rank, linear problems, the attention unit learns to project onto the appropriate subspace before inference. Further, we show that this adaptivity relies crucially on the softmax activation and thus cannot be replicated by the linear activation often studied in prior theoretical analyses.
more »
« less
- Award ID(s):
- 2505865
- PAR ID:
- 10631876
- Publisher / Repository:
- https://doi.org/10.48550/arXiv.2402.11639
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In-Context Learning (ICL) ability has been found efficient across a wide range of applications, where the Large Language Models (LLM) learn to complete the tasks from the examples in the prompt without tuning the parameters. In this work, we conduct a comprehensive study to understand ICL from a statistical perspective. First, we show that the perfectly pretrained LLMs perform Bayesian Model Averaging (BMA) for ICL under a dynamic model of examples in the prompt. The average error analysis for ICL is then built for the perfectly pretrained LLMs with the analysis of BMA. Second, we demonstrate how the attention structure boosts the BMA implementation. With sufficient examples in the prompt, attention is proven to perform BMA under the Gaussian linear ICL model, which also motivates the explicit construction of the hidden concepts from the attention heads' values. Finally, we analyze the pretraining behavior of LLMs. The pretraining error is decomposed as the generalization error and the approximation error. The generalization error is upper bounded via the PAC-Bayes framework. Then the ICL average error of the pretrained LLMs is shown to be the sum of O(T^{-1}) and the pretraining error. In addition, we analyze the ICL performance of the pretrained LLMs with misspecified examples.more » « less
-
Prompt-tuning is an emerging strategy to adapt large language models (LLM) to downstream tasks by learning a (soft-)prompt parameter from data. Despite its success in LLMs, there is limited theoretical understanding of the power of prompt-tuning and the role of the attention mechanism in prompting. In this work, we explore prompt-tuning for one-layer attention architectures and study contextual mixture-models where each input token belongs to a context-relevant or -irrelevant set. We isolate the role of prompttuning through a self-contained prompt-attention model. Our contributions are as follows: (1) We show that softmax-prompt-attention is provably more expressive than softmax-self-attention and linear-prompt-attention under our contextual data model. (2) We analyze the initial trajectory of gradient descent and show that it learns the prompt and prediction head with near-optimal sample complexity and demonstrate how the prompt can provably attend to sparse context-relevant tokens. (3) Assuming a known prompt but an unknown prediction head, we characterize the exact finite sample performance of prompt-attention which reveals the fundamental performance limits and the precise benefit of the context information. We also provide experiments that verify our theoretical insights on real datasets and demonstrate how prompt-tuning enables the model to attend to context-relevant information.more » « less
-
Vision Transformers (ViTs) have shown impressive per-formance but still require a high computation cost as compared to convolutional neural networks (CNNs), one rea-son is that ViTs' attention measures global similarities and thus has a quadratic complexity with the number of in-put tokens. Existing efficient ViTs adopt local attention or linear attention, which sacrifice ViTs' capabilities of capturing either global or local context. In this work, we ask an important research question: Can ViTs learn both global and local context while being more efficient during inference? To this end, we propose a framework called Castling- ViT, which trains ViTs using both linear-angular attention and masked softmax-based quadratic attention, but then switches to having only linear-angular attention during inference. Our Castling- ViT leverages angular ker-nels to measure the similarities between queries and keys via spectral angles. And we further simplify it with two techniques: (1) a novel linear-angular attention mechanism: we decompose the angular kernels into linear terms and high-order residuals, and only keep the linear terms; and (2) we adopt two parameterized modules to approximate high-order residuals: a depthwise convolution and an aux-iliary masked softmax attention to help learn global and lo-cal information, where the masks for softmax attention are regularized to gradually become zeros and thus incur no overhead during inference. Extensive experiments validate the effectiveness of our Castling- ViT, e.g., achieving up to a 1.8% higher accuracy or 40% MACs reduction on classification and 1.2 higher mAP on detection under comparable FLOPs, as compared to ViTs with vanilla softmax-based at-tentions. Project page is available at here.more » « less
-
State-space models (SSMs), such as Mamba (Gu & Dao, 2023), have been proposed as alternatives to Transformer networks in language modeling, incorporating gating, convolutions, and input-dependent token selection to mitigate the quadratic cost of multi-head attention. Although SSMs exhibit competitive performance, their in-context learning (ICL) capabilities, a remarkable emergent property of modern language models that enables task execution without parameter optimization, remain less explored compared to Transformers. In this study, we evaluate the ICL performance of SSMs, focusing on Mamba, against Transformer models across various tasks. Our results show that SSMs perform comparably to Transformers in standard regression ICL tasks, while outperforming them in tasks like sparse parity learning. However, SSMs fall short in tasks involving non-standard retrieval functionality. To address these limitations, we introduce a hybrid model, MambaFormer, that combines Mamba with attention blocks, surpassing individual models in tasks where they struggle independently. Our findings suggest that hybrid architectures offer promising avenues for enhancing ICL in language models.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
