Non-asymptotic Convergence of Training Transformers for Next-token Prediction

• URL: http://arxiv.org/abs/2409.17335v2
• Date: Sun, 29 Sep 2024 21:08:33 GMT
• Title: Non-asymptotic Convergence of Training Transformers for Next-token Prediction
• Authors: Ruiquan Huang, Yingbin Liang, Jing Yang,
• Abstract summary: Transformers have achieved extraordinary success in modern machine learning due to their excellent ability to handle sequential data. This paper provides a fine-grained non-asymptotic analysis of the training dynamics of a one-layer transformer. We show that the trained transformer presents non-token prediction ability with dataset shift.
• Score: 48.9399496805422
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Transformers have achieved extraordinary success in modern machine learning due to their excellent ability to handle sequential data, especially in next-token prediction (NTP) tasks. However, the theoretical understanding of their performance in NTP is limited, with existing studies focusing mainly on asymptotic performance. This paper provides a fine-grained non-asymptotic analysis of the training dynamics of a one-layer transformer consisting of a self-attention module followed by a feed-forward layer. We first characterize the essential structural properties of training datasets for NTP using a mathematical framework based on partial orders. Then, we design a two-stage training algorithm, where the pre-processing stage for training the feed-forward layer and the main stage for training the attention layer exhibit fast convergence performance. Specifically, both layers converge sub-linearly to the direction of their corresponding max-margin solutions. We also show that the cross-entropy loss enjoys a linear convergence rate. Furthermore, we show that the trained transformer presents non-trivial prediction ability with dataset shift, which sheds light on the remarkable generalization performance of transformers. Our analysis technique involves the development of novel properties on the attention gradient and further in-depth analysis of how these properties contribute to the convergence of the training process. Our experiments further validate our theoretical findings.

Related papers

• 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)
• Training Dynamics of Transformers to Recognize Word Co-occurrence via Gradient Flow Analysis [97.54180451650122]
  We study the dynamics of training a shallow transformer on a task of recognizing co-occurrence of two designated words. We analyze the gradient flow dynamics of simultaneously training three attention matrices and a linear layer. We prove a novel property of the gradient flow, termed textitautomatic balancing of gradients, which enables the loss values of different samples to decrease almost at the same rate and further facilitates the proof of near minimum training loss.
  arXiv  Detail & Related papers  (2024-10-12T17:50:58Z)
• Unveil Benign Overfitting for Transformer in Vision: Training Dynamics, Convergence, and Generalization [88.5582111768376]
  We study the optimization of a Transformer composed of a self-attention layer with softmax followed by a fully connected layer under gradient descent on a certain data distribution model. Our results establish a sharp condition that can distinguish between the small test error phase and the large test error regime, based on the signal-to-noise ratio in the data model.
  arXiv  Detail & Related papers  (2024-09-28T13:24:11Z)
• Learning on Transformers is Provable Low-Rank and Sparse: A One-layer Analysis [63.66763657191476]
  We show that efficient numerical training and inference algorithms as low-rank computation have impressive performance for learning Transformer-based adaption. We analyze how magnitude-based models affect generalization while improving adaption. We conclude that proper magnitude-based has a slight on the testing performance.
  arXiv  Detail & Related papers  (2024-06-24T23:00:58Z)
• Understanding Optimal Feature Transfer via a Fine-Grained Bias-Variance Analysis [10.79615566320291]
  We explore transfer learning with the goal of optimizing downstream performance. We introduce a simple linear model that takes as input an arbitrary pretrained feature. We identify the optimal pretrained representation by minimizing the downstream risk averaged over an ensemble of downstream tasks.
  arXiv  Detail & Related papers  (2024-04-18T19:33:55Z)
• 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)
• Learning Stochastic Graph Neural Networks with Constrained Variance [18.32587282139282]
  graph neural networks (SGNNs) are information processing architectures that learn representations from data over random graphs. We propose a variance-constrained optimization problem for SGNNs, balancing the expected performance and the deviation. An alternating gradient-dual learning procedure is undertaken that solves the problem by updating the SGNN parameters with descent and the dual variable with ascent.
  arXiv  Detail & Related papers  (2022-01-29T15:55:58Z)

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.