On the Training Convergence of Transformers for In-Context Classification

• URL: http://arxiv.org/abs/2410.11778v1
• Date: Tue, 15 Oct 2024 16:57:14 GMT
• Title: On the Training Convergence of Transformers for In-Context Classification
• Authors: Wei Shen, Ruida Zhou, Jing Yang, Cong Shen,
• Abstract summary: This work aims to theoretically study the training dynamics of transformers for in-context classification tasks. We demonstrate that, for in-context classification of Gaussian mixtures under certain assumptions, a single-layer transformer trained via gradient descent converges to a globally optimal model at a linear rate.
• Score: 20.980349268151546
• License:
• Abstract: While transformers have demonstrated impressive capacities for in-context learning (ICL) in practice, theoretical understanding of the underlying mechanism enabling transformers to perform ICL is still in its infant stage. This work aims to theoretically study the training dynamics of transformers for in-context classification tasks. We demonstrate that, for in-context classification of Gaussian mixtures under certain assumptions, a single-layer transformer trained via gradient descent converges to a globally optimal model at a linear rate. We further quantify the impact of the training and testing prompt lengths on the ICL inference error of the trained transformer. We show that when the lengths of training and testing prompts are sufficiently large, the prediction of the trained transformer approaches the Bayes-optimal classifier. Experimental results corroborate the 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)
• Trained Transformer Classifiers Generalize and Exhibit Benign Overfitting In-Context [25.360386832940875]
  We show that when linear transformers are pre-trained on random instances for linear regression tasks, they make predictions using an algorithm similar to that of ordinary least squares. In some settings, these trained transformers can exhibit "benign overfitting in-context"
  arXiv  Detail & Related papers  (2024-10-02T17:30:21Z)
• 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)
• 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)
• 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)
• Trained Transformers Learn Linear Models In-Context [39.56636898650966]
  Attention-based neural networks as transformers have demonstrated a remarkable ability to exhibit inattention learning (ICL) We show that when transformer training over random instances of linear regression problems, these models' predictions mimic nonlinear of ordinary squares.
  arXiv  Detail & Related papers  (2023-06-16T15:50:03Z)
• 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)
• Don't Sweep your Learning Rate under the Rug: A Closer Look at Cross-modal Transfer of Pretrained Transformers [1.9662978733004601]
  Self-supervised pre-training of large-scale transformer models on text corpora followed by finetuning has achieved state-of-the-art on a number of natural language processing tasks. In our work, we find that this result is, in fact, an artifact of not tuning the learning rates.
  arXiv  Detail & Related papers  (2021-07-26T20:20:48Z)
• Scalable Transformers for Neural Machine Translation [86.4530299266897]
  Transformer has been widely adopted in Neural Machine Translation (NMT) because of its large capacity and parallel training of sequence generation. We propose a novel scalable Transformers, which naturally contains sub-Transformers of different scales and have shared parameters. A three-stage training scheme is proposed to tackle the difficulty of training the scalable Transformers.
  arXiv  Detail & Related papers  (2021-06-04T04:04:10Z)
• Pretrained Transformers as Universal Computation Engines [105.00539596788127]
  We investigate the capability of a transformer pretrained on natural language to generalize to other modalities with minimal finetuning. We study finetuning it on a variety of sequence classification tasks spanning numerical computation, vision, and protein fold prediction. We find that such pretraining enables FPT to generalize in zero-shot to these modalities, matching the performance of a transformer fully trained on these tasks.
  arXiv  Detail & Related papers  (2021-03-09T06:39:56Z)

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.