Pretrained Transformers are Deep Optimizers: Provable In-Context Learning for Deep Model Training
Keywords: foundation model, transformer, in-context learning
Abstract: We investigate the transformer's capability for in-context learning (ICL) to simulate the training process of deep models.
Our key contribution is providing a positive example of using a pretrained transformer to train a deep neural network by gradient descent in an implicit fashion via ICL.
Specifically, we provide an explicit construction of a $(2N+4)L$-layer transformer capable of simulating $L$ gradient descent steps of an $N$-layer ReLU network through ICL.
We also give the theoretical guarantees for the approximation within any given error and the convergence of the ICL gradient descent.
Additionally, we extend our analysis to the more practical setting using Softmax-based transformers.
We validate our findings on synthetic datasets for 3-layer, 4-layer, and 6-layer neural networks.
The results show that ICL performance matches that of direct training.
Supplementary Material: zip
Primary Area: foundation or frontier models, including LLMs
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Submission Number: 1668
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