In-Context Deep Learning via Transformer Models
This provides a theoretical foundation for in-context deep learning, potentially enabling more efficient training methods, though it is incremental as it builds on existing transformer and gradient descent concepts.
The paper tackles the problem of using transformers to simulate gradient descent training of deep neural networks via in-context learning, showing that a constructed transformer can match the performance of direct training on synthetic datasets.
We investigate the transformer's capability to simulate the training process of deep models via in-context learning (ICL), i.e., in-context deep learning. Our key contribution is providing a positive example of using a 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.