The key insights from the content are:
The authors show that under a specific choice of Transformer parameters and non-linear activation function ˜h, the Transformer's forward pass can implement functional gradient descent in the Reproducing Kernel Hilbert Space (RKHS) induced by the kernel ˜h.
When the data labels are generated from a Kernel Gaussian Process, and the Transformer's non-linear activation ˜h matches the generating kernel K, the Transformer's prediction converges to the Bayes optimal predictor as the number of layers increases.
The authors generalize this result to multi-head Transformers, showing that a single multi-head Transformer can implement functional gradient descent with respect to a composite kernel formed by combining the kernels of the individual attention heads.
The authors analyze the loss landscape of Transformers on non-linear data, characterizing certain stationary points that correspond to the functional gradient descent construction. They verify empirically that these stationary points are consistently learned during training.
The experiments identify scenarios where ReLU Transformers outperform softmax Transformers, and vice versa, depending on the data distribution.
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by Xiang Cheng,... às arxiv.org 04-23-2024
https://arxiv.org/pdf/2312.06528.pdfPerguntas Mais Profundas