Attention-Only Transformers and Implementing MLPs with Attention Heads

Abstract: The transformer architecture is widely used in machine learning models and consists of two alternating sublayers: attention heads and MLPs. We prove that an MLP neuron can be implemented by a masked attention head with internal dimension 1 so long as the MLP's activation function comes from a restricted class including SiLU and close approximations of ReLU and GeLU. This allows one to convert an MLP-and-attention transformer into an attention-only transformer at the cost of greatly increasing the number of attention heads. We also prove that attention heads can perform the components of an MLP (linear transformations and activation functions) separately. Finally, we prove that attention heads can encode arbitrary masking patterns in their weight matrices to within arbitrarily small error.