Performer is a Transformer architecture which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. To approximate softmax attention-kernels, Performers use a Fast Attention Via positive Orthogonal Random features approach (FAVOR+), leveraging new methods for approximating softmax and Gaussian kernels.