Title: You Only Sample (Almost) Once: Linear Cost Self-Attention Via Bernoulli Sampling. Abstract: Transformer-based models have come to dominate the landscape in a wide range of natural language processing (NLP) applications. The heart of the transformer model is the self-attention mechanism, which captures the interactions of token pairs in the input sequences and consequently, depends quadratically on the input sequence length. It is known that training such models on longer sequences is quite expensive, and often, prohibitively so. We show that a Bernoulli sampling attention mechanism based on Locality Sensitive Hashing (LSH), decreases the quadratic complexity to linear. We bypass the quadratic cost by considering self-attention as a sum of individual tokens associated with Bernoulli random variables that can, in principle, be sampled at once by a single hash (although in practice, this number may be a small constant). This leads to an efficient sampling scheme to estimate self-attention which relies on specific modifications of LSH (based on feasibility of deployment on GPU architectures). We evaluate our proposed algorithm on the GLUE benchmark with standard 512 sequence length and our method achieves comparable or even slightly better performance than a standard pretrained Transformer. To evaluate whether our method can indeed handle longer sequences, we conduct experiments on long sequence (4096) language model pretraining and achieve consistent results as standard self-attention, while observing sizable inference speed-ups and memory savings.