Random Projection-Based Locality-Sensitive Hashing in a Memristor Crossbar Array with Stochasticity for Sparse Self-Attention-Based Transformer

Self-attention mechanism is critically central to the state-of-the-art transformer models. Because the standard full self-attention has quadratic complexity with respect to the input's length L, resulting in prohibitively large memory for very long sequences, sparse self-attention enabled by random projection (RP)-based locality-sensitive hashing (LSH) has recently been proposed to reduce the complexity to O(L log L). However, in current digital computing hardware with a von Neumann architecture, RP, which is essentially a matrix multiplication operation, incurs unavoidable time and energy-consuming data shuttling between off-chip memory and processing units. In addition, it is known that digital computers simply cannot generate provably random numbers. With the emerging analog memristive technology, it is shown that it is feasible to harness the intrinsic device-to-device variability in the memristor crossbar array for implementing the RP matrix and perform RP-LSH computation in memory. On this basis, sequence prediction tasks are performed with a sparse self-attention-based Transformer in a hybrid software-hardware approach, achieving a testing accuracy over 70% with much less computational complexity. By further harnessing the cycle-to-cycle variability for multi-round hashing, 12% increase in the testing accuracy is demonstrated. This work extends the range of applications of memristor crossbar arrays to the state-of-the-art large language models (LLMs).