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Big data has grown exponentially in recent years, providing machine-learning models with unprecedented rich and multifaceted information to reveal underlying data patterns for analysis and prediction. Matrix-vector multiplication (MVM) is the fundamental operation that dominates 90% of runtime in most ML models. Various electronic computing architectures have been employed in hardware to parallelize MVM, such as graphics processing units, field-programmable gate arrays and application-specific integrated circuits. In addition, memristive crossbar arrays have been explored for analogue in-memory computing. Photonic MVM is emerging as a next-generation alternative with the advantages of low latency, low energy consumption and high throughput.