Inverse-Designed Dot Product Engine

Abstract: The work presents an inverse-designed optical cavity that can direct light from two sources such that if the sources were to represent any number in the range [-1,1] with magnitude encoded through the power emitted by the source and sign by switching the direction of source current, the photocurrent generated at the two output ports is proportional to the product of the two numbers. Let us say that the two sources encode x and y, which are two numbers $\in$ [-1,1]. Multiplication is reduced to the form $(x+y)^2 - (x-y)^2 = 4xy \propto xy$. The addition and subtraction operations of the numbers are supported by constructive and destructive interference, respectively. The work shows that replacing the DDOT dot product engine of the Lightening Transformer with the optical cavity proposed to calculate the dot product can lead to a reduction in the area occupied by the photonic core by 88 \%, can reduce the power consumption by lasers by around 23.43 \%, and bring down energy consumption while training DeiT models by 0.88 \%. The cavities can generate photocurrents of the form $1.057 xy + 0.249$ with $R^2=0.88,$ thus showing a relationship of direct proportionality between the target product $xy$ and the output of the cavity in response to stimuli encoding $x$ and $y$.