Here we introduce a Fourier-Theorem based convolution processors in silicon photonics. The systems leverages an algorithmic homomorphism that utilizes the Fourier transformation provided by a lens along with high-speed optoelectronic signal modulation and read-out. We demonstrate convolution filtering for image processing, convolutional neural network classification tasks. An on-chip lens performs the convolution operation, whereas electro-optic modulators perform the weighting in the Fourier domain at high-speed, followed by detection at a detector array after a 2nd Fourier lens, all on a PIC. Using this accelerator, we demonstrate image filtering and machine learning inference tasks. Given the high SWAP, these accelerators are useful for network-edge AI for the coming Industry-4.0 era.
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