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The success of artificial neural networks (ANNs) in machine vision techniques has driven hardware researchers to explore more efficient computing elements for energy-expensive operations such as vector-matrix multiplication (VMM). In this work, InP-based floating-gate photo-field-effective transistors (FG-PFETs) are demonstrated as computing elements that integrate both photodetection and initial signal processing at the sensor level. These devices are fabricated from semiconductor channels grown via a back-end CMOS compatible templated liquid phase (TLP) approach. Individual devices are shown to exhibit programmable responsivity, mimicking the effect of a synapse connecting the photodetector to a neuron. Using these devices, a simulated optical neural network (ONN) where the experimentally measured performance of FG-PFETs is used as an input shows excellent image recognition accuracy for color-mixed handwritten digits.