Over the past few years, extensive work on optical neural networks has been investigated in hopes of achieving orders of magnitude improvement in energy efficiency and compute density via all-optical matrix-vector multiplication. However, these solutions are limited by a lack of high-speed power power-efficient phase tuners, on-chip non-volatile memory, and a proper material platform that can heterogeneously integrate all the necessary components needed onto a single chip. We address these issues by demonstrating embedded multi-layer HfO2/Al2O3 memristors with III-V/Si photonics which facilitate non-volatile optical functionality for a variety of devices such as Mach-Zehnder Interferometers, and (de-)interleaver filters. The Mach-Zehnder optical memristor exhibits non-volatile optical phase shifts > π with ~33 dB signal extinction while consuming 0 electrical power consumption. We demonstrate 6 non-volatile states each capable of 4 Gbps modulation. (De-) interleaver filters were demonstrated to exhibit memristive non-volatile passband transformation with full set/reset states. Time duration tests were performed on all devices and indicated non-volatility up to 24 hours and beyond. We demonstrate non-volatile III-V/Si optical memristors with large electric-field driven phase shifts and reconfigurable filters with true 0 static power consumption. As a result, co-integrated photonic memristors offer a pathway for in-memory optical computing and large-scale non-volatile photonic circuits.