Controlling changes in the optical properties of photonic devices allows photonic integrated circuits (PICs) to perform useful functions, leading to a breadth of applications in communications, computing, and sensing. Many mechanisms to change optical properties exist, but few allow doing so in a reversible, non-volatile manner. This leads to power inefficiency in reconfigurable circuits and requires external memory elements. In this work, we propose and experimentally demonstrate reversible, non-volatile phase actuation of a silicon nitride PIC with thermally-stable photochromic organic molecules. The use of a high-core-index platform allows, for the first time, the photochemical actuation of a planar-resonator-based photonic memory unit, which enables high performance and permits integrated spectroscopic analysis. We show novel properties of this all-optical memory for a silicon photonics platform, including complete transparency in the optical C-band, as well as first-order photokinetics of the photoconversion that lead to bidirectional scalable switching rates and continuous tuning. Such features are critical for memories in analog applications, such as quantum, microwave, and neuromorphic photonics, where low loss and precision are paramount.