Apparatus and method for recommending collaborative filtering based on learnable-time ordinary differential equation

A collaborative filtering recommending apparatus based on a learnable-time ordinary differential equation, the apparatus comprising:

• an initial-embedding generation module configured to generate first and second initial embeddings;
• a dual co-evolving ordinary differential equation module comprising first and second ordinary differential equation processing members which repeat, for a specific time, a process of receiving first and second previous embeddings, respectively, and outputting first and second subsequent embeddings, respectively, through mutual influence as a learning time elapses, the first and second previous embeddings initially corresponding to the first and second initial embeddings, respectively;
• and
• a final-embedding generation module configured to generate a first final embedding by cumulative summing the first previous and subsequent embeddings, and to generate a second final embedding by cumulative summing the second previous and subsequent embeddings,
• wherein the process repeated by the dual co-evolving ordinary differential equation module for the specific time extracts a plurality of user embedding matrixes at a first set of time points and a plurality of product embedding matrixes at a second set of time points within a continuous time domain, wherein each time point is implemented as a learnable parameter stored in computer memory that is iteratively updated during training by:
• (i) computing a gradient of a loss function with respect to the time point using an adjoint sensitivity method that performs reverse-mode integration through the neural ordinary differential equations;
• and
• (ii) adjusting a numerical value of the time point stored in the memory based on the computed gradient, and
• wherein the initial-embedding generation module, the dual co-evolving ordinary differential equation module, and the final-embedding generation module are each implemented via at least one processor.