Abstract: A collaborative filtering recommending apparatus includes 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.