Ultra-massive multiple-input multiple-output (UM-MIMO) is a cutting-edge technology that promises to revolutionize wireless networks by providing an unprecedentedly high spectral and energy efficiency. The enlarged array aperture of UM-MIMO facilitates the accessibility of the near-field region, thereby offering a novel degree of freedom for communications and sensing. Nevertheless, the transceiver design for such systems is challenging because of the enormous system scale, the complicated channel characteristics, and the uncertainties in propagation environments. Therefore, it is critical to study scalable, low-complexity, and robust algorithms that can efficiently characterize and leverage the properties of the near-field channel. In this article, we will advocate two general frameworks from an artificial intelligence (AI)-native perspective, which are tailored for the algorithmic design of near-field UM-MIMO transceivers. Specifically, the frameworks for both iterative and non-iterative algorithms are discussed. Near-field beam focusing and channel estimation are presented as two tutorial-style examples to demonstrate the significant advantages of the proposed AI-native frameworks in terms of various key performance indicators.