In this paper, a new reconfigurable intelligent surface (RIS) hardware architecture, called self-organized RIS (SORIS), is proposed. The architecture incorporates a microcontroller connected to a single-antenna receiver operating at the same frequency as the RIS unit elements, operating either in transmission or reflection mode. The transmitting RIS elements enable the low latency estimation of both the incoming and outcoming channels at the microcontroller's side. In addition, a machine learning approach for estimating the incoming and outcoming channels involving the remaining RIS elements operating in reflection mode is devised. Specifically, by appropriately selecting a small number of elements in transmission mode, and based on the channel reciprocity principle, the respective channel coefficients are first estimated, which are then fed to a low-complexity neural network that, leveraging spatial channel correlation over RIS elements, returns predictions of the channel coefficients referring to the rest of elements. In this way, the SORIS microcontroller acquires channel state information, and accordingly reconfigures the panel's metamaterials to assist data communication between a transmitter and a receiver, without the need for separate connections with them. Moreover, the impact of channel estimation on the proposed solution, and a detailed complexity analysis for the used model, as well as a wiring density and control signaling analysis, is performed. The feasibility and efficacy of the proposed self-organized RIS design and operation are verified by Monte Carlo simulations, providing useful guidelines on the selection of the RIS elements for operating in transmission mode for initial channel estimation.