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With the advances in wireless communications towards beyond 5G (B5G) and 6G networks, new signal processing and resource management methods need to be explored to overcome the channel impairments and other radio and computing obstacles. In contrast to the conventional methods which are based on classic digital communications structures, B5G and 6G will leverage artificial intelligence (AI) to configure or adapt the radios and networks to the operational context. This requires the ability to reformulate legacy transceiver structures and drive research, development and standardization that can leverage the amount of data that is available and that can be processed with the available computing technology. This paper describes this vision and discusses successful research that justifies it as well as the remaining challenges. We numerically analyze some of the tradeoffs when replacing the physical layer receiver processing with an artificial neural network (ANN).