Systems and components for use with neural networks. An execution block and a system architecture using that execution block are disclosed. The execution block uses a fully connected stack of layers and one output is a forecast for a time series while another output is a backcast that can be used to determine a residual from the input to the execution block. The execution block uses a waveform generator sub-unit whose parameters can be judiciously selected to thereby constrain the possible set of waveforms generated. By doing so, the execution block specializes its function. The system using the execution block has been shown to be better than the state of the art in providing solutions to the time series problem.