  This paper answers a fundamental question in artificial neural network (ANN)
design: We do not need to build ANNs layer-by-layer sequentially to guarantee
the Directed Acyclic Graph (DAG) property. Drawing inspiration from biological
intelligence (BI), where neurons form a complex, graph-structured network, we
introduce the groundbreaking Cyclic Neural Networks (Cyclic NNs). It emulates
the flexible and dynamic graph nature of biological neural systems, allowing
neuron connections in any graph-like structure, including cycles. This offers
greater adaptability compared to the DAG structure of current ANNs. We further
develop the Graph Over Multi-layer Perceptron, which is the first detailed
model based on this new design paradigm. Experimental validation of the Cyclic
NN's advantages on widely tested datasets in most generalized cases,
demonstrating its superiority over current BP training methods through the use
of a forward-forward (FF) training algorithm. This research illustrates a
totally new ANN design paradigm, which is a significant departure from current
ANN designs, potentially leading to more biologically plausible AI systems.
