Super Neurons.

Operational Neural Networks (ONNs) are new generation network models that can perform any (non-linear) transformation with a proper combination of "nodal" and "pool" operators. However, they still have a certain restriction, which is the sole usage of a single nodal operator for all (synaptic) connections of each neuron. The idea behind the "generative neurons" was born as a remedy for this restriction where each nodal operator can be "customized" during the training in order to maximize the learning performance. Self-Organized ONNs (Self-ONNs) composed with the generative neurons can achieve an utmost level of diversity even with a compact configuration; however, it still suffers from the last property that was inherited from the CNNs: localized kernel operations which imposes a severe limitation to the information flow between layers. It is, therefore, desirable for the neurons to gather information from a larger area in the previous layer maps without increasing the kernel size. For certain applications, it might be even more desirable "to learn" the kernel locations of each connection during the training process along with the customized nodal operators so that both can be optimized simultaneously. This study introduces the super (generative) neuron models that can accomplish this without altering the kernel sizes and will enable a significant diversity in terms of information flow. The two models of super neurons proposed in this study vary on the localization process of the kernels: i) randomly localized kernels within a bias range set for each layer, ii) optimized locations of each kernel during the Back-Propagation (BP) training. The extensive set of comparative evaluations show that Self-ONNs with super-neurons can indeed achieve a superior learning and generalization capability without any significant rise of the computational complexity.