Brain-inspired approaches emphasize the need for highly connected complex networks with long-range adaptive connections (the distant synapses). If implemented with non-biological technologies, these are raising problems with respect to: charging/discharging, cross-talk, delays, losses and heating, i.e. scalability issues well-known from CMOS technologies. Instead, SYMONE will explore the functionalities of bio-inspired scalable near-neighbour (locally-connected) networks and systolic-like array architectures. The SYMONE long-term vision is to build multi-scale bio-/neuro-inspired systems interfacing/connecting molecular-scale devices to macroscopic systems for unconventional information processing with scalable neuromorphic architectures. The SYMONE computational substrate is a memristive/synaptic network controlled by a multi-terminal structure of input/output ports and internal gates embedded in a classical digital CMOS environment. The SYMONE goal is the exploration of a multiscale platform connecting molecular-scale devices into networks for the development and testing of synaptic devices and scalable neuromorphic architectures, and for investigating materials and components with new functionalities. The generic breakthrough concerns proof-of-concept of unconventional information processing involving flow of information via near-neighbour short-range (local) interactions through a network of non-linear elements: switches, memristors/synapses. These will require several breakthroughs concerning the functionality of reasonably complex networks of simple components, and the fabrication of networks of devices, including self-assembly and multi-scale interfacing/contacting between such networks