New computational paradigms are required to overcome the von-Neumann bottleneck by reducing main memory access. Neuromorphic and in-memory computing has brought on much promise for improving efficiency in a subset of tasks, and emerging memory technologies are inextricably tied to localized memory accesses. However, the sneak path current (SPC) through unselected neighboring cells is a major challenge occurring in high density storage application in the crossbar array configuration. In this work, carbon-based self-selective memory is shown to overcome the SPC problem and additionally is demonstrated to be a potential candidate as a nanodevice for resource-constrained in-memory supervised learning, by taking advantage of its analog synaptic behaviors. Device variation and non-idealities are characterized in the context of neural network regularization, in fulfilling the aim to reduce the ever-increasing power demands of modern computing.