Noise exists in nearly all physical systems ranging from simple electronic devices such as transistors to complex systems such as neural networks. To understand a system's behavior, it is vital to know the origin of the noise and its characteristics. Recently, it was shown that the nonlinear electronic properties of a disordered dopant atom network in silicon can be exploited for efficiently executing classification tasks through "material learning." Here, we study the dopant network's intrinsic 1/f noise arising from Coulomb interactions, and its impact on the features that determine its computational abilities, viz., the nonlinearity and the signal-to-noise ratio (SNR), is investigated. The findings on optimal SNR and nonlinear transformation of data by this nonlinear network provide a guideline for the scaling of physical learning machines and shed light on neuroscience from a new perspective.