Spatial Partial Functionalization of Neural Networks based on Noise Fields
Noise in neural computation is typically regarded as a disturbance, but its spatial distribution may also actively regulate which parts of a network participate in computation. This paper investigates the spatial partial functionalization of Noise-modulated Neural Networks using noise fields. We first present an activation function suitable for this goal, the crossing activation function, using the sample-level, statistical-level, and analytical-level implementations, and examine parameter reuse across these implementations. We then introduce a virtual noise field, an auxiliary continuous space for generating spatially structured network noise fields that activate partially overlapping subnetworks. Using one-dimensional function approximation tasks, we evaluate how multiple functions can be stored in a single network when each function is assigned to a different noise-field location. The results show that memory capacity improves when the spatial arrangement of noise fields reflects the proximity relationships among the functions to be learned, whereas mismatches in noise field structure can reduce effective capacity. These findings suggest that structured noise can serve not only as a perturbation but also as a topology-defining factor for functional subnetwork selection.