🤖 AI Summary
This work proposes a novel approach to spatially localizing functional specialization in neural networks through structured noise, enabling a single network to efficiently store and distinguish multiple functions. By introducing a virtual noise field that generates spatially structured noise in a continuous auxiliary space, the method activates partially overlapping subnetworks and leverages cross-activation functions to achieve multi-level parameter sharing at the sample, statistical, and analytical levels. The key innovation lies in repurposing noise from a source of interference into an active regulatory mechanism that defines the topological structure of functional subnetworks. Experiments on one-dimensional function approximation demonstrate that memory capacity significantly increases when the spatial configuration of the noise field aligns with the similarity structure of target functions, while misalignment leads to degraded performance, revealing a critical relationship between noise structure and function representation.
📝 Abstract
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.