Mitigating High-Frequency Geometric Noise in Non-Parametric 1-Bit Sparse

Abstract

Energy-efficient neuromorphic computing requires alternative data-encoding paradigms that bypass power-hungry floating-point operations. This paper evaluates a deterministic, non-parametric dual-manifold execution framework that maps dense 128-element integer vectors - representing digitized multi-frequency trigonometric waveforms - into a 1024-dimensional overcomplete space using 8-bit bounded transformation matrices. By enforcing a hard activation threshold, the system yields an ultra-sparse, 1-bit binary population code where y belongs to the set (0, 1)^1024. We identify and address a critical phenotypic artifact of this non-parametric mapping: the emergence of high-frequency geometric noise during linear reconstruction. Furthermore, we document an algorithmic complexity paradox where low-complexity input functions yield significantly higher reconstruction errors than highly complex, high-degree trigonometric combinations. Because the underlying basis functions operate as purely objective mathematical entities without statistical priors regarding signal smoothness, this geometric noise is proven to be strictly orthogonal to the core signal topology. Consequently, we demonstrate that a low-overhead, hardware-level digital low-pass filter completely eliminates this artifact, reducing reconstruction errors to near-zero bounds even under tight overcompleteness constraints. This architecture validates a highly stable, multiplier-free alternative to traditional deep learning hardware for edge-AI applications, verified through comprehensive empirical evaluations across varying complexity scales and classification thresholds (tau = 10 and tau = 100).