A Spectral Energy Unit for Non-Linear Logic and Regression

The fundamental unit of modern deep learning, the Perceptron, is constrained bylinear separability, rendering it unable to solve non-linear problems like XOR withouta hidden layer. Furthermore, its memory capacity is strictly limited by the VCdimension of a linear classifier. We introduce the Quantum-Inspired Neuron (QIN),a novel computational unit based on Euler’s formula that processes inputs as phaseangles in a spectral sum. By utilizing a "Vectorized Spectral Calculus"—separatingreal and imaginary pathways for efficient gradient descent—we demonstrate that a single QIN can solve the XOR problem with >99% accuracy, perform non-linearanalog regression (MSE < 0.07), and achieve a memory capacity of 15 distinctpatterns in a 2D space (5x the theoretical limit of a standard perceptron). Thissuggests that spectral activation functions can significantly increase thecomputational density of neural networks by moving complexity from the networkarchitecture to the neuron itself.for Collabs contact: [email protected]