What question did this study set out to answer?

The aim is to address the limitations of traditional neural networks in solving non-linear problems.

February 19, 20260 citationsOpen Access

A Spectral Energy Unit for Non-Linear Logic and Regression

Key Points

The aim is to address the limitations of traditional neural networks in solving non-linear problems.
Introduction of the Quantum-Inspired Neuron (QIN) based on Euler’s formula.
Utilization of Vectorized Spectral Calculus for processing inputs as phase angles.
Conducting tests to evaluate the performance of QIN on the XOR problem and regression tasks.
QIN achieved over 99% accuracy on the XOR problem.
Demonstrated mean squared error (MSE) less than 0.07 in non-linear regression.
Showed a memory capacity of 15 distinct patterns in 2D space, surpassing standard perceptron limits by 5 times.

Abstract

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: shubi.shubham.malik@gmail.com

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