Quantum-Inspired Probability Folding Network (QPF-Net): A Novel Neural Network Architecture for High-Dimensional Feature Compression and Representation

Jincheng Zhang

Published Jul 11, 2026• 0 citations

Abstract

With the widespread application of deep learning across various domains, conventional neural networks face increasingly severe challenges in handling high-dimensional complex probability distributions, model compression, and non-linear feature extraction. To overcome these bottlenecks, this paper proposes a novel network architecture named the Quantum-Inspired Probability Folding Network (QPF-Net). Drawing inspiration from the state space theory and wave function collapse mechanism in quantum mechanics, this network innovatively maps continuous or discrete probability distributions into "folding state representations" within the complex vector space. By designing unique folding and unfolding operators, QPF-Net achieves ultra-high feature compression and non-linear reconstruction of high-dimensional probabilistic features in an extremely low-dimensional space. This paper provides an in-depth exploration of the theoretical foundations, network topology, and the mathematical mechanisms of forward and backward propagation of QPF-Net based on Wirtinger calculus. Theoretical analysis and mathematical derivations demonstrate that QPF-Net maintains an exceptionally high feature compression ratio while exhibiting powerful expressiveness and flexibility in non-linear mapping. This work delivers a brand-new quantum-inspired computational paradigm for the efficient feature representation and dimensionality reduction of large-scale complex systems.

DOI: 10.5281/zenodo.21304899

Related papers

Quantum-Inspired Neural Networks for Feature Extraction

Jincheng Zhang

This paper explores the potential of quantum-inspired neural networks (QINNs) for enhanced feature extraction. Traditional neural networks operate based on deterministic, sequential processing, limiting their ability to fully explore the vast space of possible feature combinations. We hypothesize that mimicking quantum superposition principles can significantly improve feature extraction capabilities. This work proposes a novel network architecture where nodes can exist in multiple states concurrently, allowing for parallel exploration of potential feature combinations. The core concept involves introducing probabilistic transitions between network states, mirroring the quantum phenomenon of superposition. Mathematical formulations detailing the network architecture and training process are presented. Preliminary analysis suggests that QINNs can achieve superior feature representations compared to conventional neural networks, particularly in scenarios demanding high dimensionality and complex feature interactions. The research aims to provide a foundational understanding of this new approach and pave the way for future investigations.

Aug 31, 20260 citations

基于量子概率模型的超深层神经网络

Jincheng Zhang

This paper explores the potential of utilizing quantum probabilistic models to enhance the efficiency and expressiveness of deep neural networks. Traditional deep learning architectures often struggle with high-dimensional data, necessitating computationally intensive operations. We propose a novel algorithm that integrates quantum probability models into the core computation process of neural networks. This integration leverages the inherent advantages of quantum mechanics, particularly superposition and entanglement, to improve representation learning and parameter estimation. The core mechanism involves mapping the neural network's activation functions and gradient computations into quantum states, allowing for parallel processing and potentially accelerating training and inference. We analyze the theoretical and practical implications of this approach, demonstrating its potential to overcome limitations associated with classical neural networks in specific scenarios. The research emphasizes the benefits of quantum-enhanced representations and efficient parameter estimation.

Sep 3, 20260 citations

Quantum-Inspired Neural Networks for Feature Selection

Jincheng Zhang

This paper explores the application of quantum-inspired neural networks (QINNs) for feature selection, addressing the limitations of classical feature selection techniques in high-dimensional datasets. Traditional methods frequently struggle to pinpoint truly relevant features, often relying on heuristics or statistical measures that can be misleading. We propose leveraging quantum-inspired algorithms, specifically amplitude amplification, to efficiently identify the most pertinent features. The core idea is to mimic the principles of quantum measurement, where a superposition of states collapses into a single, highly probable outcome. QINNs utilize a network architecture designed to emulate this process, iteratively amplifying the amplitudes associated with the relevant features while suppressing those of the irrelevant ones. The resulting feature selection process demonstrates the potential for improved accuracy and efficiency compared to conventional methods. We present a detailed framework for implementing QINNs for feature selection, outlining the network architecture, training methodology, and evaluation metrics. The theoretical underpinning of this approach is discussed, highlighting the connection to quantum measurement theory. The results of simulations and theoretical analysis demonstrate the efficacy of this method in identifying key features and reducing dimensionality while maintaining predictive performance.

Sep 2, 20260 citations

基于量子神经网络的非线性学习

Jincheng Zhang

Quantum Neural Networks (QNNs) offer a fundamentally different approach to neural network learning compared to classical networks, leveraging the unique properties of quantum mechanics. This paper investigates the potential of QNNs to achieve more efficient and powerful non-linear learning, particularly when handling high-dimensional data and complex patterns. We propose a novel algorithm that utilizes quantum entanglement and superposition to enhance the learning process and feature extraction capabilities. This work explores the potential of these quantum properties to overcome limitations inherent in current neural network architectures, specifically in areas requiring sophisticated pattern recognition. The core of our approach focuses on designing quantum units within the QNN architecture to facilitate enhanced learning and memory. The paper details the proposed algorithm, its theoretical underpinnings, and preliminary experimental results demonstrating its effectiveness in a simulated environment. We conclude with a discussion of future research directions, emphasizing the transformative potential of integrating quantum principles into neural network learning.

Sep 7, 20260 citations

Quantum-Inspired Neural Network Architectures for Symbolic Computation

Jincheng Zhang

This paper explores the potential of quantum-inspired neural network architectures for enhancing symbolic computation. Traditional neural networks often struggle with the inherent structure and logical reasoning required in symbolic tasks. We propose a novel framework leveraging principles from quantum mechanics—specifically non-locality and entanglement—to design neural networks that can more effectively perform symbolic manipulation and reasoning. The core idea involves introducing non-local connections and mimicking entanglement-like interactions within the network architecture. This approach aims to overcome limitations of conventional neural networks by incorporating probabilistic and interconnected representations reminiscent of quantum systems. The resulting architectures, termed Quantum-Inspired Neural Networks (QINNs), are hypothesized to offer improved efficiency and accuracy in symbolic computation, potentially bridging the gap between classical computation and quantum processing paradigms. We outline the key architectural components and theoretical underpinnings of QINNs, focusing on how they translate quantum concepts into a neural network setting. The goal is to demonstrate a viable pathway for harnessing quantum-inspired ideas to tackle complex symbolic problems.

Aug 29, 20260 citations

Fundamentals of Quantum-Inspired Neural Computing

Rebwar Khalid Muhammed, Aso Mohammed Aladdin, Rebwar Khalid Hamad +2 more

This chapter offers a clear and accessible introduction to the field of quantum-inspired neural computing. This area combines ideas from quantum mechanics with traditional neural network models to create new possibilities in machine learning and optimization metaheuristic algorithms. Unlike actual quantum computing, quantum-inspired approaches work on classical computers but borrow key concepts like superposition, entanglement, and probabilistic behaviour to improve how neural networks learn and process information. The study begins by explaining why researchers are interested in using quantum principles in neural networks. It then introduces the basic mathematical ideas behind these concepts, such as quantum states and transformations, and shows how they can be used to design more powerful and flexible learning systems. It focuses on discussing current models, outlining the distinctions between quantum-inspired and true quantum systems, and evaluating the potential benefits and challenges of this approach. In addition, Quantum-inspired neural computing introduces a novel framework that bridges classical artificial intelligence with principles derived from quantum mechanics. By simulating quantum behaviours on classical hardware, it opens new avenues for developing more adaptive and efficient learning models. This emerging approach offers promising advantages in areas such as optimization, parallel processing, and high-dimensional data representation. Finally, despite its potential, the field faces notable limitations and challenges. These include the lack of limited theoretical formalization, and difficulties in scaling models for complex real-world applications. Moreover, distinguishing genuine quantum-inspired advantages from conservative algorithmic improvements remains an current research apprehension.

CRC Press eBooksMay 20, 20260 citations