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.
Quantifying the dynamics of tumor burden reveals useful information about cancer evolution concerning treatment effects and drug resistance, which play a crucial role in advancing model-informed drug developments (MIDD) towards personalized medicine and precision oncology. The emergence of Quantum Machine Intelligence offers unparalleled insights into tumor dynamics via a quantum mechanics perspective. This paper introduces a novel hybrid quantum-classical neural architecture named
η−Net that enables quantifying quantum dynamics of tumor burden concerning treatment effects. We evaluate our proposed neural solution on two major use cases, including cohort-specific and patient-specific modeling. In silico numerical results show a high capacity and expressivity of
η−Net to the quantified biological problem. Moreover, the close connection to representation learning - the foundation for successes of modern AI, enables efficient transferability of empirical knowledge from relevant cohorts to targeted patients. Finally, we leverage Bayesian optimization to quantify the epistemic uncertainty of model predictions, paving the way for
η−Net towards reliable AI in decision-making for clinical usages.
A neural network architecture suitable for learning and generalization is discussed and developed. The architecture is inspired and modeled after quantum electronic devices and circuits where coherent electronic wavefunctions traveling through different parts of the circuit are combined together and result in interferences at detection nodes. These wavefunctions, represented by complex numbers, are implemented as complex weights in our neural net architecture to efficiently and accurately facilitate certain computations. Although similar to the radial basis function (RBF) net, our computational model called quantum net (QN) has demonstrated a considerable gain in performance and efficiency in number of applications compared to RBF net. Its better performance in classification tasks is explained by the cross-product terms in internal representation of its basis functions introduced parsimoniously. These cross-products are the results of interferences naturally occurring in coherent electronic systems. Although we primarily discuss the software implementation of QN on Von Neuman computers, its hardware implementation is also briefly discussed. A number of examples, solved using QN and other networks, are used to illustrate the desirable characteristics of QN.