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Cheng-Fang Su

Publications and source records attributed to Cheng-Fang Su.

6 recordsLinked to original sources
arXiv2026

Sphere Retraction Normalizations

Residual connections are the de facto mechanism for training deep neural networks stably. Geodesic Normalization (GeoNorm) recasts them on a Riemannian manifold, orthogonalizing each layer output against the current hidden state and applying the resulting update through the Riemannian exponential map. Every hidden state thus keeps a constant $\ell_{2}$-norm, confining the residual stream to a hypersphere. The exponential map, however, is only one member of a broad family of retraction maps. We show that on the hypersphere this entire family collapses to a single scalar design choice. What distinguishes one retraction from another is only how the magnitude of an update is converted into a rotation angle within the plane spanned by the hidden state and the update. This view places Euclidean residual connections and GeoNorm in one framework. Instantiating it with the metric projection retraction and the Cayley retraction yields Proj-SpheretNorm and Cay-SpheretNorm, which are exactly norm-preserving yet require only algebraic operations. Both prove to be members of a one-parameter family of angular retractions, $p$-SpheretNorm, whose rotation angle saturates rather than growing without bound. The two methods above are recovered exactly at $p = 1$ and $p = 2$, while the identity map and GeoNorm arise only as limits at either end. On nanoGPT, all three methods outperform existing lightweight deep connection schemes, and the best validation loss is attained at finite $p$, indicating that the exponential map is not the preferred retraction for spherical residual streams but merely one end of a spectrum.

cs.LG↗
arXiv2026

Real analytic solutions to the divergence equation

In this paper, we develop a differential-topological method to yield explicit real analytic solutions $v$ to the divergence equation $div_{\mathbb{R}^n} v = f$ on any annali $A(R_1 ,R_2) = \{ x \in \mathbb{R}^n : R_1 < |x| < R_2\}$, with $n \geq 2$, and $0 < R_1 < R_2 < \infty$. The prescribed source term $f$ is supposed to be real analytic on $\overline{A(R_1 , R_2)} = \{ x \in \mathbb{R}^n : R_1 \leq |x| \leq R_2\}$ satisfying the zero integral condition on $A(R_1, R_2)$. The resulting solution $v$ is a real analytic vector field on $\overline{A(R_1 , R_2)}$, which vanishes on $\partial \big( A(R_1, R_2 ) \big )$. The method which we develop here is different from the standard Bogovski approach and the Kapitanskii-Pileckas approach. The first main step our method is a clever differential-topological argument, which we develop under the inspiration and guidance of the standard proof of the cohomological statement $H_c^n \big ( \mathbb{R}^n\big ) = \mathbb{R}$ in Spviak book A Comprehensive Introduction to Differential Geometry, Vol I. This allows us to reduce the problem to that of solving a linear algebra problem.

math.AP↗
arXiv2025

Relativistic Quantum Simulation of Hydrogen Sulfide for Hydrogen Energy via Hybrid Quantum-Classical Algorithms

We present a relativistic quantum simulation framework for modeling hydrogen sulfide (H2S) decomposition relevant to hydrogen energy applications. The approach integrates Dirac-Coulomb relativistic quantum chemistry with the variational quantum eigensolver (VQE), implemented on a hybrid quantum-classical architecture. Using quantum algorithms based on Jordan-Wigner encoding and relativistic integrals, we simulate ground-state energies and potential energy surfaces for H2, H2O, and H2S molecules. Results demonstrate that the relativistic VQE correctly reproduces known energy shifts and molecular trends. Optimizer performance, energy variance, and Pauli term complexity are also evaluated. The findings offer insight into scalable quantum simulations of chemically and physically significant systems involving heavy atoms.

quant-ph↗
arXiv2025

Comparative Analysis of Quantum Support Vector Machines and Variational Quantum Classifiers for B-cell Epitope Prediction in Vaccine Design

Quantum computing offers new opportunities for addressing complex classification tasks in biomedical applications. This study investigates two quantum machine learning models-the Quantum Support Vector Machine (QSVM) and the Variational Quantum Classifier (VQC)-in the context of B-cell epitope prediction, a key step in modern vaccine design. QSVM builds upon the classical SVM framework by using quantum circuits to encode nonlinear kernel computations, while VQC replaces the entire classification pipeline with trainable quantum circuits optimized variationally. A benchmark dataset from the Immune Epitope Database (IEDB) is used for model evaluation. Each epitope is represented by 10 physicochemical features, and dimensionality reduction via Principal Component Analysis (PCA) is applied to assess model performance across different feature spaces. We also examine the effect of sample size on prediction outcomes. Experimental results show that QSVM performs well under limited data conditions, while VQC achieves higher accuracy in larger datasets. These findings highlight the potential of quantum-enhanced models for bioinformatics tasks, particularly in supporting efficient and scalable epitope-based vaccine development.

quant-ph↗
arXiv2023

Certified Robustness of Quantum Classifiers against Adversarial Examples through Quantum Noise

Recently, quantum classifiers have been found to be vulnerable to adversarial attacks, in which quantum classifiers are deceived by imperceptible noises, leading to misclassification. In this paper, we propose the first theoretical study demonstrating that adding quantum random rotation noise can improve robustness in quantum classifiers against adversarial attacks. We link the definition of differential privacy and show that the quantum classifier trained with the natural presence of additive noise is differentially private. Finally, we derive a certified robustness bound to enable quantum classifiers to defend against adversarial examples, supported by experimental results simulated with noises from IBM's 7-qubits device.

quant-ph↗