arXiv subjects

Hao Duan

Publications and source records attributed to Hao Duan.

13 recordsLinked to original sources

arXiv2026

Robustness Verification of Polynomial Neural Networks

We study robustness verification of neural networks via metric algebraic geometry. For polynomial neural networks, certifying a robustness radius amounts to computing the distance to the algebraic decision boundary. We use the Euclidean distance (ED) degree as an intrinsic measure of the complexity of this problem, analyze the associated ED discriminant, and introduce a parameter discriminant that detects parameter values at which the ED degree drops. We derive formulas for the ED degree for several network architectures and characterize the expected number of real critical points in the infinite-width limit. We develop symbolic elimination methods to compute these quantities and homotopy-continuation methods for exact robustness certification. Finally, experiments on lightning self-attention modules reveal decision boundaries with strictly smaller ED degree than generic cubic hypersurfaces of the same ambient dimension.

stat.ML↗

arXiv2026

Algebraic Invariants of Lightning Self-Attention

We study the polynomial coefficients of lightning self-attention as coordinates of an algebraic variety. In the single-token case, we characterize the coefficient variety as a rank-constrained Chow-type variety and derive algebraic equations from this description. For multiple tokens, linear relations reduce the nonlinear geometry to coefficients involving interactions between distinct tokens. We characterize the resulting variety by a common linear factor together with a low-rank condition on the remaining factors. This structure yields explicit families of determinantal, Veronese-type, and Sylvester resultant-based invariants. In the rank-one case, natural pencil and flattening equations define the variety set-theoretically. We complement these results with computations in small dimensions, where the theoretical constructions recover the generators of the defining ideals. Overall, the paper gives a structural description of the algebraic constraints imposed on polynomial coefficient arrays by lightning self-attention and provides explicit certificates of non-realizability.

math.AG↗

arXiv2025

PGTuner: An Efficient Framework for Automatic and Transferable Configuration Tuning of Proximity Graphs

Approximate Nearest Neighbor Search (ANNS) plays a crucial role in many key areas. Proximity graphs (PGs) are the leading method for ANNS, offering the best balance between query efficiency and accuracy. However, their performance heavily depends on various construction and query parameters, which are difficult to optimize due to their complex inter-dependencies. Given that users often prioritize specific accuracy levels, efficiently identifying the optimal PG configurations to meet these targets is essential. Although some studies have explored automatic configuration tuning for PGs, they are limited by inefficiencies and suboptimal results. These issues stem from the need to construct numerous PGs for searching and re-tuning from scratch whenever the dataset changes, as well as the failure to capture the complex dependencies between configurations, query performance, and tuning objectives. To address these challenges, we propose PGTuner, an efficient framework for automatic PG configuration tuning leveraging pre-training knowledge and model transfer techniques. PGTuner improves efficiency through a pre-trained query performance prediction (QPP) model, eliminating the need to build multiple PGs. It also features a deep reinforcement learning-based parameter configuration recommendation (PCR) model to recommend optimal configurations for specific datasets and accuracy targets. Additionally, PGTuner incorporates out-of-distribution detection and deep active learning for efficient tuning in dynamic scenarios and transferring to new datasets. Extensive experiments demonstrate that PGTuner can stably achieve the top-level tuning effect across different datasets while significantly improving tuning efficiency by up to 14.69X, with a 14.64X boost in dynamic scenarios. The code and data for PGTuner are available online at https://github.com/hao-duan/PGTuner.

cs.DB↗

arXiv2025

Understanding Learning Invariance in Deep Linear Networks

Equivariant and invariant machine learning models exploit symmetries and structural patterns in data to improve sample efficiency. While empirical studies suggest that data-driven methods such as regularization and data augmentation can perform comparably to explicitly invariant models, theoretical insights remain scarce. In this paper, we provide a theoretical comparison of three approaches for achieving invariance: data augmentation, regularization, and hard-wiring. We focus on mean squared error regression with deep linear networks, which parametrize rank-bounded linear maps and can be hard-wired to be invariant to specific group actions. We show that the critical points of the optimization problems for hard-wiring and data augmentation are identical, consisting solely of saddles and the global optimum. By contrast, regularization introduces additional critical points, though they remain saddles except for the global optimum. Moreover, we demonstrate that the regularization path is continuous and converges to the hard-wired solution.

stat.ML↗

arXiv2025

Joint Modelling Histology and Molecular Markers for Cancer Classification

Cancers are characterized by remarkable heterogeneity and diverse prognosis. Accurate cancer classification is essential for patient stratification and clinical decision-making. Although digital pathology has been advancing cancer diagnosis and prognosis, the paradigm in cancer pathology has shifted from purely relying on histology features to incorporating molecular markers. There is an urgent need for digital pathology methods to meet the needs of the new paradigm. We introduce a novel digital pathology approach to jointly predict molecular markers and histology features and model their interactions for cancer classification. Firstly, to mitigate the challenge of cross-magnification information propagation, we propose a multi-scale disentangling module, enabling the extraction of multi-scale features from high-magnification (cellular-level) to low-magnification (tissue-level) whole slide images. Further, based on the multi-scale features, we propose an attention-based hierarchical multi-task multi-instance learning framework to simultaneously predict histology and molecular markers. Moreover, we propose a co-occurrence probability-based label correlation graph network to model the co-occurrence of molecular markers. Lastly, we design a cross-modal interaction module with the dynamic confidence constrain loss and a cross-modal gradient modulation strategy, to model the interactions of histology and molecular markers. Our experiments demonstrate that our method outperforms other state-of-the-art methods in classifying glioma, histology features and molecular markers. Our method promises to promote precise oncology with the potential to advance biomedical research and clinical applications. The code is available at https://github.com/LHY1007/M3C2

cs.CV↗

arXiv2024

Time Series Diffusion Method: A Denoising Diffusion Probabilistic Model for Vibration Signal Generation

Diffusion models have demonstrated powerful data generation capabilities in various research fields such as image generation. However, in the field of vibration signal generation, the criteria for evaluating the quality of the generated signal are different from that of image generation and there is a fundamental difference between them. At present, there is no research on the ability of diffusion model to generate vibration signal. In this paper, a Time Series Diffusion Method (TSDM) is proposed for vibration signal generation, leveraging the foundational principles of diffusion models. The TSDM uses an improved U-net architecture with attention block, ResBlock and TimeEmbedding to effectively segment and extract features from one-dimensional time series data. It operates based on forward diffusion and reverse denoising processes for time-series generation. Experimental validation is conducted using single-frequency, multi-frequency datasets, and bearing fault datasets. The results show that TSDM can accurately generate the single-frequency and multi-frequency features in the time series and retain the basic frequency features for the diffusion generation results of the bearing fault series. It is also found that the original DDPM could not generate high quality vibration signals, but the improved U-net in TSDM, which applied the combination of attention block and ResBlock, could effectively improve the quality of vibration signal generation. Finally, TSDM is applied to the small sample fault diagnosis of three public bearing fault datasets, and the results show that the accuracy of small sample fault diagnosis of the three datasets is improved by 32.380%, 18.355% and 9.298% at most, respectively.

cs.LG↗

arXiv2022

Enhanced proton-boron nuclear fusion cross sections in intense high-frequency laser

We investigate the proton-boron nuclear fusion cross sections under the influence of the intense linearly polarized monochromatic laser fields with high frequency. First, we rewrite the time-dependent Schrödinger equation using Kramers-Henneberger (KH) transformation which allows for shifting all time dependence of the problem into the potential function. Then, for the intense laser fields that satisfy the high frequency limit, the time-averaged scheme in the KH framework should be valid. We can use WKB approximation to evaluate Coulomb barrier penetrability and then calculate proton-boron nuclear fusion cross sections by a phenomenological Gamow form. We show that the corresponding Coulomb barrier penetrability increases significantly due to the depression of the time-averaged potential barrier. As a result, we find that proton-boron nuclear fusion cross sections can be enhanced effectively depending on a dimensionless quantity $n_{\mathrm{d}}$, which equals the ratio of the quiver oscillation amplitude to the geometrical touching radius of the proton and boron nucleus. For $n_{\mathrm{d}}=9$, we predict that the resonance peak of the fusion cross-section is enhanced by about $26$ times at the incident energy of $\varepsilon=148$ keV. And for another incident energy of $\varepsilon=586$ keV, the resonance peak of fusion cross-section is not only enhanced but also shifted to lower energy of $\varepsilon=392$ keV due to the mechanism of over-barrier fusion.

nucl-th↗

arXiv2021

Resonant tunneling of deuteron-triton fusion in strong high-frequency electromagnetic fields

We investigate deuteron-triton (DT) fusion in the presence of linearly polarized strong electromagnetic fields in high-frequency limit, in which a complex spherical square-well potential is exploited to describe the nuclear potential. Within the framework of the Kramers-Henneberger (KH) transformation, we have calculated the total and angular differential fusion cross sections by investigating the asymptotical phase shifts of the Coulomb wavefunctions. With introducing a dimensionless quantity of $n_d$ representing the ratio of the particle quiver oscillation amplitude to the radius of nuclear potential, we find that, even though the tunneling probability of passing through the Coulomb repulsive potential keeps almost identical to that in the absence of electromagnetic fields, the peak of total fusion sections shows an apparent shift from the well known value of 110 keV to 78 keV for $n_d=0.01$. The angular differential cross sections also show some resonance peaks that shift from zero inclination angle to $π/2$ with increasing the parameter $n_d$. The corresponding astrophysical $S$-factors are found to be enhanced by several times in amplitudes. With the help of Wentzel-Kramers-Brillouin (WKB) approximate wavefunctions, the shape-resonance tunneling mechanism of the above findings are uncovered and some implications are discussed.

nucl-th↗

arXiv2021

Optical potential parameters of light nuclear fusion based on precise Coulomb wave functions

Based on precise Coulomb wave functions (CWFs), we attempt to calculate the fusion cross sections of light nuclei in a complex spherical square-well nuclear potential (i.e., optical potential model). Comparing with experimental benchmark cross section data, we can calibrate optical potential parameters associated with D+D, D+T, D+3He, p+D, p+6Li and p+7Li fusion reactions. Surprisingly, we find that our calculated optical potential parameters are quite different from those of many previous results (e.g., Phys. Rev. C. 61 (2000) 024610, Nucl. Phys. A 986 (2019) 98, etc.), in which approximate Coulomb wave functions (ACWFs) with only retaining the leading terms are exploited for the continuity conditions at the radius of nuclear potential. Furthermore, with the obtained optical potential parameters, we compare the fusion cross sections and astrophysical S-factors with that formulated from ACWFs approach, and also find apparent deviations especially for the fusion reactions with resonance peaks such as D+T and D+3He fusion reactions. We then calculate the phase diagrams of the fusion cross sections with respect to the optical potential parameters and demonstrate several narrow shape resonance belts. It implies that a small deviation of ACWFs from the exact CWFs at nuclear radius might lead to fall off the resonance regimes and therefore causes the big difference on the optical parameters as well as the cross sections.

nucl-th↗

arXiv2021

Phase-dependent cross sections of deuteron-triton fusion in dichromatic intense fields with high-frequency limit

We investigate the influence of strong dichromatic laser fields (i.e. 1ω-2ω and 1ω-3ω) with high-frequency limit on the cross sections of deuteron-triton(DT) fusion in Kramers-Henneberger(KH) frame. We focus on the transitions of phase-dependent effects depending on a dimensionless quantity n_{d} , which equals the ratio of the quiver oscillation amplitude to the geometrical touching radius of the deuteron and triton as defined in our previous research. Theoretical calculations show that the angle-dependent as well as phase-dependent Coulomb barrier penetrabilities can be enhanced in dichromatic intense fields, and the corresponding angle-averaged penetrabilities and the fusion cross sections increase significantly compared with field-free case. Moreover, we find that there are twice shifts of the peak in the cross sections whenever the frequency becomes sufficiently low or the intensity sufficiently high. The reason for the first shift is the angle-dependence effects for sub-barrier fusion, while the second shift is due to the accumulation of over-barrier fusion, these mechanisms are analyzed in detail in this paper.

nucl-th↗

arXiv2021

Deuterium-tritium fusion process in strong laser fields: Semiclassical simulation

In this paper, we investigate the deuterium-tritium (DT) fusion process in the presence of strong laser fields with a semiclassical (SC) method. In this model, two nuclei with a given incident kinetic energy that closely approach each other are simulated by tracing the classical Newtonian trajectories in the combined Coulomb repulsive potentials and laser fields. At the nearest position or classical turning point, quantum tunneling through the Coulomb barrier emerges, and its penetrability is estimated with the Wentzel-Kramers-Brillouin formula. Nuclear fusion occurs after the tunneling, and the total fusion cross section takes the Gamow form. We find that the tunneling penetrability can be enhanced dramatically because the nuclei can closely approach each other due to the quiver motion of the charged nuclei driven by the intense laser fields. We then calculate the DT fusion section for a wide range of laser parameters according to various incident nuclei kinetic energies and obtain the phase diagrams for the enhanced DT fusion. We compare our SC results with the quantum results of the Kramers-Henneberger approximation and the Volkov state approximation.

nucl-th↗

arXiv2021

Dissecting the Performance of Chained-BFT

Permissioned blockchains employ Byzantine fault-tolerant (BFT) state machine replication (SMR) to reach agreement on an ever-growing, linearly ordered log of transactions. A new paradigm, combined with decades of research in BFT SMR and blockchain (namely chained-BFT, or cBFT), has emerged for directly constructing blockchain protocols. Chained-BFT protocols have a unifying propose-vote scheme instead of multiple different voting phases with a set of voting and commit rules to guarantee safety and liveness. However, distinct voting and commit rules impose varying impacts on performance under different workloads, network conditions, and Byzantine attacks. Therefore, a fair comparison of the proposed protocols poses a challenge that has not yet been addressed by existing work. We fill this gap by studying a family of cBFT protocols with a two-pronged systematic approach. First, we present an evaluation framework, Bamboo, for quick prototyping of cBFT protocols and that includes helpful benchmarking facilities. To validate Bamboo, we introduce an analytic model using queuing theory which also offers a back-of-the-envelope guide for dissecting these protocols. We build multiple cBFT protocols using Bamboo and we are the first to fairly compare three representatives (i.e., HotStuff, two-chain HotStuff, and Streamlet). We evaluated these protocols under various parameters and scenarios, including two Byzantine attacks that have not been widely discussed in the literature. Our findings reveal interesting trade-offs (e.g., responsiveness vs. forking-resilience) between different cBFT protocols and their design choices, which provide developers and researchers with insights into the design and implementation of this protocol family.

cs.CR↗

arXiv2013

Ultracold collision in the presence of synthetic spin-orbit coupling

We present an analytic description of ultracold collision between two spin-$\frac{1}{2}$ fermions with isotropic spin-orbit coupling of the Rashba type. We show that regardless of how weak the spin-orbit coupling may be, the ultracold collision at sufficiently low energies is significantly modified, including the ubiquitous Wigner threshold behavior. We further show that the particles are preferably scattered into the lower-energy helicity state due to the break of parity conservation, thus establishing interaction with spin-orbit coupling as one mechanism for the spontaneous emergence of handedness.

physics.atom-ph↗