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Delu Zeng

Delu Zeng contributes to research discovery and scholarly infrastructure.

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Computer Vision Machine Learning math.NA Numerical Analysis eess.IV math.OC

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preprint2026arXiv

AQKA: Active Quantum Kernel Acquisition Under a Shot Budget

Estimating an $N \times N$ quantum kernel from circuit fidelities requires $Θ(N^2 S)$ measurement shots, the dominant bottleneck for deployment on near-term hardware. Existing budget-saving methods (Nyström-QKE, ShoFaR, kernel-target alignment) sub-sample \emph{which} entries to measure but allocate shots \emph{uniformly} within their chosen subset, ignoring how much each entry drives the downstream classifier. We close this gap with two contributions. \textbf{First, a complete regime decomposition} for shot-budgeted quantum kernel learning: a principled menu of when each allocator wins. Our method, \emph{AQKA}, dominates the budget-limited regime ($B \lesssim 16 n_{\mathrm{pairs}}$) on sparse-sensitivity KRR, with the gap \emph{growing} from $+8$ to $+25$ pts over uniform as $N$ scales $225{\to}1000$ and reaching $+26$--$32$ pts on an \texttt{ibm\_pittsburgh} (156-qubit Heron) hardware kernel; Nyström-QKE wins at saturating budgets on planted-sparse via low-rank reconstruction; ShoFaR is competitive only at extreme low budgets. \textbf{Second, a closed-form pair-level acquisition theory}: $s_{ij}^{\star} \propto |g_{ij}|\sqrt{K_{ij}(1-K_{ij})}$ with explicit gradient $g_{ij}$ for KRR (Lemma~1, $|β_iα_j+β_jα_i|\sqrt{K_{ij}(1-K_{ij})}$) and SVM via the envelope theorem ($|η_i^*η_j^*|\sqrt{K_{ij}(1-K_{ij})}$); a \emph{corrected} sparsity-aware Cauchy--Schwarz rate $ρ\le 2m/N$ matching empirics (vs.\ the naive $m^2/N^2$); an explicit-constant plug-in regret bound (Theorem~2); and a tighter SVM ceiling $ρ^{\mathrm{SVM}} \le m_{\mathrm{sv}}^2/N^2$. We close with the first multi-seed live online adaptive shot allocation on quantum hardware: $+17.0 \pm 4.8$ pts at $N{=}20$ on \texttt{ibm\_aachen} ($3.5σ$, 5 seeds), with the advantage holding at $N{=}30$ at higher budget on \texttt{ibm\_berlin} ($+14.0 \pm 8.5$ pts, 5 seeds).

preprint2026arXiv

Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation

In quantum machine learning (QML), classical data are often encoded as quantum pure states and processed directly as quantum representations, motivating representation-level generative modeling that samples new quantum states from an underlying pure-state ensemble rather than re-preparing them from perturbed classical inputs. However, extending \emph{score-based} diffusion models with well-defined reverse-time samplers to quantum pure-state ensembles remains challenging, due to the non-Euclidean geometry of the complex projective space $\mathbb{CP}^{d-1}$ and the intractability of transition densities. We propose \emph{Stochastic Schrödinger Diffusion Models} (SSDMs), an intrinsic score-based generative framework on $\mathbb{CP}^{d-1}$ endowed with the Fubini--Study (FS) metric. SSDMs formulate a forward Riemannian diffusion with a stochastic Schrödinger equation (SSE) realization, and derive reverse-time dynamics driven by the Riemannian score $\nabla_{\mathrm{FS}} \log p_t$. To enable training without analytic transition densities, we introduce a local-time objective based on a local Euclidean Ornstein--Uhlenbeck approximation in FS normal coordinates, yielding an analytic teacher score mapped back to the manifold. Experiments show that SSDMs faithfully capture target pure-state ensemble statistics, including observable moments, overlap-kernel MMD, and entanglement measures, and that SSDM-generated quantum representations improve downstream QML generalization via representation-level data augmentation.

preprint2022arXiv

Tighter Bound Estimation for Efficient Biquadratic Optimization Over Unit Spheres

Bi-quadratic programming over unit spheres is a fundamental problem in quantum mechanics introduced by pioneer work of Einstein, Schrödinger, and others. It has been shown to be NP-hard; so it must be solve by efficient heuristic algorithms such as the block improvement method (BIM). This paper focuses on the maximization of bi-quadratic forms, which leads to a rank-one approximation problem that is equivalent to computing the M-spectral radius and its corresponding eigenvectors. Specifically, we provide a tight upper bound of the M-spectral radius for nonnegative fourth-order partially symmetric (PS) tensors, which can be considered as an approximation of the M-spectral radius. Furthermore, we showed that the proposed upper bound can be obtained more efficiently, if the nonnegative fourth-order PS-tensors is a member of certain monoid semigroups. Furthermore, as an extension of the proposed upper bound, we derive the exact solutions of the M-spectral radius and its corresponding M-eigenvectors for certain classes of fourth-order PS-tensors. Lastly, as an application of the proposed bound, we obtain a practically testable sufficient condition for nonsingular elasticity M-tensors with strong ellipticity condition. We conduct several numerical experiments to demonstrate the utility of the proposed results. The results show that: (a) our proposed method can attain a tight upper bound of the M-spectral radius with little computational burden, and (b) such tight and efficient upper bounds greatly enhance the convergence speed of the BIM-algorithm, allowing it to be applicable for large-scale problems in applications.

preprint2022arXiv

TO-FLOW: Efficient Continuous Normalizing Flows with Temporal Optimization adjoint with Moving Speed

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on large datasets due to the incremental complexity of the neural ODE training. Optimal Transport theory has been applied to regularize the dynamics of the ODE to speed up training in recent works. In this paper, a temporal optimization is proposed by optimizing the evolutionary time for forward propagation of the neural ODE training. In this appoach, we optimize the network weights of the CNF alternately with evolutionary time by coordinate descent. Further with temporal regularization, stability of the evolution is ensured. This approach can be used in conjunction with the original regularization approach. We have experimentally demonstrated that the proposed approach can significantly accelerate training without sacrifying performance over baseline models.

preprint2021arXiv

Deep Learning for Scene Classification: A Survey

Scene classification, aiming at classifying a scene image to one of the predefined scene categories by comprehending the entire image, is a longstanding, fundamental and challenging problem in computer vision. The rise of large-scale datasets, which constitute the corresponding dense sampling of diverse real-world scenes, and the renaissance of deep learning techniques, which learn powerful feature representations directly from big raw data, have been bringing remarkable progress in the field of scene representation and classification. To help researchers master needed advances in this field, the goal of this paper is to provide a comprehensive survey of recent achievements in scene classification using deep learning. More than 200 major publications are included in this survey covering different aspects of scene classification, including challenges, benchmark datasets, taxonomy, and quantitative performance comparisons of the reviewed methods. In retrospect of what has been achieved so far, this paper is also concluded with a list of promising research opportunities.

preprint2021arXiv

Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning

Weak Gaussian perturbations on a plane wave background could trigger lots of rogue waves, due to modulational instability. Numerical simulations showed that these rogue waves seemed to have similar unit structure. However, to the best of our knowledge, there is no relative result to prove that these rogue waves have the similar patterns for different perturbations, partly due to that it is hard to measure the rogue wave pattern automatically. In this work, we address these problems from the perspective of computer vision via using deep neural networks. We propose a Rogue Wave Detection Network (RWD-Net) model to automatically and accurately detect RWs on the images, which directly indicates they have the similar computer vision patterns. For this purpose, we herein meanwhile have designed the related dataset, termed as Rogue Wave Dataset-$10$K (RWD-$10$K), which has $10,191$ RW images with bounding box annotations for each RW unit. In our detection experiments, we get $99.29\%$ average precision on the test splits of the RWD-$10$K dataset. Finally, we derive our novel metric, the density of RW units (DRW), to characterize the evolution of Gaussian perturbations and obtain the statistical results on them.

preprint2020arXiv

Ro-SOS: Metric Expression Network (MEnet) for Robust Salient Object Segmentation

Although deep CNNs have brought significant improvement to image saliency detection, most CNN based models are sensitive to distortion such as compression and noise. In this paper, we propose an end-to-end generic salient object segmentation model called Metric Expression Network (MEnet) to deal with saliency detection with the tolerance of distortion. Within MEnet, a new topological metric space is constructed, whose implicit metric is determined by the deep network. As a result, we manage to group all the pixels in the observed image semantically within this latent space into two regions: a salient region and a non-salient region. With this architecture, all feature extractions are carried out at the pixel level, enabling fine granularity of output boundaries of the salient objects. What's more, we try to give a general analysis for the noise robustness of the network in the sense of Lipschitz and Jacobian literature. Experiments demonstrate that robust salient maps facilitating object segmentation can be generated by the proposed metric. Tests on several public benchmarks show that MEnet has achieved desirable performance. Furthermore, by direct computation and measuring the robustness, the proposed method outperforms previous CNN-based methods on distorted inputs.

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