arXiv subjects

Zhaoqi Zhou

Publications and source records attributed to Zhaoqi Zhou.

4 recordsLinked to original sources

arXiv2026

Score Approximation for Diffusion Models on Arbitrary Low-Dimensional Structures

The remarkable success of score-based diffusion models has spurred significant efforts to establish their theoretical foundations. However, existing complexity bounds for score approximation rely heavily on restrictive assumptions like Lipschitz continuous densities or smooth manifold supports, which are routinely violated by the singularities, sharp boundaries, and disjoint clusters inherent to real-world perceptual data. This work establishes a universal score approximation theorem that works for any distribution supported on any compact set of upper Minkowski dimension $d$. Using a novel discrete-mixture formulation, we prove that the score function can be approximated with a ReLU network whose complexity grows exponentially only with $d$, thus breaking the exponential curse of ambient dimensionality. Combined with existing theories on accurately solving the backward diffusion SDE for arbitrary compact distributions, our work shows that diffusion models readily adapt to irregular, non-smooth data structures, explaining their competence in real-world generative tasks.

cs.LG↗

arXiv2026

Sparse Neighborhood Graph-Based Approximate Nearest Neighbor Search Revisited: Theoretical Analysis and Optimization

Graph-based approaches to approximate nearest neighbor search (ANNS) enable fast, high-recall retrieval on billion-scale vector datasets. Among them, the Sparse Neighborhood Graph (SNG) is widely used due to its strong search performance. However, the lack of theoretical understanding of SNG leads to expensive tuning of the truncation parameter that controls graph sparsification. In this work, we present OPT-SNG, a principled framework for analyzing and optimizing SNG construction. We introduce a martingale-based model of the pruning process that characterizes the stochastic evolution of candidate sets during graph construction. Using this framework, we prove that SNG has a maximum out-degree of $O(n^{2/3+ε})$, where $ε>0$ is an arbitrarily small constant, and an expected search path length of $O(\log n)$. Building on these insights, we derive a closed-form rule for selecting the optimal truncation parameter $R$, thereby eliminating the need for costly parameter sweeping. Extensive experiments on real-world datasets demonstrate that OPT-SNG achieves an average $5.9\times$ speedup in index construction time, with peak improvements reaching $15.4\times$, while consistently maintaining or improving search performance.

cs.DS↗

arXiv2025

Downsizing Diffusion Models for Cardinality Estimation

Learned cardinality estimation requires accurate model designs to capture the local characteristics of probability distributions. However, existing models may fail to accurately capture complex, multilateral dependencies between attributes. Diffusion models, meanwhile, can succeed in estimating image distributions with thousands of dimensions, making them promising candidates, but their heavy weight and high latency prohibit effective implementation. We seek to make diffusion models more lightweight by introducing Accelerated Diffusion Cardest (ADC), the first "downsized" diffusion model framework for efficient, high-precision cardinality estimation. ADC utilizes a hybrid architecture that integrates a Gaussian Mixture-Bayesnet selectivity estimator with a score-based density estimator to perform precise Monte Carlo integration. Addressing the issue of prohibitive inference latencies common in large generative models, we provide theoretical advancements concerning the asymptotic behavior of score functions as time $t$ approaches zero and convergence rate estimates as $t$ increases, enabling the adaptation of score-based diffusion models to the moderate dimensionalities and stringent latency requirements of database systems. Through experiments conducted against five learned estimators, including the state-of-the-art Naru, we demonstrate that ADC offer superior robustness when handling datasets with multilateral dependencies, which cannot be effectively summarized using pairwise or triple-wise correlations. In fact, ADC is 10 times more accurate than Naru on such datasets. Additionally, ADC achieves competitive accuracy comparable to Naru across all tested datasets while maintaining latency half that of Naru's and requiring minimal storage (<350KB) on most datasets.

cs.DB↗

arXiv2015

Explicit non-canonical symplectic algorithms for charged particle dynamics

We study the non-canonical symplectic structure, or K-symplectic structure inherited by the charged particle dynamics. Based on the splitting technique, we construct non-canonical symplectic methods which is explicit and stable for the long-term simulation. The key point of splitting is to decompose the Hamiltonian as four parts, so that the resulting four subsystems have the same structure and can be solved exactly. This guarantees the K-symplectic preservation of the numerical methods constructed by composing the exact solutions of the subsystems. The error convergency of numerical solutions is analyzed by means of the Darboux transformation. The numerical experiment display the long-term stability and efficiency for these methods.

physics.comp-ph↗