Xinran Ma

Xinran Ma, Zhaoqi Zhou, Chuan Zhou et al.

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.

Xinran Ma, Z. C. Tu, Shi-Ju Ran

Human experts cannot efficiently access the physical information of quantum many-body states by simply "reading" the coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. In this work, we demonstrate that convolutional neural network (CNN) can learn from the coefficients of local reduced density matrices to estimate the physical parameters of the many-body Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states (or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work illuminates a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generalizations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.