arXiv subjects

Yuchen Cong

Publications and source records attributed to Yuchen Cong.

3 recordsLinked to original sources

arXiv2026

On the Approximation Complexity of Matrix Product Operator (MPO) Born Machines

Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, yet their approximation capabilities remain poorly understood in theory. In this paper, we characterize these capabilities from both negative and positive perspectives. As a negative result, we prove that constructing a polynomial-bond MPO-BM approximation to an arbitrary continuous target with bounded KL error is NP-hard. On the positive side, for score-based variational inference, we prove that targets satisfying a log-Sobolev inequality admit polynomial-bond MPO-BM approximations with provable KL guarantees when the loss-induced Hamiltonian is local and has a constant spectral gap. Furthermore, under the same conditions, we construct local importance-sampling estimators and prove that polynomially many local score queries suffice to preserve the KL guarantees.

cs.LG↗

arXiv2026

QuanVI: Score-based Variational Inference via Quantum Maximally Mixed States

Score-based variational inference (VI) provides an alternative to Kullback--Leibler (KL)-based VI by minimizing the Fisher divergence between the variational distribution and the target. A prior score-VI approach formulates this optimization as an eigenvalue problem, with the variational distribution constructed from low-energy eigenstates. However, this eigenvalue-based formulation faces two high-dimensional obstacles: an intractably large parameter count due to exponential scaling and non-uniqueness of individual eigenvectors in degenerate or nearly degenerate low-energy subspaces. We propose QuanVI, a scalable quantum-inspired algorithm that combines a mixed-state density-operator formulation with a quantum tensor network (QTN) parameterization using the matrix product operator (MPO) structure. In degenerate low-energy subspaces, the density-operator formulation represents the subspace by its maximally mixed state rather than relying on a non-unique individual eigenvector, while the QTN parameterization compresses the density operator to avoid exponential parameter growth. Experiments and ablations show that QuanVI agrees with exact solutions in low dimensions and scales to high-dimensional synthetic and Bayesian posterior-approximation benchmarks, including challenging non-Gaussian targets.

cs.LG↗

arXiv2019

Color Recognition for Rubik's Cube Robot

In this paper, we proposed three methods to solve color recognition of Rubik's cube, which includes one offline method and two online methods. Scatter balance \& extreme learning machine (SB-ELM), a offline method, is proposed to illustrate the efficiency of training based method. We also point out the conception of color drifting which indicates offline methods are always ineffectiveness and can not work well in continuous change circumstance. By contrast, dynamic weight label propagation is proposed for labeling blocks color by known center blocks color of Rubik's cube. Furthermore, weak label hierarchic propagation, another online method, is also proposed for unknown all color information but only utilizes weak label of center block in color recognition. We finally design a Rubik's cube robot and construct a dataset to illustrate the efficiency and effectiveness of our online methods and to indicate the ineffectiveness of offline method by color drifting in our dataset.

cs.CV↗