Author

Cheng-Hua Liu

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Preprint Jul 2026

Rank-Independent Spectral Hypergraph Sparsification via Global-Dictionary Chaining

The rank-independent theorem sharpens many later guarantees that inherit their sampling bounds by strengthening the independent STOC 2023 works of Lee and Jambulapati--Liu--Sidford by removing their rank dependence and answering Lee's open question on whether this loss is inherent.

Chenghua Liu, Yuxin Zhang · 0 citations

Preprint Jul 2026

A Correlation-Gap Bound for Nonlinear Gaussian PCA

A dimension-free version of the retained-energy form of the Mallat--Zeitouni conjecture is established, showing that the KL basis is within this factor of the optimal basis, and shows that the possible advantage of optimizing over all orthonormal bases vanishes as $d$ grows.

Minbo Gao, Zheng-Feng Ji, Cheng-Hua Liu · 0 citations