Gao Huang

Ziwei Zheng, Zechuan Zhang, Yulin Wang et al.

Generic event boundary detection (GEBD), inspired by human visual cognitive behaviors of consistently segmenting videos into meaningful temporal chunks, finds utility in various applications such as video editing and. In this paper, we demonstrate that SOTA GEBD models often prioritize final performance over model complexity, resulting in low inference speed and hindering efficient deployment in real-world scenarios. We contribute to addressing this challenge by experimentally reexamining the architecture of GEBD models and uncovering several surprising findings. Firstly, we reveal that a concise GEBD baseline model already achieves promising performance without any sophisticated design. Secondly, we find that the widely applied image-domain backbones in GEBD models can contain plenty of architecture redundancy, motivating us to gradually ``modernize'' each component to enhance efficiency. Thirdly, we show that the GEBD models using image-domain backbones conducting the spatiotemporal learning in a spatial-then-temporal greedy manner can suffer from a distraction issue, which might be the inefficient villain for GEBD. Using a video-domain backbone to jointly conduct spatiotemporal modeling is an effective solution for this issue. The outcome of our exploration is a family of GEBD models, named EfficientGEBD, significantly outperforms the previous SOTA methods by up to 1.7\% performance gain and 280\% speedup under the same backbone. Our research prompts the community to design modern GEBD methods with the consideration of model complexity, particularly in resource-aware applications. The code is available at \url{https://github.com/Ziwei-Zheng/EfficientGEBD}.

Gao Huang, Song Li

This note demonstrates that we can stably recover all symmetric Toeplitz matrices $\pmb{X}_0\in\mathbb{R}^{n\times n}$ of rank at most $r$ from a number of rank-one subgaussian measurements on the order of $r\log^{2} n$ with an exponentially decreasing failure probability by employing a nuclear norm minimization program. Our approach utilizes descent cone analysis through Mendelson's small ball method with the Toeplitz constraint. The key ingredient is to determine the spectral norm of a random matrix with Toeplitz structure, which may be of independent interest. This improves upon earlier analyses and resolves the conjecture in Chen et al. (IEEE Transactions on Information Theory, 61(7):4034--4059, 2015).

Gao Huang, Song Li

In this paper, we first propose a unified framework for analyzing the stability of the phaseless operators for both amplitude and intensity measurement on an arbitrary geometric set, thereby characterizing the robust performance of phase retrieval via the empirical minimization method. We introduce the random embedding of concave lifting operators to characterize the unified analysis of any geometric set. Similarly, we investigate the robust performance of structured matrix restoration problem through the robust injectivity of a linear rank one measurement operator on an arbitrary matrix set. The core of our analysis is to establish unified empirical chaos processes characterization for various matrix sets. Talagrand's $γ_α$-functionals are employed to characterize the connection between the geometric constraints and the number of measurements required for stability or robust injectivity. We also construct adversarial noise to demonstrate the sharpness of the recovery bounds derived through the empirical minimization method in the both scenarios.