Hongjie Chen

Hongjie Chen, Tommaso d'Orsi

We consider the robust linear regression model $\boldsymbol{y} = Xβ^* + \boldsymbolη$, where an adversary oblivious to the design $X \in \mathbb{R}^{n \times d}$ may choose $\boldsymbolη$ to corrupt all but a (possibly vanishing) fraction of the observations $\boldsymbol{y}$ in an arbitrary way. Recent work [dLN+21, dNS21] has introduced efficient algorithms for consistent recovery of the parameter vector. These algorithms crucially rely on the design matrix being well-spread (a matrix is well-spread if its column span is far from any sparse vector). In this paper, we show that there exists a family of design matrices lacking well-spreadness such that consistent recovery of the parameter vector in the above robust linear regression model is information-theoretically impossible. We further investigate the average-case time complexity of certifying well-spreadness of random matrices. We show that it is possible to efficiently certify whether a given $n$-by-$d$ Gaussian matrix is well-spread if the number of observations is quadratic in the ambient dimension. We complement this result by showing rigorous evidence -- in the form of a lower bound against low-degree polynomials -- of the computational hardness of this same certification problem when the number of observations is $o(d^2)$.

Mohamed Elmoghany, Ryan Rossi, Seunghyun Yoon et al.

Despite the significant progress that has been made in video generative models, existing state-of-the-art methods can only produce videos lasting 5-16 seconds, often labeled "long-form videos". Furthermore, videos exceeding 16 seconds struggle to maintain consistent character appearances and scene layouts throughout the narrative. In particular, multi-subject long videos still fail to preserve character consistency and motion coherence. While some methods can generate videos up to 150 seconds long, they often suffer from frame redundancy and low temporal diversity. Recent work has attempted to produce long-form videos featuring multiple characters, narrative coherence, and high-fidelity detail. We comprehensively studied 32 papers on video generation to identify key architectural components and training strategies that consistently yield these qualities. We also construct a comprehensive novel taxonomy of existing methods and present comparative tables that categorize papers by their architectural designs and performance characteristics.