Recovering the skeletal shape of an animal from a monocular video is a longstanding challenge. Prevailing animal reconstruction methods often adopt a control-point driven animation model and optimize bone transforms individually without considering skeletal topology, yielding unsatisfactory shape and articulation. In contrast, humans can easily infer the articulation structure of an unknown animal by associating it with a seen articulated character in their memory. Inspired by this fact, we present CASA, a novel Category-Agnostic Skeletal Animal reconstruction method consisting of two major components: a video-to-shape retrieval process and a neural inverse graphics framework. During inference, CASA first retrieves an articulated shape from a 3D character assets bank so that the input video scores highly with the rendered image, according to a pretrained language-vision model. CASA then integrates the retrieved character into an inverse graphics framework and jointly infers the shape deformation, skeleton structure, and skinning weights through optimization.

It is a challenge to detect complicated data relationships thoroughly. Here, we propose a new statistical measure, named the absolute neighbour difference based neighbour correlation coefficient, to detect the associations between variables through examining the heteroscedasticity of the unpredictable variation of dependent variables. Different from previous studies, the new method concentrates on measuring nonfunctional relationships rather than functional or mixed associations. Either used alone or in combination with other measures, it enables not only a convenient test of heteroscedasticity, but also measuring functional and nonfunctional relationships separately that obviously leads to a deeper insight into the data associations. The method is concise and easy to implement that does not rely on explicitly estimating the regression residuals or the dependencies between variables so that it is not restrict to any kind of model assumption. The mechanisms of the correlation test are proved in theory and demonstrated with numerical analyses.

Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains less understood. In this paper, we formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks that consist of interleaved encoding circuit blocks and trainable circuit blocks. First, we prove that single-qubit quantum neural networks can approximate any univariate function by mapping the model to a partial Fourier series. We in particular establish the exact correlations between the parameters of the trainable gates and the Fourier coefficients, resolving an open problem on the universal approximation property of QNN. Second, we discuss the limitations of single-qubit native QNNs on approximating multivariate functions by analyzing the frequency spectrum and the flexibility of Fourier coefficients. We further demonstrate the expressivity and limitations of single-qubit native QNNs via numerical experiments. We believe these results would improve our understanding of QNNs and provide a helpful guideline for designing powerful QNNs for machine learning tasks.

How close are we to the sci-fi vision of autonomous humanoid robots? I visited 11 companies in five Chinese cities to find out

By Chang Che. Read by Vincent Lai