Hao Li

Chun-Kai Fan, Xiaowei Chi, Xiaozhu Ju et al.

As world models gain momentum in Embodied AI, an increasing number of works explore using video foundation models as predictive world models for downstream embodied tasks like 3D prediction or interactive generation. However, before exploring these downstream tasks, video foundation models still have two critical questions unanswered: (1) whether their generative generalization is sufficient to maintain perceptual fidelity in the eyes of human observers, and (2) whether they are robust enough to serve as a universal prior for real-world embodied agents. To provide a standardized framework for answering these questions, we introduce the Embodied Turing Test benchmark: WoW-World-Eval (Wow,wo,val). Building upon 609 robot manipulation data, Wow-wo-val examines five core abilities, including perception, planning, prediction, generalization, and execution. We propose a comprehensive evaluation protocol with 22 metrics to assess the models' generation ability, which achieves a high Pearson Correlation between the overall score and human preference (>0.93) and establishes a reliable foundation for the Human Turing Test. On Wow-wo-val, models achieve only 17.27 on long-horizon planning and at best 68.02 on physical consistency, indicating limited spatiotemporal consistency and physical reasoning. For the Inverse Dynamic Model Turing Test, we first use an IDM to evaluate the video foundation models' execution accuracy in the real world. However, most models collapse to $\approx$ 0% success, while WoW maintains a 40.74% success rate. These findings point to a noticeable gap between the generated videos and the real world, highlighting the urgency and necessity of benchmarking World Model in Embodied AI.

Hao Tang, Hao Chen, Hao Li et al.

Spherical deep learning has been widely applied to a broad range of real-world problems. Existing approaches often face challenges in balancing strong spherical geometric inductive biases with the need to model real-world heterogeneity. To solve this while retaining spherical geometry, we first introduce a designable Green's function framework (DGF) to provide new spherical operator solution strategy: Design systematic Green's functions under rotational group. Based on DGF, to model biological heterogeneity, we propose Green's-Function Spherical Neural Operator (GSNO) fusing 3 operator solutions: (1) Equivariant Solution derived from Equivariant Green's Function for symmetry-consistent modeling; (2) Invariant Solution derived from Invariant Green's Function to eliminate nuisance heterogeneity, e.g., consistent background field; (3) Anisotropic Solution derived from Anisotropic Green's Function to model anisotropic systems, especially fibers with preferred direction. Therefore, the resulting model, GSNO can adapt to real-world heterogeneous systems with nuisance variability and anisotropy while retaining spectral efficiency. Evaluations on spherical MNIST, Shallow Water Equation, diffusion MRI fiber prediction, cortical parcellation and molecule structure modeling demonstrate the superiority of GSNO.