Recent advances in generative models have democratized the creation of high-quality static 3D assets, yet animating these meshes remains a labor-intensive bottleneck. Traditional pipelines fracture this process into sequential stages—rigging, skinning, and motion synthesis—ignoring the inherent coupling between morphological structure and motor function. To bridge this gap, we introduce ACT, a unified generative framework that reformulates rigging and animation not as independent tasks, but as complementary views of a single hyper-kinematic process. Our key insight is to model the joint distribution of skeletal topology and temporal motion within a shared latent space. ACT utilizes a Vision Language Model (VLM) to extract semantic topological priors from arbitrary meshes, which then condition a Diffusion Transformer (DiT) backbone. By treating static rest poses and dynamic trajectories as a unified sequence, our model employs a task-aware masking strategy to flexibly perform zero-shot rigging, text-guided motion generation, and motion completion within a single end-to-end architecture. Furthermore, a geometry-guided decoder ensures that surface deformations are tightly coupled with the generated kinematics. Extensive experiments demonstrate that ACT generalizes robustly to diverse, non-humanoid characters without retraining. By replacing brittle cascaded pipelines with a holistic prior, our method enables novel applications such as semantic-driven topology editing and generative in-betweening, offering a versatile and efficient solution for automating 3D character animation.

Hierarchical and overlapping clustering are two prevalent phenomena that often coexist in real-world system. While numerous studies have examined these two structures separately, characterizing and evaluating their hybrid forms remains an open challenge. To bridge this gap, we initiate the study of hierarchical overlapping clustering on graphs by introducing a new cost function and establishing its rationality through several intuitive properties. We further develop an approximation algorithm that achieves a constant approximation factor for its dual version. Our approach employs a recursive overlapping bipartition framework based on local search, enabling a highly scalable speed-up variant. Experimental results demonstrate that this speed-up algorithm outperforms all baseline methods significantly in both effectiveness (across synthetic and real datasets) and scalability.

The seminal work of \citep{dasgupta2016cost} has introduced a combinatorial cost function for hierarchical graph clustering that has inspired numerous follow-up studies adopting similar combinatorial approaches. In this paper, we investigate this problem from the \emph{information-theoretic} perspective. We formulate a new cost function that is fully explainable and establish the relationship between combinatorial and information-theoretic perspectives. We present two algorithms for expander-like and well-clustered cardinality weighted graphs, respectively, and show that both of them achieve $O(1)$-approximation for our new cost function. Addressing practical needs, we consider non-binary hierarchical clustering problem, and propose a hyperparameter-free framework HCSE that recursively stratifies cluster trees through sparsity-aware partitioning, automatically determining the optimal hierarchy depth via an interpretable mechanism. Extensive experimental results demonstrate the superiority of our cost function and algorithms in binary clustering performance, hierarchy level identification, and reconstruction accuracy compared to existing approaches.