Feng Han

Guangrui Yang, Jianfei Li, Ming Li et al.

In this paper, we explore the approximation theory of functions defined on graphs. Our study builds upon the approximation results derived from the $K$-functional. We establish a theoretical framework to assess the lower bounds of approximation for target functions using Graph Convolutional Networks (GCNs) and examine the over-smoothing phenomenon commonly observed in these networks. Initially, we introduce the concept of a $K$-functional on graphs, establishing its equivalence to the modulus of smoothness. We then analyze a typical type of GCN to demonstrate how the high-frequency energy of the output decays, an indicator of over-smoothing. This analysis provides theoretical insights into the nature of over-smoothing within GCNs. Furthermore, we establish a lower bound for the approximation of target functions by GCNs, which is governed by the modulus of smoothness of these functions. This finding offers a new perspective on the approximation capabilities of GCNs. In our numerical experiments, we analyze several widely applied GCNs and observe the phenomenon of energy decay. These observations corroborate our theoretical results on exponential decay order.

Team Seedance, Heyi Chen, Siyan Chen et al.

Recent strides in video generation have paved the way for unified audio-visual generation. In this work, we present Seedance 1.5 pro, a foundational model engineered specifically for native, joint audio-video generation. Leveraging a dual-branch Diffusion Transformer architecture, the model integrates a cross-modal joint module with a specialized multi-stage data pipeline, achieving exceptional audio-visual synchronization and superior generation quality. To ensure practical utility, we implement meticulous post-training optimizations, including Supervised Fine-Tuning (SFT) on high-quality datasets and Reinforcement Learning from Human Feedback (RLHF) with multi-dimensional reward models. Furthermore, we introduce an acceleration framework that boosts inference speed by over 10X. Seedance 1.5 pro distinguishes itself through precise multilingual and dialect lip-syncing, dynamic cinematic camera control, and enhanced narrative coherence, positioning it as a robust engine for professional-grade content creation. Seedance 1.5 pro is now accessible on Volcano Engine at https://console.volcengine.com/ark/region:ark+cn-beijing/experience/vision?type=GenVideo.