Temporal Knowledge Graph(TKG) serves as an efficacious way to store dynamic facts in real-world. Extrapolation reasoning on TKGs, which aims at predicting possible future events, has attracted consistent research interest. Recently, some rule-based methods have been proposed, which are considered more interpretable compared with embedding-based methods. Existing rule-based methods apply rules through path matching or subgraph extraction, which falls short in inference ability and suffers from missing facts in TKGs. Besides, during rule application period, these methods consider the standing of facts as a binary 0 or 1 problem and ignores the validity as well as frequency of historical facts under temporal settings. In this paper, by designing a novel paradigm for rule application, we propose INFER, a neural-symbolic model for TKG extrapolation. With the introduction of Temporal Validity Function, INFER firstly considers the frequency and validity of historical facts and extends the truth value of facts into continuous real number to better adapt for temporal settings. INFER builds Temporal Weight Matrices with a pre-trained static KG embedding model to enhance its inference ability. Moreover, to facilitates potential integration with existing embedding-based methods, INFER adopts a rule projection module which enables it apply rules through conducting matrices operation on GPU. This feature also improves the efficiency of rule application. Experimental results show that INFER achieves state-of-the-art performance on various TKG datasets and significantly outperforms existing rule-based models on our modified, more sparse TKG datasets, which demonstrates the superiority of our model in inference ability.

Video generation requires modeling a vast spatiotemporal space, which demands significant computational resources and data usage. To reduce the complexity, the prevailing approaches employ a cascaded architecture to avoid direct training with full resolution latent. Despite reducing computational demands, the separate optimization of each sub-stage hinders knowledge sharing and sacrifices flexibility. This work introduces a unified pyramidal flow matching algorithm. It reinterprets the original denoising trajectory as a series of pyramid stages, where only the final stage operates at the full resolution, thereby enabling more efficient video generative modeling. Through our sophisticated design, the flows of different pyramid stages can be interlinked to maintain continuity. Moreover, we craft autoregressive video generation with a temporal pyramid to compress the full-resolution history. The entire framework can be optimized in an end-to-end manner and with a single unified Diffusion Transformer (DiT). Extensive experiments demonstrate that our method supports generating high-quality 5-second (up to 10-second) videos at 768p resolution and 24 FPS within 20.7k A100 GPU training hours. All code and models are open-sourced at https://pyramid-flow.github.io.

Multi-hop logical reasoning over knowledge graph plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding methods for reasoning focus on static KGs, while temporal knowledge graphs have not been fully explored. Reasoning over TKGs has two challenges: 1. The query should answer entities or timestamps; 2. The operators should consider both set logic on entity set and temporal logic on timestamp set. To bridge this gap, we introduce the multi-hop logical reasoning problem on TKGs and then propose the first temporal complex query embedding named Temporal Feature-Logic Embedding framework (TFLEX) to answer the temporal complex queries. Specifically, we utilize fuzzy logic to compute the logic part of the Temporal Feature-Logic embedding, thus naturally modeling all first-order logic operations on the entity set. In addition, we further extend fuzzy logic on timestamp set to cope with three extra temporal operators (**After**, **Before** and **Between**). Experiments on numerous query patterns demonstrate the effectiveness of our method.