A Semantic Search Engine for Mathlib4

The interactive theorem prover, Lean, enables the verification of formal mathematical proofs and is backed by an expanding community. Central to this ecosystem is its mathematical library, mathlib4, which lays the groundwork for the formalization of an expanding range of mathematical theories. However, searching for theorems in mathlib4 can be challenging. To successfully search in mathlib4, users often need to be familiar with its naming conventions or documentation strings. Therefore, creating a semantic search engine that can be used easily by individuals with varying familiarity with mathlib4 is very important. In this paper, we present a semantic search engine for mathlib4 that accepts informal queries and finds the relevant theorems. We also establish a benchmark for assessing the performance of various search engines for mathlib4.

GLOBER: Coherent Non-autoregressive Video Generation via GLOBal Guided Video DecodER

Video generation necessitates both global coherence and local realism. This work presents a novel non-autoregressive method GLOBER, which first generates global features to obtain comprehensive global guidance and then synthesizes video frames based on the global features to generate coherent videos. Specifically, we propose a video auto-encoder, where a video encoder encodes videos into global features, and a video decoder, built on a diffusion model, decodes the global features and synthesizes video frames in a non-autoregressive manner. To achieve maximum flexibility, our video decoder perceives temporal information through normalized frame indexes, which enables it to synthesize arbitrary sub video clips with predetermined starting and ending frame indexes. Moreover, a novel adversarial loss is introduced to improve the global coherence and local realism between the synthesized video frames. Finally, we employ a diffusion-based video generator to fit the global features outputted by the video encoder for video generation. Extensive experimental results demonstrate the effectiveness and efficiency of our proposed method, and new state-of-the-art results have been achieved on multiple benchmarks.