Learning-assisted Theorem Proving with Millions of Lemmas

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck.Comment: journal version of arXiv:1310.2797 (which was submitted to LPAR conference

Content-based Propagation of User Markings for Interactive Segmentation of Patterned Images

Efficient and easy segmentation of images and volumes is of great practical importance. Segmentation problems that motivate our approach originate from microscopy imaging commonly used in materials science, medicine, and biology. We formulate image segmentation as a probabilistic pixel classification problem, and we apply segmentation as a step towards characterising image content. Our method allows the user to define structures of interest by interactively marking a subset of pixels. Thanks to the real-time feedback, the user can place new markings strategically, depending on the current outcome. The final pixel classification may be obtained from a very modest user input. An important ingredient of our method is a graph that encodes image content. This graph is built in an unsupervised manner during initialisation and is based on clustering of image features. Since we combine a limited amount of user-labelled data with the clustering information obtained from the unlabelled parts of the image, our method fits in the general framework of semi-supervised learning. We demonstrate how this can be a very efficient approach to segmentation through pixel classification.Comment: 9 pages, 7 figures, PDFLaTe

Mobile Video Object Detection with Temporally-Aware Feature Maps

This paper introduces an online model for object detection in videos designed to run in real-time on low-powered mobile and embedded devices. Our approach combines fast single-image object detection with convolutional long short term memory (LSTM) layers to create an interweaved recurrent-convolutional architecture. Additionally, we propose an efficient Bottleneck-LSTM layer that significantly reduces computational cost compared to regular LSTMs. Our network achieves temporal awareness by using Bottleneck-LSTMs to refine and propagate feature maps across frames. This approach is substantially faster than existing detection methods in video, outperforming the fastest single-frame models in model size and computational cost while attaining accuracy comparable to much more expensive single-frame models on the Imagenet VID 2015 dataset. Our model reaches a real-time inference speed of up to 15 FPS on a mobile CPU.Comment: In CVPR 201