Learning-Assisted Automated Reasoning with Flyspeck

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of answering a wide range of mathematical queries automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39% of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided

Benefits of data augmentation for NMT-based text normalization of user-generated content

One of the most persistent characteristics of written user-generated content (UGC) is the use of non-standard words. This characteristic contributes to an increased difficulty to automatically process and analyze UGC. Text normalization is the task of transforming lexical variants to their canonical forms and is often used as a pre-processing step for conventional NLP tasks in order to overcome the performance drop that NLP systems experience when applied to UGC. In this work, we follow a Neural Machine Translation approach to text normalization. To train such an encoder-decoder model, large parallel training corpora of sentence pairs are required. However, obtaining large data sets with UGC and their normalized version is not trivial, especially for languages other than English. In this paper, we explore how to overcome this data bottleneck for Dutch, a low-resource language. We start off with a publicly available tiny parallel Dutch data set comprising three UGC genres and compare two different approaches. The first is to manually normalize and add training data, a money and time-consuming task. The second approach is a set of data augmentation techniques which increase data size by converting existing resources into synthesized non-standard forms. Our results reveal that a combination of both approaches leads to the best results

Orientation covariant aggregation of local descriptors with embeddings

Image search systems based on local descriptors typically achieve orientation invariance by aligning the patches on their dominant orientations. Albeit successful, this choice introduces too much invariance because it does not guarantee that the patches are rotated consistently. This paper introduces an aggregation strategy of local descriptors that achieves this covariance property by jointly encoding the angle in the aggregation stage in a continuous manner. It is combined with an efficient monomial embedding to provide a codebook-free method to aggregate local descriptors into a single vector representation. Our strategy is also compatible and employed with several popular encoding methods, in particular bag-of-words, VLAD and the Fisher vector. Our geometric-aware aggregation strategy is effective for image search, as shown by experiments performed on standard benchmarks for image and particular object retrieval, namely Holidays and Oxford buildings.Comment: European Conference on Computer Vision (2014