In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Human reasoning involves recognising common underlying principles across many examples by utilising variables. The by-products of such reasoning are invariants that capture patterns across examples such as "if someone went somewhere then they are there" without mentioning specific people or places. Humans learn what variables are and how to use them at a young age, and the question this paper addresses is whether machines can also learn and use variables solely from examples without requiring human pre-engineering. We propose Unification Networks that incorporate soft unification into neural networks to learn variables and by doing so lift examples into invariants that can then be used to solve a given task. We evaluate our approach on four datasets to demonstrate that learning invariants captures patterns in the data and can improve performance over baselines.
End-to-end learning of invariant representations with variables across examples such as if someone went somewhere then they are there.

Word alignments are useful for tasks like statistical and neural machine translation (NMT) and annotation projection. Statistical word aligners perform well, as do methods that extract alignments jointly with translations in NMT. However, most approaches require parallel training data and quality decreases as less training data is available. We propose word alignment methods that require little or no parallel data. The key idea is to leverage multilingual word embeddings – both static and contextualized – for word alignment. Our multilingual embeddings are created from monolingual data only without relying on any parallel data or dictionaries. We find that traditional statistical aligners are outperformed by contextualized embeddings – even in scenarios with abundant parallel data. For example, for a set of 100k parallel sentences, contextualized embeddings achieve a word alignment F1 that is more than 5% higher (absolute) than eflomal.
We use representations trained without any parallel data for creating word alignments.

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve good results on-par with state-of-the-art for 3D shape retrieval task, and new state-of-the-art for point cloud to surface reconstruction task.

We use non-Euclidean Fourier Transformation of shapes defined by a simplicial complex for deep learning, achieving significantly better results than point-based sampling techiques used in current 3D learning literature.