论文标题
晶格表示学习
Lattice Representation Learning
论文作者
论文摘要
在本文中，我们介绍了学习离散表示形式的理论和算法，这些表示构成了嵌入在欧几里得空间中的晶格。 Lattice representations possess an interesting combination of properties: a) they can be computed explicitly using lattice quantization, yet they can be learned efficiently using the ideas we introduce in this paper, b) they are highly related to Gaussian Variational Autoencoders, allowing designers familiar with the latter to easily produce discrete representations from their models and c) since lattices satisfy the axioms of a group, their adoption can lead into a way of learning simple通过符号形式主义在对象之间建模二进制操作的代数，但是还使用分化技术来正式学习这些结构。本文将重点介绍探索和利用前两个属性的基础，包括一个新的数学结果，链接培训和推理时间中使用的表达式以及两个流行数据集的实验验证。
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be computed explicitly using lattice quantization, yet they can be learned efficiently using the ideas we introduce in this paper, b) they are highly related to Gaussian Variational Autoencoders, allowing designers familiar with the latter to easily produce discrete representations from their models and c) since lattices satisfy the axioms of a group, their adoption can lead into a way of learning simple algebras for modeling binary operations between objects through symbolic formalisms, yet learn these structures also formally using differentiation techniques. This article will focus on laying the groundwork for exploring and exploiting the first two properties, including a new mathematical result linking expressions used during training and inference time and experimental validation on two popular datasets.
