The world is fundamentally compositional, so it is natural to think of visual
recognition as the recognition of basic visually primitives that are composed
according to well-defined rules. This strategy allows us to recognize unseen
complex concepts from simple visual primitives. However, the current trend in
visual recognition follows a data greedy approach where huge amounts of data
are required to learn models for any desired visual concept. In this paper, we
build on the compositionality principle and develop an "algebra" to compose
classifiers for complex visual concepts. To this end, we learn neural network
modules to perform boolean algebra operations on simple visual classifiers.
Since these modules form a complete functional set, a classifier for any
complex visual concept defined as a boolean expression of primitives can be
obtained by recursively applying the learned modules, even if we do not have a
single training sample. As our experiments show, using such a framework, we can
compose classifiers for complex visual concepts outperforming standard
baselines on two well-known visual recognition benchmarks. Finally, we present
a qualitative analysis of our method and its properties.

本文提出了一种使用神经网络模块执行布尔代数运算来构建分类器的方法，通过递归应用这些模块，即使没有单个训练样本，也可以获得任何由基本元素的布尔表达式定义的复杂视觉概念的分类器，实验证明，使用这种框架可以组合复杂的视觉概念分类器，并在两个知名的视觉识别基准测试中优于标准基准线。