Neural Algebra of Classifiers

TL;DR

This paper introduces a neural algebra framework that composes classifiers for complex visual concepts using learned boolean operations, enabling recognition without extensive data for each concept.

Contribution

It develops neural modules that perform boolean algebra on classifiers, allowing compositional recognition of complex concepts without direct training samples.

Findings

Outperforms standard baselines on recognition benchmarks.

Enables recognition of complex concepts from primitives without training samples.

Provides qualitative analysis of the compositional framework.

Abstract

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.