# Neural Algebra of Classifiers

arXiv: https://arxiv.org/abs/1801.08676 · HTML: https://mlsanity.com/paper/1801.08676/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2018.

## Built on by (most cited first, 7 of 7)

- [Relation-aware Compositional Zero-shot Learning for Attribute-Object Pair Recognition](https://mlsanity.com/paper/2108.04603/) (2021)
- [On the Element-Wise Representation and Reasoning in Zero-Shot Image Recognition: A Systematic Survey](https://mlsanity.com/paper/2408.04879/) (2024)
- [Large-Scale Attribute-Object Compositions](https://mlsanity.com/paper/2105.11373/) (2021)
- [Smoothness and effective regularizations in learned embeddings for shape matching](https://mlsanity.com/paper/2112.07289/) (2021)
- [Algebraic Approach to Ridge-Regularized Mean Squared Error Minimization in Minimal ReLU Neural Network](https://mlsanity.com/paper/2508.17783/) (2025)
- [Self-Attention with State-Object Weighted Combination for Compositional Zero Shot Learning](https://mlsanity.com/paper/2512.18969/) (2025)
- [When Rule Violations Are Rare: Chimera Training for Logical Anomaly Detection](https://mlsanity.com/paper/2605.26171/) (2026)

## Abstract (arXiv)

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.