# Representing Sets as Summed Semantic Vectors

arXiv: https://arxiv.org/abs/1809.08823 · HTML: https://mlsanity.com/paper/1809.08823/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2018.

## Built on by (most cited first, 1 of 1)

- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)

## Abstract (arXiv)

Representing meaning in the form of high dimensional vectors is a common and powerful tool in biologically inspired architectures. While the meaning of a set of concepts can be summarized by taking a (possibly weighted) sum of their associated vectors, this has generally been treated as a one-way operation. In this paper we show how a technique built to aid sparse vector decomposition allows in many cases the exact recovery of the inputs and weights to such a sum, allowing a single vector to represent an entire set of vectors from a dictionary. We characterize the number of vectors that can be recovered under various conditions, and explore several ways such a tool can be used for vector-based reasoning.