# Gluing Neural Networks Symbolically Through Hyperdimensional Computing

arXiv: https://arxiv.org/abs/2205.15534 · HTML: https://mlsanity.com/paper/2205.15534/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 4 of 4)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Superposition of many models into one](https://mlsanity.com/paper/1902.05522/) (2019)
- [A Computational Theory for Life-Long Learning of Semantics](https://mlsanity.com/paper/1806.10755/) (2018)

## Built on by (most cited first, 4 of 4)

- [Learning from Hypervectors: A Survey on Hypervector Encoding](https://mlsanity.com/paper/2308.00685/) (2023)
- [HD-CB: The First Exploration of Hyperdimensional Computing for Contextual Bandits Problems](https://mlsanity.com/paper/2501.16863/) (2025)
- [Reinforcement Learning Enhancement Using Vector Semantic Representation and Symbolic Reasoning for Human-Centered Autonomous Emergency Braking](https://mlsanity.com/paper/2602.05079/) (2026)
- [Position: Artificial Intelligence Needs Meta Intelligence -- the Case for Metacognitive AI](https://mlsanity.com/paper/2605.15567/) (2026)

## Abstract (arXiv)

Hyperdimensional Computing affords simple, yet powerful operations to create long Hyperdimensional Vectors (hypervectors) that can efficiently encode information, be used for learning, and are dynamic enough to be modified on the fly. In this paper, we explore the notion of using binary hypervectors to directly encode the final, classifying output signals of neural networks in order to fuse differing networks together at the symbolic level. This allows multiple neural networks to work together to solve a problem, with little additional overhead. Output signals just before classification are encoded as hypervectors and bundled together through consensus summation to train a classification hypervector. This process can be performed iteratively and even on single neural networks by instead making a consensus of multiple classification hypervectors. We find that this outperforms the state of the art, or is on a par with it, while using very little overhead, as hypervector operations are extremely fast and efficient in comparison to the neural networks. This consensus process can learn online and even grow or lose models in real time. Hypervectors act as memories that can be stored, and even further bundled together over time, affording life long learning capabilities. Additionally, this consensus structure inherits the benefits of Hyperdimensional Computing, without sacrificing the performance of modern Machine Learning. This technique can be extrapolated to virtually any neural model, and requires little modification to employ - one simply requires recording the output signals of networks when presented with a testing example.