# Improved Cleanup and Decoding of Fractional Power Encodings

arXiv: https://arxiv.org/abs/2412.00488 · HTML: https://mlsanity.com/paper/2412.00488/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 30 Nov 2024.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A comparison of Vector Symbolic Architectures](https://mlsanity.com/paper/2001.11797/) (2020)
- [Computing on Functions Using Randomized Vector Representations](https://mlsanity.com/paper/2109.03429/) (2021)
- [Vector Symbolic Architectures as a Computing Framework for Emerging Hardware](https://mlsanity.com/paper/2106.05268/) (2021)
- [Robust computation with rhythmic spike patterns](https://mlsanity.com/paper/1901.07718/) (2019)
- [Binding in hippocampal-entorhinal circuits enables compositionality in cognitive maps](https://mlsanity.com/paper/2406.18808/) (2024)
- [Hyperdimensional Computing with Spiking-Phasor Neurons](https://mlsanity.com/paper/2303.00066/) (2023)

## Abstract (arXiv)

High-dimensional vectors have been proposed as a neural method for representing information in the brain using Vector Symbolic Algebras (VSAs). While previous work has explored decoding and cleaning up these vectors under the noise that arises during computation, existing methods are limited. Cleanup methods are essential for robust computation within a VSA. However, cleanup methods for continuous-value encodings are not as effective. In this paper, we present an iterative optimization method to decode and clean up Fourier Holographic Reduced Representation (FHRR) vectors that are encoding continuous values. We combine composite likelihood estimation (CLE) and maximum likelihood estimation (MLE) to ensure convergence to the global optimum. We also demonstrate that this method can effectively decode FHRR vectors under different noise conditions, and show that it outperforms existing methods.