Improved Cleanup and Decoding of Fractional Power Encodings

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.