New Hyperdimensional Computing Architecture Realizes Marcus's Algebraic Mind

A novel hyperdimensional computing framework, PyVaCoAl/VaCoAl, has been created, incorporating the three crucial elements identified by Gary Marcus for cognitive architectures: operations on variables, recursively structured representations, and a differentiation between mental representations of individuals and categories. In his 2001 publication, The Algebraic Mind, Marcus contended that conventional multilayer perceptrons did not facilitate any of these components, and that a neural approach utilizing registers and treelets through developmental programs was merely a hypothesis. Now, 25 years later, the necessary substrate has been realized. This architecture utilizes XOR-and-shift over GF(2), executed by primitive-polynomial linear-feedback shift registers, enabling reversible variable binding and non-commutative compositional bundling.