A Neodymium-Inspired Fractal State-Space Generator for Neuromorphic Control

Published June 25, 2026 | Version v3

Preprint Open

Modern software typically represents memory as a data structure: arrays,

buffers, queues, key-value stores, or attention contexts. In time-critical

control, however, expanding the memory structure directly increases memory

traffic, latency, and engineering complexity. This preprint proposes

NdFractal, a neodymium-inspired fractal state-space generator for neuromorphic

control. Instead of storing past inputs as an ever-growing sequence, NdFractal

lets past inputs deform a compact dynamical state space. New sensory inputs

then flow through this deformed space, where attractor-like dynamics separate

control-relevant regimes. In this view, memory is not only stored in data; it is

formed into the geometry of the state space itself.

NdFractal is motivated by three converging ideas: reservoir computing,

fractional or power-law memory, and the spin/hysteresis/remanence metaphor of

neodymium-like magnetic materials. The proposed role of NdFractal is not to

replace the neuromorphic controller, but to act as a front-end state-space

generator for spiking liquid neural networks and related adaptive control

systems. Conceptually, the distinction can be summarized as follows:

Transformers unfold memory into addressable context; state-space models such as

Mamba fold memory into recurrent state; NdFractal folds and unfolds the memory

space itself as a function.

Preliminary internal observations suggest that neodymium-inspired fractal

preprocessing can improve already-optimized neuromorphic control systems by

single-digit relative margins in selected domains, while also improving state

separation and temporal basis richness. These observations are presented here

only as motivation. This manuscript does not provide a reproducible

implementation.

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