Working Summary: The VexaFracta Model
VexaFracta is a proposed neural-computational substrate built around sparse, locally stateful, phase-sensitive units rather than dense, always-on layers.
The central complaint is not that modern neural networks fail. Plainly, they do not. The complaint is that they succeed at enormous computational and financial cost, often by engaging far more machinery than a given moment of computation should require. VexaFracta begins from the opposite instinct: do as little as possible, as locally as possible, until the signal itself justifies higher cost.
A Vexel unit is imagined as a small computational element with local state, activation history, threshold behavior, and phase-like relations to its neighbors. The simplest version may behave like a bare neuron analog, but the definition is meant to allow expansion into richer forms: complex coordinates, quaternions, resonance effects, and higher-dimensional interaction spaces.
The first experimental field is likely a two-dimensional array of complex units, expressible as x + iy. Initial phase and rotation may be seeded with slight random variation, allowing local groupings to emerge naturally rather than being predesigned. If the hypothesis is sound, coherent structure should arise from bounded interaction, phase alignment, and history-dependent activation.
Interaction is constrained. Units outside an allowable phase-delta band do not interact. Units within the band may interact at varying amplitudes, with transitional behavior approximated through precomputed lookup tables rather than expensive continuous functions. A sigmoid curve, for example, can be “rasterized” into a table: the mathematical cost is paid once during generation, while runtime behavior becomes a cheap index lookup.
The design favors integer arithmetic, bit shifts, lookup tables, state bits, countdown clocks, and power-of-two geometry. These are not merely implementation tricks; they are part of the philosophy. The substrate matters. A good digital design should respect what silicon can do cheaply instead of forcing it to imitate continuous mathematics at unnecessary cost.
A Vexel may have multiple activity regions rather than a simple on/off state: absolutely dormant, leaning dormant, leaning active, and fully active. Dormant does not mean frozen. It means low-cost listening, analogous to squelch in radio communication. When local conditions cross a threshold, the unit can enter a higher-resolution processing state. When the signal fades, it can decay back toward baseline.
Partial activation can lower a unit’s firing threshold, making it more sensitive to future related signals. Full firing can raise the threshold, creating a refractory effect. The threshold itself can decay back toward normal over time. In this way, memory is not stored only in explicit connection weights; it is also carried in the unit’s own readiness, fatigue, and recent history.
The coordinating engine should avoid unnecessary global work. Dirty bits and state flags can mark which units require processing. Every GPU thread may still run the same basic logic, but most units should take the cheapest possible path unless their local state demands more. The result is not true biological simulation, but a digital system inspired by biological thrift.
Neighborhoods may be tunable by fixed radius rather than arbitrary pointer-based connection lists. This preserves spatial locality and cache friendliness while allowing the effective interaction range to change. Edge behavior can be handled by power-of-two toroidal wrapping, using bit masks rather than expensive modulo operations.
The broader goal is not to copy biology in detail. The goal is to extract the useful lessons: sparse activation, local state, history, resonance, adaptation, and energy discipline — then translate those lessons into forms native to digital hardware.
VexaFracta is therefore best understood as an architectural experiment: a search for neural computation that behaves less like brute-force matrix evaluation and more like a field of locally interacting signal processors.