1. Initial goals and expectations – a self-interacting computational field:
Fractal-like and harmonic organization emerges from bulk interaction rather than from computation within individual units.
2. Core Data Layer – The Sigmoid LUT (TANH to be considered separately):
At the foundation sits a highly optimized 256-entry lookup table (LUT) generated via a classic logistic sigmoid function mapped across a strict domain from -6.0 to 6.0. The table itself becomes an instantaneous index function, while filtering the input layer through the math.
- Model Symmetry: The table leverages the symmetry of the logistic function around its midpoint.
- Fixed-Point Scaling: Continuous values are crushed into discrete 16-bit unsigned integers (
uint16_t) scaled up to65535. - Soft Crossover Dynamics: Mapping the normalized input range from −6 to +6 across 256 discrete entries produces a gentle, viscous gradient through the crossover region. Near the midpoint, the maximum change between adjacent entries is approximately 1.2% of the full output range, or about 2.4% relative to the local output value, providing a smooth transition within digital constraints.
3. Information Compression – The 2-Bit State Machine:
To avoid burning processing power on heavy floating-point numbers or handling complex noise, this system compresses activating inputs down into a crisp, 2-bit primary output state. This functions as a localized information filter with four precise operational phases:
00— Inactive: The unit is completely dormant. The global engine can safely skip heavy processing of these nodes, short-circuiting computational waste.01— Approaching Inactive: The signal is decaying. The system acts as a resistance buffer by slightly raising its activation threshold to prevent the unit from fluttering chaotically due to minor noise.10— Approaching Active: The unit is priming itself by slightly lowering its threshold, indicating a rapid buildup of localized energy or density.11— Active: Full execution/firing state.
4. Dynamic Feedback Loops – Shifting Thresholds:
The 2-bit state history feeds directly back into the input processing logic, giving each unit an organic sense of memory, fatigue, and physical readiness without needing global network weight adjustments:
- The Refractory Period (after state
11): Once a unit fires, it enters a high-threshold fatigue state. The system applies a sharp positive offset to the local threshold, making it much harder to fire again immediately and enforcing a natural wave decay. - The Priming State (
10): As a unit approaches activation, its local threshold is subtly lowered. This sensitizes the unit, making it more responsive to incoming activity and allowing clustered regions to fire cleanly together.
5. Extended Field Mechanics – Phase and Rotation:
To transition from a simple cellular automaton into a complex wave-resonance field, secondary, finer-grained states add to the primary 2-bit state:
- Phase Alignment: Units evaluate whether they are in or out of phase with their neighbors. Matching phases constructively interfere to accelerate threshold crossings, while mismatched phases damp the signal.
- Rotational Vectors: This introduces directional momentum and spatial coherence. Activation waves can spin, warp, and propagate with structural bias across the computational field
- Computational Economy: The engine only pays the heavy processing cost for computing these continuous phase-shifts and rotational updates after a unit’s cheap 2-bit state passes its threshold validation.
6. Threshold decay function – Follow the field:
The threshold value itself should follow an R/C like decay curve toward its normal resting, non-zero value – absent new activation, likely also involving a lookup table: Tt+1=T_rest+(Tt−T_rest)e−Δt/τ. T_rest can be further modified by a slower historical function, but cannot be zero.