The number 5 in F5 is not arbitrary. L2H’s designers found that most adaptive control problems exhibit Markov-like properties up to 5 steps; beyond that, environmental noise dominates. EF-F5 is computed as:
EF-F5 = (1/5) Σ_t=1 to 5 [ Stability(t) × Adaptation_Gain(t) ] l2hforadaptivity ef f1 f3 f5
The core innovation lies in its : instead of fixing which sensors connect to which actuators, L2H allows the hierarchy to compress and decompress its own structure based on environmental volatility. This is where the evaluation functions – EF F1, F3, and F5 – enter the stage. The Three Evaluation Functions: EF-F1, EF-F3, EF-F5 Within L2HforAdaptivity, adaptivity quality is not monolithic. The framework defines three distinct evaluation functions (EF), each addressing a different system performance axis. Note that "ef f1 f3 f5" in the keyword likely designates these three specific functions (skipping even-numbered indices to avoid redundancy). EF-F1: Fidelity of Layer-to-Hierarchy Translation Purpose : Measures how accurately the hierarchical representation captures the underlying lower-layer dynamics. The number 5 in F5 is not arbitrary
A score of 1.0 indicates no negative impact from adaptivity. Scores below 0.5 suggest the hierarchy reconfiguration consumes more resources than it saves. L2HforAdaptivity uses EF-F3 to trigger a “lazy hierarchy” mode where L2 operates semi-autonomously without continuous H updates. Purpose : Assesses the system’s ability to maintain effective adaptivity over a rolling horizon of five decision steps. This is where the evaluation functions – EF
Unlike F1 (accuracy of mapping), F3 focuses on . It measures:
In adaptive systems, a high EF-F1 score means the system’s abstract view (the “H” part) is not hallucinating features nor missing critical details. For example, in a swarm robotics L2H system, EF-F1 ensures that the swarm’s macroscopic state correctly represents individual robot failures or task completions. Purpose : Evaluates how gracefully the system reshuffles its L2-H mapping when computational or energy resources are limited.