E-LAB-06 · EntropyLab · April 2026

ENTRO-NET

Distributed Entropy Synchronization Protocols for Collective Neural Networks.
From self-calibrating individuals to physically synchronized collectives — preventing cascading failure.

Ψ_norm · Network Entropy State · Collective Synchronization

0.07

Ψ_norm (target = 0.339)

SYNC · Collective AEW active

GitHub Repository DOI: 10.5281/zenodo.19474217

01 · Core Innovation

Entropy Sync · Collective AEW · θ_net

ENTRO-NET extends adaptive entropy weighting from individual systems to distributed networks. Multiple nodes physically share stability states, preventing cascading failure through synchronized entropy flow.

Ψ-Sync Protocol

E_sync,i = Σ κ·(Ψ_j - Ψ_i)

Entropy exchange law — stability flows from lower-entropy to higher-entropy nodes

Collective-AEW

∇L_collective = ∇L_local + β·∇L_network

β = cooperation coefficient · nodes learn from collective stability history

Networked Threshold

θ_net = θ_base + γ·Var(Ψ_i)

γ = variance sensitivity · higher variance → higher caution

02 · Scaling Results

Extended Analysis N = 20, 30, 50

N (Nodes) Variance (mean ± std) Linear Prediction Deviation

20 0.165380 ± 0.002169 0.1689 -0.0035

30 0.197713 ± 0.002204 0.2699 -0.0722

50 0.221481 ± 0.000677 0.4719 -0.2504

Linear Regime (N ≤ 15)

σ² = 0.0101·N - 0.0331

CORRELATION

R² = 0.986

SLOPE

0.0101

INTERCEPT

-0.0331

INTERPRETATION

Internal damping

Saturation Regime (N ≥ 25)

σ² → 0.22

SATURATION CEILING

σ²_max ≈ 0.228

CHARACTERISTIC SCALE

N₀ ≈ 16.2

SATURATION MODEL

σ² = σ²_max·(1 - e^{-N/N₀})

GOODNESS OF FIT

R² = 0.992

Key Scientific Insight

No Catastrophic Failure

BREAKDOWN OF LINEARITY

N ≈ 20

CROSSOVER REGION

N = 15-25

MAX TESTED N

50 (stable)

PRACTICAL LIMIT

N ≤ 30

# pip install entro-net
from entro_net import PsiSync, CollectiveAEW, NetThreshold

sync = PsiSync(n_nodes=5, kappa=1.0)
aew = CollectiveAEW(eta=0.01, target=0.339, beta=1.0)
threshold = NetThreshold(theta_base=1.4, gamma=10.0)

# Distributed control loop
synced_psi = sync.broadcast(psi_states)
weights = aew.step(avg_psi, avg_d_psi, avg_d2_psi, network_errors)
theta_net = threshold.update(psi_states)

# → Output
Variance reduction: 57.1% · Final weights [0.794, 0.103, 0.104]

"Stability is not an individual property — it is a collective effort.
ENTRO-NET proves that synchronized entropy flow prevents cascading failure
and creates networks of physically honest intelligence."

— Samir Baladi · ENTRO-NET · April 2026