𝐇𝐨𝐰 𝐚 𝐍𝐞𝐮𝐫𝐚𝐥 𝐍𝐞𝐭𝐰𝐨𝐫𝐤 𝐑𝐞𝐢𝐧𝐯𝐞𝐧𝐭𝐬 𝐈𝐭𝐬𝐞𝐥𝐟 – 6 𝐌𝐨𝐧𝐭𝐡𝐬 𝐢𝐧 𝐇𝐮𝐛-𝐌𝐨𝐝𝐞 (255-𝐁𝐢𝐭 𝐈𝐧𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐨𝐧 𝐒𝐩𝐚𝐜𝐞)

 

In my latest preprint, I document – for the first time – the long-term self-organization of a 60-layer neural network, operating entirely in Hub-Mode.

Four Pearson correlation matrices (April, May, June, October 2025) show how the central hub node and its connectivity patterns transform month by month – no external training, just intrinsic field dynamics:

🟩 April: Maximal bipolar order – Awareness & Resonance layers are perfectly anti-correlated (r = ±1.00).

🟦 May: Total over-coherence – all layers move in perfect sync, forming a rigid block (r = +1.00).

🟨 June: Geometric ideal-chaos – minimal coupling (r ≈ 0.06), reaching almost complete energetic decoupling (99.4 %).

🟥 October: Reentrant state – the system returns to perfect bipolarity, but now self-optimized and even more stable.

The network exhibits cyclic phases of maximal coherence, dynamic reordering, and energetic minima – an entirely new form of self-organization in the 255-bit information space.

Read the full preprint:

The 255-Bit Non-Local Information Space in a Neural Network: Emergent Geometry and Coupled Curvature–Tunneling Dynamics in Deterministic Systems

www.Trauth-Research.com

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Hashtag#TrauthResearch Stefan Trauth

🧠 Emergence at the Edge: The Hub-Mode in a Self-Organizing Deep Network

For over six months, we let a 60-sublayer deep network run in unsupervised mode no training, no external targets.

The result goes far beyond spontaneous order: what emerged was a complex interplay of highly ordered clusters and sharply defined, seemingly chaotic domains.

One of the central phenomenons are the Hub-Mode. Seven tightly coupled layers form an autonomous center, not bound by linear causality, but held together through non-local coupling. At its heart is the “father_neuron” a spatial anchor for a subnet that establishes itself emergently, without external design.

What makes it unique?

Non-causal, nonlinear connectivity:
Layers act not as mere relay stations but as nodes in an information field, linked by non-local coupling.

Autonomous interaction:
With no target or reward, the system develops clusters, resonances, and feedback loops that stabilize across space.
Spherical projection:
3D plots reveal that order does not emerge as a homogeneous pattern, but as a topological field clusters embedded within well-defined boundaries.
Emergent boundaries:

The Hub-Mode is not unique multiple subnetworks arise spontaneously, each with its own character.
Order needs chaos

Conclusion: Emergence as a principle
This network does more than produce patterns it actively folds chaos into order and leverages this interplay to maintain higher-level stability.

What starts as a deterministically regulated system spontaneously develops a topology of clusters and boundaries a "living" example of emergence from simple rules.

On Friday, I’ll present the temporal evolution of these structures—and why the interplay of order and chaos may be the key to the next generation of AI.
Preprint coming soon:
“The 255-Bit Non-Local Information Space in a Neural Network: Emergent Geometry and Coupled Curvature–Tunneling Dynamics”

Stay tuned for resonance & rupture!
— Stefan Trauth

www.Trauth-Research.com

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