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An Innovative Perspective to Profound Functions of the Brain: Hypothesis of Resonance of Closed Neural Network Geometries

This paper proposes the Resonance of Closed Neural Network Geometries (RCNNG) framework, which posits that perception and consciousness emerge from stable resonant attractors in recurrent neural circuits, where perceptual stability and subjective experience ("innergence") arise from the mapping of input-driven closed neural geometries to their intrinsic resonant identities rather than their physical structures.

Original authors: Hasan Niazi

Published 2026-07-21✓ Author reviewed ⓘ

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Hasan Niazi

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

The Brain's Secret Symphony

Imagine your brain as a massive, bustling city. For a long time, scientists thought this city worked like a giant library or a computer hard drive. In that old view, every thought, memory, or feeling was like a specific book stored on a specific shelf. To remember something, your brain would just "look up" the address of that shelf, pull out the book, and read it. But here's the problem: the brain is messy. The connections between its cells (neurons) are constantly changing, growing, and shrinking. There are no stable "addresses" or "shelves" to look up. If the brain worked like a library, it would be impossible to find anything because the map is always being redrawn.

So, how does the brain actually work? How does a fleeting spark of electricity turn into the solid, stable feeling of seeing a red apple or remembering a song? This is the big mystery the paper tackles. It moves away from the idea of "searching for files" and looks at the brain as a dynamic, flowing system. Instead of static storage, it focuses on resonance—the same physics that makes a guitar string vibrate when you pluck a matching note, or a bridge shake when a marching band steps in rhythm. The paper asks: What if our thoughts aren't stored in a place, but are actually the vibration itself?

The Brain's Musical Geometry

Enter Hasan Niazi's new idea, called the Hypothesis of Resonance of Closed Neural Network Geometries (RCNNG). It's a mouthful, but the concept is surprisingly musical and geometric.

Niazi suggests that the brain doesn't store information in a specific location. Instead, when you see, hear, or feel something, your brain creates a closed loop—a circular path where signals travel around and around, like a race car on a track. When the signal matches the "speed" of the track, it creates a resonance. Think of it like pushing a child on a swing. If you push at just the right moment, the swing goes higher and higher. In the brain, the percept of red arises when a closed geometry tuned to the spectral properties of red enters resonance.

The paper argues that perception is simply the moment this specific closed geometry, tuned to the input, begins to resonate. It's not that the brain "finds" a memory of red; the specific closed geometry becomes the resonant identity of that experience. The paper explicitly rules out the idea that perception happens in a straight line (like a chain of dominoes falling) or in a branching tree. Those shapes are too simple. You need a closed loop to create the stable, repeating pattern that feels like a real experience.

The "Innergence" of Being

Here is where it gets really cool. The paper introduces a new word: Innergence.

Usually, when we observe something, we are outside looking in (like you looking at a tree). But in this theory, the subjective first-person experience arises from the resonant state of closed geometries. The loop isn't just a machine processing data; the act of the loop vibrating is the feeling of experiencing. When a closed geometry resonates, it creates a "first-person" experience from the inside out. It's like the difference between a recording of a song playing on a speaker (external) and the feeling of the music vibrating in your own chest (internal). The paper suggests that consciousness is what happens when multiple closed geometries across the network resonate, either simultaneously or sequentially, linking up to create a complex, global symphony of experience.

How the Brain "Remembers" Without a Map

If the brain doesn't have shelves, how does it remember? Niazi proposes Resonant Retrieval.

Imagine you have a room full of tuning forks. You don't need to know which fork is which to find the one you want. You just strike a tuning fork that matches the note you're looking for. The matching fork will start vibrating loudly, while the others stay quiet.

In the brain, if you want to remember a face, you don't look up an address. You send a signal that matches the "frequency" of that face. The specific closed loop that was formed when you first saw that face will start to resonate again, bringing the memory back to life. The paper's simulations show that when you repeat a signal (like seeing the same face often), the brain builds more loops tuned to that signal, making the memory stronger and easier to find. It's like having a whole choir of tuning forks all ready to sing the same note.

What the Simulations Showed

The author didn't just dream this up; they used adaptive recurrent networks of 50 to 5,000 nodes to test it.

The Findings: When they fed the networks a repeating signal (like a steady beat), the networks naturally formed closed loops that vibrated in sync with that beat. These loops were stable and didn't fall apart, even when the signal was a little noisy.
The Linking: When they played two signals at the same time, the loops for those signals started to link up. This explains how we associate things (like smelling coffee and remembering morning).
The Math: The paper uses heavy math (like "persistent homology," which is a fancy way of counting loops in a shape) to prove that these vibrating loops are real, stable structures, not just random glitches. The simulations showed that as the network grew, it could hold more of these loops, creating a richer, more complex "inner world."

What This Means (and What It Doesn't)

The paper is very clear about what it has and hasn't done. It hasn't proven that this is exactly how the human brain works in real life yet. It hasn't found a "consciousness meter" to measure these loops in a living person.

Instead, the paper suggests that this is a plausible, physics-based way to explain how the brain could create stable thoughts and feelings without needing a rigid map. It argues that the "feeling" of being you is the result of these closed loops resonating. It rules out the idea that we need a special "address" to find our memories. It also rules out the idea that simple, straight-line signals can create consciousness.

The author proposes that if this theory is right, scientists should be able to find these specific, stable vibrating loops in real brain data using special tools. Until then, RCNNG offers a beautiful, musical picture of the mind: not a library of dusty books, but a living, breathing orchestra of vibrating loops, where every thought is a song the brain sings to itself.

Technical Summary: Hypothesis of Resonance of Closed Neural Network Geometries (RCNNG)

1. Problem Statement

The central challenge addressed by this research is the lack of a principled mechanism explaining how temporally structured sensory inputs are transformed into stable, reproducible perceptual states and first-person phenomenology. While empirical work has characterized cortical dynamics and recurrent circuit motifs, existing computational frameworks (e.g., predictive coding, attractor networks, global workspace) fail to specify how distinct neural activity patterns instantiate the same perceptual experience or how perceptual stability emerges from high-dimensional recurrent dynamics. Specifically, there is no formalized link between resonant closed geometries and subjective phenomenology, nor a mechanism for non-addressable memory retrieval that accounts for the emergence of consciousness.

2. Methodology

The paper proposes the Resonance of Closed Neural Network Geometries (RCNNG) framework, combining theoretical modeling, dynamical systems analysis, and large-scale simulations.

Theoretical Framework

Closed Neural Geometries (CRGs): The core hypothesis posits that perception arises from the formation of physically instantiated closed neural geometries (recurrent loops) whose resonance profiles reflect the temporal-spectral structure of sensory inputs.
Innergence: A novel term coined to describe the intrinsic first-person phenomenological property arising from the resonance of these closed geometries. In this view, the geometry acts as both the observer and the perceiver.
Non-Addressable Storage: Unlike traditional models relying on spatial addressing, RCNNG proposes that information is stored in the configuration structure of topologies and network graphs. Retrieval occurs via resonant reactivation, where inputs matching the natural frequency of a stored geometry amplify it, rather than accessing a specific spatial address.

Mathematical Formalization

Dynamical Systems: The network is modeled as a recurrent system evolving in Euclidean space $X = \mathbb{R}^n$ with a time-dependent weight matrix $W(t)$ . The dynamics are governed by $\dot{x}(t) = -x(t) + W(t)\phi(x(t)) + I(t)$ , where $I(t)$ is periodic forcing.
Bifurcation Analysis: The emergence of CRGs is linked to Hopf-type bifurcations. When the real part of complex eigenvalues crosses zero, the system transitions from a stable equilibrium to a stable limit cycle (the closed geometry).
Topological Data Analysis (TDA): The authors utilize Persistent Homology (specifically Vietoris–Rips filtrations) to analyze the trajectory point clouds of neural activity. They focus on $H_1$ homology groups to identify independent cycles. Long-lived $H_1$ features (high persistence) are interpreted as topological signatures of stable CRGs, distinguishing them from transient noise.
Fourier Decomposition: Complex inputs are decomposed into sinusoidal components. The framework posits that each frequency component acts as an independent driver, recruiting specific loops whose natural frequencies match the input, leading to the superposition of CRGs for multi-frequency stimuli.

Simulation Approach

Network Architecture: Simulations were conducted on adaptive recurrent networks ranging from $N=50$ to $N=5000$ neurons.
Mechanisms: The model incorporates frequency-specific gating (Gaussian gating based on spectral matching), adaptive branching (synaptogenesis driven by rising activation), and synaptic plasticity.
Validation: The study analyzed spectral content (FFT), phase locking (Hilbert transform), correlation matrices, and cycle extraction algorithms to verify the formation of CRGs under sinusoidal and multi-frequency stimulation.

3. Key Contributions

RCNNG Framework: Introduction of a unified theoretical model where perception is the resonance of closed geometries and consciousness is the global resonance of multiple linked or unlinked geometries.
Concept of Innergence: Formalization of "innergence" as the intrinsic phenomenological property of resonant state space identities, bridging physical resonance and first-person experience without requiring an external observer.
Mathematical Proof of Existence: Theoretical proofs (using Brouwer's Fixed Point Theorem and Floquet multipliers) demonstrating the existence of stable periodic orbits (CRGs) under periodic forcing.
Topological Signature of Perception: The application of persistent homology to demonstrate that stable perceptual states correspond to long-lived $H_1$ cycles in the network's state space, providing a topological measure of perceptual stability.
Mechanisms for Association and Memory:
- Associative Binding: Synchronous inputs induce linking between distinct CRGs, explaining how simultaneous stimuli become dynamically coupled.
- Representational Strengthening: Repeated stimulation increases the number of CRGs tuned to a specific frequency, providing a mechanism for memory consolidation and perceptual robustness.

4. Results

Dynamical Transition: Simulations revealed a systematic transition from low-dimensional, synchronized activity in small networks to high-dimensional, chaotic dynamics with localized correlation patches in large networks ( $N=5000$ ).
CRG Formation: Under periodic stimulation, the network consistently formed stable limit cycles (CRGs). The number of these geometries increased with repeated stimulation or increased input amplitude.
Linking and Propagation: Synchronous inputs successfully induced phase-locking and stable synaptic links between distinct geometries, facilitating resonance propagation and associative recall.
Topological Persistence: Gradient persistence diagrams confirmed that CRGs correspond to highly persistent $H_1$ features (red in the diagram), whereas transient structures correspond to short-lived features (blue). This confirms that resonant geometries are robust attractors, not transient artifacts.
Fourier Alignment: The spectral structure of the input directly dictated the geometry of the attractors. Multi-frequency inputs produced composite attractors that were the geometric superposition of individual CRGs.

5. Significance and Claims

The paper claims that RCNNG provides a physics-based mechanism for storage, recall, and mental experience that does not rely on spatial addressing. By distinguishing between the physical formation of closed geometries and their resonant identities, the framework offers a unified account of:

Perceptual Stability: Explained by the robustness of limit cycles against noise.
Memory Recall: Achieved through resonant reactivation rather than positional access.
Consciousness: Emerges from the simultaneous or sequential resonance of multiple geometries across the network.
Phenomenological Emergence: The concept of "innergence" characterizes the first-person aspect of these resonant states.

The authors assert that recent empirical findings (e.g., decision-related activity in early sensory cortices via feedback loops) align with the RCNNG prediction that perceptual states are instantiated within closed recurrent geometries. The paper concludes by proposing falsifiability criteria, including the absence of persistent $H_1$ cycles in the absence of stable percepts and the failure of artificial stimulation to reproduce percepts if the resonance mechanism is disrupted.

Note: The paper explicitly states that the motivational citations in the introduction belong to the cited works and does not claim to have solved the hard problem of consciousness, but rather offers a candidate mechanism ("innergence") and a dynamical foundation for understanding the emergence of stable perceptual states.