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A Spiking Neural Network Model of Elementary Self-Consciousness via Endogenous Default Mode Network Dynamics

R. Lahoz-Beltra

arXiv:2609.29984v1q-bio.NCcs.NE

TL;DR

Modeling how passive sensory reception becomes active, self-sustaining internal states remains a challenge for computational accounts of consciousness. The paper proposes a spiking neural network with sensory and DMN pacemaker subsystems. It reports synthetic information integration during coactivation, while leaving the substrate dependence of phenomenal experience unresolved.

  • Problem

    Computational models often focus on feedforward sensory hierarchies or global workspace architectures, while capturing the shift to active, self-sustaining internal states with biologically realistic spiking networks remains a challenge.

    Source: §1 · pp. 1–2

  • Method

    The paper models baseline self-consciousness with a 10,000-neuron Izhikevich network combining a sensory layer and DMN pacemaker module, tonic neuromodulatory currents, and asymmetric top-down weights.

    Source: §1 · p. 2

  • Results

    The model synthetically generated complex information integration, with φ reaching 12.5–15.0 bits during sustained DMN–sensory coactivation, without resolving phenomenal experience’s substrate dependency.

    Source: §3 · p. 10, §4 · p. 11

  • Takeaways & Limitations

    The model provides an algorithmic framework for examining complex information integration, while leaving the substrate dependence of phenomenal experience unresolved.

    Source: §4 · p. 11

    Because digital computers process algorithms sequentially on classical hardware, the numerical model is a structural copy whose non-zero φ values are an informational proxy, not subjective feel.

    Source: §4 · p. 11

Abstract

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Understanding the neurobiological mechanisms underlying self-referential cognition and baseline self-consciousness remains a fundamental challenge in computational neuroscience. In this work, we propose a large-scale computational model incorporating a 10,000-neuron spiking neural network (SNN) based on Izhikevich dynamics. The network is structured into two interacting subsystems: a sensory processing layer (5,000 regular-spiking cortical neurons) and an endogenous Default Mode Network (DMN) pacemaker subsystem (5,000 intrinsically bursting neurons). The DMN layer is modulated by continuous tonic currents reflecting ascending brainstem neuromodulation, maintaining intrinsic, autonomous bioelectric rhythms independent of external sensory input. To represent top-down cognitive modulation, synaptic weights are hierarchically structured such that DMN-to-network projections exceed sensory-level connections. Through numerical simulations using a modified two-step Euler integration scheme, we demonstrate how endogenous pacemaker activity interacts with transient external sensory perturbations, providing an elementary mathematical framework for the emergence of a persistent, self-sustaining neural representation of "Self".

1. Introduction

The introduction frames baseline self-consciousness as rooted in endogenous DMN activity and presents a spiking-neural-network model in which tonic neuromodulation and stronger top-down connections sustain activity amid sensory perturbations.

1. Introduction

  • The introduction associates self-referential processing, mind-wandering, and baseline self-awareness with the DMN, which maintains rhythmic activity without sensory input or goal-directed tasks (Raichle et al., 2001; Raichle, 2015).It describes the DMN as including posterior cingulate, medial prefrontal, and thalamic hubs (Steriade, 2006).Source: §1 · p. 1
  • The authors identify a need for biologically realistic spiking networks with intrinsic bursting and pacemaker oscillations to model transitions from passive sensory reception to self-sustaining internal states.They note that computational models often focus instead on feedforward sensory hierarchies or global workspace architectures.Source: §1 · pp. 1–2
  • The proposed 10,000-neuron model uses tonic neuromodulatory currents and asymmetrical top-down weights to maintain an autonomous bioelectric “pulse of the Self” amid sensory perturbations.It divides the network into a 5,000-neuron sensory layer and a 5,000-neuron DMN pacemaker module.Source: §1 · p. 2
  • Figure 1 specifies a 5,000-neuron regular-spiking sensory layer and a 5,000-neuron intrinsically bursting DMN, with wDMN = 0.6, wSensory = 0.4, and Itonic = 7.0 pA.The figure also describes integrated-information calculations from binary spike matrices and continuous dynamic φ trajectories for simulated Qualia states.Source: Figure 1 · p. 2, §1 · p. 2

2. Model Formulation and Biophysical Dynamics · 2.1 Bioelectric Engine: Izhikevich Spiking Dynamics

The model uses Izhikevich spiking dynamics to govern individual neurons, with membrane potential and recovery evolving under input current and an after-spike reset rule.

2.1 Bioelectric Engine: Izhikevich Spiking Dynamics

  • Each neuron follows a two-dimensional system of coupled ordinary differential equations based on Izhikevich (2003).The equations are presented as equation (1).Source: §2.1 · p. 2
  • When membrane potential reaches 30 mV, the after-spike rule resets v to c and increments u by d.Source: §2.1 · p. 3
  • The membrane potential v and recovery variable u evolve under total input current I, which combines external stimuli, synaptic integration, and intrinsic tonic drive.The recovery variable provides negative feedback to v.Source: §2.1 · p. 3
  • Parameters a, b, c, and d set the firing dynamics: recovery timescale, subthreshold sensitivity, voltage reset, and recovery increment, respectively.Source: §2.1 · p. 3

2.2 Network Architecture and Heterogeneity

The 10,000-neuron network pairs a heterogeneous sensory layer of regular-spiking cortical neurons with a DMN pacemaker subsystem whose designated core produces autonomous bursting pulses representing the basal core of the “Self”.

2.2 Network Architecture and Heterogeneity

  • The network comprises 10,000 spiking neurons divided into sensory-processing and DMN pacemaker sub-networks.The architecture is shown in Figure 2.Source: §2.2 · p. 3
  • The sensory layer contains 5,000 cortical excitatory pyramidal neurons with regular-spiking dynamics and randomly drawn resetting parameters to capture physiological heterogeneity.The passage states that the baseline reset potential is centered around -65 mV.Source: §2.2 · p. 3
  • The DMN subsystem contains 5,000 pacemaker-like bursting units representing thalamocortical and posterior cingulate assemblies.A designated 1,000-neuron core is assigned deterministic parameters c_i = -55.0 mV and d_i = 4.0.Source: §2.2 · p. 3
  • Elevating the core neurons’ c_i to -55 mV shortens their refractory period, induces intrinsically bursting behavior, and generates an autonomous bioelectric pulse representing the basal core of the “Self”.Source: §2.2 · p. 3

2.3 Synaptic Connectivity and Hierarchical Topology

The network uses sparse connectivity and hierarchical synaptic weights that give DMN-to-sensory projections greater strength than sensory-level connections. Its micro-cortex block contains 10,000 neurons and 10 million synapses.

2.3 Synaptic Connectivity and Hierarchical Topology

  • Each neuron has K = 1,000 random outgoing projections, and the network stores 107 total synaptic connections in sparse format.Source: §2.3 · p. 3
  • DMN-to-sensory projections have weight 0.6, versus 0.4 for lower-level sensory connections, enabling the “Self” network to modulate sensory representations.The passage attributes this asymmetry to the functional supremacy of the DMN (Varela et al., 2001).Source: §2.3 · p. 4
  • The micro-cortex block contains 10,000 neurons and 10 million synapses, with a boundary between DMN and sensory layers.Source: Figure 2 · p. 4

2.4 Biological Model of Self-Consciousness and Input Currents

The model’s neuronal input current combines endogenous tonic drive, transient sensory input, synaptic transmission, and stochastic noise. It specifies how these inputs sustain intrinsic DMN activity and allow sensory-driven changes in network synchrony.

Input-current integration

  • Each millisecond, neuronal input integrates endogenous, exogenous, synaptic, and stochastic currents, including recurrent DMN and sensory input.Figure 3 depicts these four sources as neuromodulatory tonic input, recurrent DMN input, sensory synaptic input, and noise.Source: §2.4 · p. 4, Figure 3 · p. 5

Endogenous tonic current

  • Continuous dopaminergic and cholinergic brainstem neuromodulation supplies tonic current to core DMN pacemaker neurons 5,000–5,999.The passage identifies this input as important for wakefulness and intrinsic DMN activity.Source: §2.4 · p. 4

Exogenous transient stimuli

  • A step-current stimulus targets 1,500 sensory neurons during the 300–600 ms window.Source: §2.4 · p. 4

Synaptic current integration

  • Synaptic currents propagate spikes through the connectivity matrix, altering “Self” synchrony and shifting the network from an internal baseline to an attentional state.The passage defines presynaptic firing for propagation as a membrane potential of at least 30 mV in that millisecond.Source: §2.4 · p. 5

2.5 Numerical Integration

Network dynamics are evaluated with a modified two-step (half-step) Euler method at a fixed 1.0 ms time step, balancing numerical stability and computational efficiency without the overhead of 4th-order Runge-Kutta schemes.

2.5 Numerical Integration

  • The modified two-step (half-step) Euler method uses a fixed 1.0 ms time step to balance stability and efficiency while avoiding 4th-order Runge-Kutta overhead.Source: §2.5 · p. 5
  • Equations (11)–(13) specify the voltage and recovery-variable updates used by the integration scheme.Source: §2.5 · p. 6

2.6 Quantification of Conscious Experience and Qualia via Integrated Information Theory (IIT)

The section operationalizes IIT’s φ as a measure of informational integration and dynamic coupling between sensory activity and the DMN. It estimates this coupling from spiking patterns and cross-network covariance, comparing the full system with a partition that treats the two subsystems as independent.

2.6 Quantification of Conscious Experience and Qualia via Integrated Information Theory (IIT)

  • φ measures informational integration and, in this model, the dynamic functional coupling between sensory activity and the DMN as sensory perturbations modify endogenous “Self” dynamics.IIT frames integration as information generated by the unified whole exceeding the sum generated by isolated parts.Source: §2.6 · p. 6

2.6.1 Temporal Window Selection and Binary Spiking Matrix

  • Activity is analyzed in discrete windows of duration τ ms by selecting up to 200 active neurons and encoding their spikes in a binary neuron-by-time state matrix.The matrix element X_i,t indicates whether neuron i fired at time t.Source: §2.6.1 · pp. 6–7

2.6.2 Firing Rates and Cross-Covariance Matrix

  • Mean firing rates and pairwise cross-covariances characterize population synchrony; positive covariance indicates systematic co-activation or phase-locking within the window.The pairwise values form a global empirical covariance matrix for the selected population.Source: §2.6.2 · p. 7

2.6.3 System Bipartition and Integrated Information (φ )

  • For the integrated-information calculation, active neurons are partitioned by anatomy into sensory and DMN submatrices, and a block-diagonal covariance matrix treats them as functionally independent.Source: §2.6.3 · p. 7
  • The covariance-based φ compares the determinant of the full-system matrix with its partitioned counterpart: zero cross-network correlation yields φ = 0, while stronger reciprocal covariance from sensory-driven DMN changes increases φ.The section interprets increased φ as signaling integrated phenomenal consciousness or Qualia.Source: §2.6.3 · p. 8

3. Results

Across a 900 ms simulation, persistent DMN pacemaker activity alternated with synchronized bursts that recruited the sensory layer. Integrated information rose with cross-network coupling and peaked during burst co-activation.

3. Results

  • During quiescent windows, sensory neurons remained silent while core DMN pacemakers fired persistently and asynchronously at low frequency under a 7.0 pA tonic current.The reported windows include 150–300 ms, 430–480 ms, and 650–780 ms.Source: §3 · p. 8
  • Four synchronized population events occurred near 30, 330, 550, and 830 ms, with DMN excitation and top-down projections recruiting sensory neurons and driving firing rates to ≈1000 Hz.The cited figure describes transitions from low-firing regimes of 0–10 Hz to saturated burst states.Source: §3 · pp. 8–9, Figure 5 · p. 9
  • Integrated information peaked at φ ≈12.5–15.0 bits during sustained sensory–DMN co-activation in the third and fourth burst windows.The peaks occurred around 530–590 ms and 820–880 ms, when cross-covariances surged.Source: Figure 5 · p. 9, §3 · pp. 9–10
  • Integrated information was ≈0 bits in isolated states and ≈1–2.5 bits in pre-burst priming states, rising as sparse coupling bridged DMN and sensory populations.Without sensory–DMN interaction, the global covariance matrix became block-diagonal; priming before bursts broke this independence and raised φ.Source: §3 · p. 9

4. Discussion

The model’s integrated information is near zero during isolated, asynchronous baseline activity and rises to approximately 12.5–15.0 bits during sensory-triggered cross-network bursts. The authors frame these values as evidence of synthetic information integration, not proof of phenomenal consciousness, and outline hardware, plasticity, and biological-validation extensions.

4. Discussion

  • Near zero, φ during isolated baseline activity rises to approximately 12.5–15.0 bits during sensory-triggered bursts with cross-network co-activation and phase synchrony.The network pairs 5,000 regular-spiking sensory neurons with 5,000 intrinsically bursting DMN pacemakers; DMN-to-network weights are 0.6 versus 0.4 for sensory connections.Source: §4 · p. 10
  • The computed φ is an informational proxy, not subjective experience: the digital model simulates access consciousness without establishing phenomenal consciousness.The authors describe the implementation as a functional simulation or P-zombie, and say synthetic integration does not resolve the substrate dependency of phenomenal experience.Source: §4 · pp. 10–11
  • Chalmers (1996) argues functional organization could suffice for experience, whereas Searle (1980, 1992) holds that simulation lacks consciousness without biological causal powers.The discussion presents φ as a structural metric for the Hard Problem (Chalmers, 1995), while noting Searle’s view that computation manipulates syntax without semantic understanding or subjective awareness.Source: §4 · p. 11
  • Future work proposes porting the DMN architecture to neuromorphic hardware and adding STDP so synaptic weights can adapt with co-activation history.The proposed plasticity is intended to support long-term memory traces and self-organization of top-down modulatory weights during prolonged sensory exposure (Indiveri et al., 2011).Source: §4 · p. 11
  • The authors propose comparing simulated φ(t) trajectories with electrophysiological recordings from living human organoid networks to biologically validate the DMN–sensory integration hypothesis.The proposed platform pairs 3D cortical organoids with microelectrode arrays (Smirnova et al., 2023).Source: §4 · p. 11
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