Neuron-Subnetworks: Formation and Function

• Neuron-subnetworks are modular assemblies with strong internal connectivity that specialize in specific processing tasks.
• Biologically plausible STDP rules—including excitatory Hebbian and two forms of inhibitory plasticity—drive self-organization and competitive segregation.
• Spontaneous reactivation within subnetworks reinforces memory consolidation and enables dynamic integration between specialized modules.

Neuron-subnetworks are structurally and functionally distinct subnetworks embedded within larger neural systems—biological or artificial—characterized by strong internal connectivity, possible specialization for particular processing tasks, or modular computational properties. In both biological and artificial systems, the compartmentalization of neurons into subnetworks supports specialized information processing, integration, and adaptability. Recent research elucidates the mechanisms by which these subnetworks form, how they persist and change, and their importance for both segregated (specialized) and integrated (binding) information processing in nervous systems and neuromorphic designs.

1. Formation of Modularity via Local Plasticity Rules

The emergence of neuron-subnetworks (modules) in recurrent spiking neural networks can be driven by biologically plausible, local spike-timing-dependent plasticity (STDP) mechanisms that require no external control or homeostasis (Bergoin et al., 28 May 2024). In models composed of excitatory and two inhibitory neuron subpopulations, distinct STDP rules induce modular structure:

• Excitatory STDP (asymmetric, Hebbian): Drives potentiation within synchronously firing neuron groups subjected to targeted stimuli, reinforcing intra-module excitatory connections.
• Inhibitory STDP (two types):
  • Hebbian inhibitory STDP: Provides homeostatic, within-module feedback inhibition, stabilizing activity and preventing runaway excitation.
  • Anti-Hebbian inhibitory STDP: Enforces lateral (between-module) competition, sharpening selectivity by introducing competitive inhibition between different neuronal assemblies.

During learning, alternating stimuli to distinct subgroups cause their spontaneous synchronization and the strengthening of internal synapses. This results in the self-organization of stable modules—sets of neurons with intensive intra-cluster and suppressed inter-cluster connectivity (see Table below).

Inhibitory Population	Plasticity Rule	Functional Role
Hebbian	Symmetric “Mexican hat”	Maintains firing rate, homeostasis
Anti-Hebbian	Negative “Mexican hat”	Pattern selectivity, lateral inhibition

After learning, the network exhibits modular architecture, with each module representing a distinct stored memory or sensory feature.

2. Post-learning Spontaneous Dynamics and Subnetwork Consolidation

Following learning, neurons and synapses are not frozen; spontaneous asynchronous irregular activity persists even in the absence of further stimuli (Bergoin et al., 28 May 2024). This “resting” network state has several distinctive features:

• Low-rate, desynchronized firing: Neurons fire at low rates reminiscent of in vivo cortical recordings, reflected by a Kuramoto order parameter scaling as $1/\sqrt{N}$ with network size.
• Transient, partial synchrony (“spontaneous memory recalls”): Occasionally, subsets (modules) of neurons synchronously fire, reactivating internal synapses through ongoing STDP updates.
• Ongoing consolidation: These spontaneous recalls reinforce intra-module synapses, maintaining memory representations over long timescales by counterbalancing any slow synaptic depression ("forgetting") present in the plasticity rule.

A plausible implication is that continuous, spontaneous activity-driven reactivation in subnetworks is fundamental for the long-term consolidation and stability of memories in biological systems.

3. Roles of Inhibitory Subpopulations in Functional Segregation and Integration

The modular organization crucially depends on the interplay between different inhibitory STDP subpopulations (Bergoin et al., 28 May 2024):

• Hebbian inhibition provides feedback within modules, maintaining stable firing rates and preventing hyperactivity or epileptiform events.
• Anti-Hebbian inhibition shapes the selectivity landscape by reinforcing distinctness between modules, ensuring that when one memory or functional group is reactivated, it suppresses spurious activation in others.

This division of labor underpins the coexistence of vastly segregated specialized subnetworks (e.g., representing different sensory features) and the potential for selective integration or “binding” when required. Experiments with overlapping stimuli in the model lead to “hub neurons” with mixed selectivity—nodes that can mediate integration between specialized subnetworks, reflecting the known concept of “mixed selectivity” in higher cortical areas.

4. Biological Plausibility and Structural Constraints

The network model ensures a high degree of biological realism, encoding crucial features:

• Dale’s principle: Excitatory and inhibitory cells are distinct, with fixed sign synaptic outputs.
• Plasticity rules: All synaptic changes are local, depending only on the timing of pre- and post-synaptic spikes.
• Continuous adaptation: Unlike traditional machine learning settings, synaptic plasticity operates continuously, not only during a fixed “training” phase.
• Noise and heterogeneity: The system embeds ongoing noisy input and neuronal parameter heterogeneity, resulting in irregular activity and realistic state transitions.

These constraints guarantee that the phenomena observed—modular subnetwork formation, recall, stabilization—are not artifacts of artificial design but likely reflections of genuine neural circuit organization principles.

5. Mechanistic Basis for the Segregation–Integration Balance

A persistent question in neuroscience is how the brain achieves both specialization (segregation) and flexible grouping (integration) required for higher cognition. The described framework demonstrates that the combination of local learning rules, distinct inhibitory circuitry, and ongoing plasticity is sufficient for:

• Specialization: Stable, persistent subnetworks selective for stimulus-defined features or memories.
• Integration: Maintenance of mixed-selectivity hubs and the potential for dynamic binding via recurrent activation, enabling the exchange or transformation of information across subnetworks.

The dynamic balance between excitation, Hebbian inhibition, and anti-Hebbian inhibition allows for the maintenance of discrete assemblies and their flexible recombination.

6. Broader Implications for Network Organization and Function

Several broader consequences emerge from these findings:

• Self-organization: Modular subnetwork architecture can be achieved autonomously, without explicit top-down control, specialized homeostatic adjustment, or optimization on global metrics.
• Memory maintenance: Spontaneous, “resting-state” reactivation events serve not only as consolidation mechanisms in biological networks but may also inspire strategies for continual learning in neuromorphic and artificial systems.
• Excitatory/inhibitory diversity: The presence of distinct inhibitory neuron types and their complementary plasticity rules is essential for the coexistence of network stability and pattern selectivity, echoing patterns seen in cortical microcircuitry.
• Potential for computational paradigms: The modular, hierarchical organization seen in these models suggests approaches for designing scalable artificial neural algorithms capable of specialization and flexible integration as seen in biological brains.

In sum, the emergence and maintenance of neuron-subnetworks—modular assemblies arising from local excitatory and diverse inhibitory STDP—provide a mechanistic account for the origin of brain modularity and its functional persistence. The framework indicates that segregated and integrated information processing are natural consequences of ongoing synaptic plasticity operating in suitably structured recurrent networks, and that spontaneous dynamical phenomena after learning are integral to the stability and specialization of subnetworks underlying complex behavior (Bergoin et al., 28 May 2024).