Topology-Dependent Emergence of Polychronous Neuronal Groups: A Recurrence-Plot Characterization

Abstract: Polychronous Neuronal Groups (PNGs) reproducible, time-locked spatiotemporal firing cascades stabilised by Spike-Timing-Dependent Plasticity (STDP) and heterogeneous axonal delays provide a combinatorially rich substrate for neural computation whose structural determinants remain poorly understood. We simulate a recurrent network of N=1000 Izhikevich neurons over ten hours of biological time and identify 1545 unique PNGs via an offline event-driven detection algorithm. A parametric Watts-Strogatz topology sweep reveals that the clusteringcoefficient C is the primary structural driver of PNG yield: the transition from a ring-lattice (C~0.35, $\sim!850$ \PNGs) to a random graph (C~!0.20$, $<!50$ \PNGs) reduces representational capacity by more than 90%. We further introduce a sparse-dot-product Recurrence Plot (RP) framework that identifies PNGs as unit-slope diagonal structures in the phase-space recurrence matrix, entirely independent of anatomical neuron labelling. Recurrence Quantification Analysis yields DET~0.65, quantifying the reproducibility of the network's dynamical trajectory. Together, the results establish small-world topology as the structural optimum for polychronization and the \RP decoder as a principled, label-free tool for PNG identification.

• The paper demonstrates that high clustering in network topology sharply increases the yield of polychronous neuronal groups.
• It introduces a label-free, recurrence plot-based methodology to detect and quantify spatiotemporal firing patterns in large-scale spiking neural networks.
• The findings offer practical insights for designing neuromorphic systems and SNNs optimized for memory, sequence processing, and complex temporal coding.

Topological Determinants and Label-Free Characterization of Polychronous Neuronal Groups

Introduction

The paper "Topology-Dependent Emergence of Polychronous Neuronal Groups: A Recurrence-Plot Characterization" (2606.25874) investigates how network topology fundamentally determines the emergence and abundance of Polychronous Neuronal Groups (PNGs)—spatiotemporal firing patterns stabilized by Spike-Timing-Dependent Plasticity (STDP) and axonal delay heterogeneity. Importantly, the paper introduces a novel label-free Recurrence Plot (RP) methodology for the principled detection and quantification of PNGs in recurrent spiking neural networks (SNNs).

Model and Methodology

The authors employ a 1,000-neuron Izhikevich SNN (80% excitatory, 20% inhibitory) with conductance-based, delay-heterogeneous synapses and plasticity governed by classical STDP with a homeostatic drift. Excitatory connections have variable axonal delays in the biologically plausible range [1, 20] ms, while inhibitory delays are fixed at 1 ms. Simulations are conducted over 10 hours of biological time with $\Delta t$=0.1 ms integration to capture fine-scale temporal structure, validated with the Brian2 simulator.

A core methodological innovation is the application of a parametric Watts-Strogatz network topology sweep—systematically interpolating clustering and randomness via rewiring probability—to explore the impact of local clustering (clustering coefficient, $C$) on PNG properties. The PNG detection pipeline is event-driven and identifies reproducible cascades triggered by triplets of presynaptic anchors (requiring multiplexed, delay-matched convergence).

For post hoc analysis, the paper introduces a sparse-dot-product Recurrence Plot framework. Rather than relying on anatomical neuron labels or online detection, the RP is computed as the time-time similarity matrix of spike-pattern vectors generated via sliding-window embeddings of the population spiking matrix. Recurring diagonal structures in this phase space indicate repeated cascades corresponding to PNGs. Recurrence Quantification Analysis (RQA)—focusing on determinism (DET), recurrence rate (RR), and entropy (ENTR)—enables quantification of spatiotemporal reproducibility, a key hallmark of PNG dynamics.

Results

STDP-Driven Network Self-Organization

Following extended STDP dynamics, the network converges to an asynchronous irregular (AI) regime—characterized by sparse, largely desynchronized excitatory firing and a strongly bimodal distribution of excitatory synaptic weights. This bimodality is a functional signature of STDP: potentiation and depression create a skeleton of privileged, delay-matched pathways forming the backbone for PNGs, while non-contributory synapses are silenced.

PNG Emergence: Numerical Yield and Structural Statistics

Running the PNG detection pipeline, the study identifies 1,545 unique PNGs in the full-size network (ER topology). The cascade-length and duration distributions of these groups are heavy-tailed, with typical groups involving 7-32 spikes and durations peaking in the 20-30 ms range, but with a tail extending beyond 50 ms. Notably, detected PNGs frequently span multiple causal layers and can propagate well beyond the maximum single-synapse delay—demonstrating genuine multi-layer, self-sustaining chains rather than shallow coincidence events.

Topology-Dependence of PNG Capacity

A parametric sweep from ring lattice ($C\approx0.35$) to random graph ($C\approx0.20$) reveals a monotonic, sharp dependence of PNG yield on the clustering coefficient:

• Highest PNG yields (≥850) occur at maximum clustering (ring-lattice).
• Yield collapses (>90% reduction, <50 PNGs) with the destruction of clustering (random graph), even as average path lengths decrease.

The phase transition in PNG capacity coincides with the classical small-world transition (rewiring probabilities $p \in$ [0.01, 0.05])—the regime in which network clustering decays before global efficiency is maximized. Additionally, both mean and maximum PNG cascade lengths decrease with clustering, linking topological locality directly to the depth and persistence of reproducible patterns.

Label-Free PNG Detection via Recurrence Plots

The RP-based analysis provides a label-independent, data-driven tool for visualizing and quantifying repeated PNG activations. While classical spike rasters appear featureless under random neuron order, RPs display unit-slope diagonals for every reactivated PNG.

• Determinism (DET) stabilizes at ~0.65, quantifying the high reproducibility of phase-space trajectories due to PNGs.
• RR and ENTR statistics further support the diversity and sparsity of cascade repeats.

The RP approach is robust to anatomical relabeling and does not rely on explicit knowledge of group membership, thus offering a substantial methodological improvement for the analysis of both simulated and experimental spiking data.

Theoretical and Practical Implications

Theoretical Implications

This work tightly links the combinatorial representational power of polychronization to explicit structural motifs—highlighting the small-world regime as the topological optimum for maximized PNG yield. The results support the hypothesis that mammalian cortical circuits—empirically situated near the small-world transition—may be optimized for the combinatorial richness required for complex temporal cognition, memory, and sequence learning.

The demonstration that clustering, rather than path length, is the essential determinant for PNG emergence contradicts prior assumptions favoring random-graph (ER) models and situates the polychronization framework in closer correspondence with empirical cortical wiring.

The RP-based methodology—by providing a label-agnostic decoder—bridges the gap between theoretical SNN models and data from in-vivo multi-electrode or calcium-imaging experiments, enabling systematic probing of temporal coding frameworks in biological tissues.

Practical Implications and Future Directions

The findings have concrete implications for neuromorphic engineering, computational neuroscience, and the analysis of large-scale neural data:

• Design of artificial SNNs: Small-world topologies should be favored when constructing SNNs intended to exploit polychronization for memory and sequence-processing applications.
• Data analysis: The RP/RQA framework enables post hoc investigation of spatiotemporal patterns in high-dimensional population recordings, circumventing the need for neuron identity tracking or real-time detection.
• Experimental translation: The approach is scalable to large neural datasets, provided sufficient sampling to observe pattern recurrence.

Limitations noted include the restriction to anchor triplets in PNG detection (potentially undercounting larger, more complex assemblies), the absence of stochastic perturbations beyond Poisson drive, and reliance on single-run statistics. Addressing these will require extension to higher-order anchor detection (e.g., with sequence hashing algorithms), ensemble and noise robustness analyses, and comprehensive finite-size scaling.

Future development may also include deployment of the RP pipeline to empirical data, delineation of phase boundaries under broader biological constraints, and the exploration of homeostatic and non-Hebbian plasticity regimes.

Conclusion

This study provides a comprehensive, quantitative, and mechanistically grounded analysis of how network topology governs the emergence of polychronous neuronal computation. By identifying the small-world regime as optimal and introducing a robust, label-free detection method based on recurrence analysis, the paper advances both theoretical understanding and practical methodology for studying complex spatiotemporal firing patterns in neural systems. These results establish a nuanced phase diagram for polychronization and constitute a bridge toward the analysis and interpretation of such dynamics in biological networks and neuromorphic architectures (2606.25874).