Spontaneous Repetition Processes

• Spontaneous repetition processes are internally generated recurrences arising from critical network dynamics and adaptive feedback, facilitating memory consolidation.
• Research uses order parameters and neural avalanche metrics to quantify phase transitions between stable attractors and intermittent replay patterns.
• Feedback mechanisms and spike-timing-dependent plasticity in neural and computational models drive emergent repetition, ensuring robust sensory coding and behavioral adaptation.

Spontaneous repetition-related processes refer to internally generated phenomena in neural, behavioral, and cognitive systems where patterns, actions, or representations recur intermittently or in bursts without explicit external cues or task constraints. These processes are increasingly understood as emergent outcomes of fundamental network dynamics near critical points, the resonance of sensory feedback with internal circuits, and adaptive learning mechanisms in biological and artificial systems. Across research domains, spontaneous repetition has been linked to mechanisms of memory consolidation, efficient neural coding, and the criticality of brain states.

1. Order Parameters, Excitability, and Phase Dynamics

The emergence and regulation of spontaneous repetition in neural networks are mechanistically described via an order parameter that quantifies the similarity between ongoing activity and stored phase-coded spatiotemporal patterns (Scarpetta et al., 2013). This parameter is constructed as an averaged overlap, $m = \max_T \langle |q(t, t+T)| \rangle$, with %%%%1%%%% indicating the time-dependent match between spike times and pattern templates. In this framework:

• High excitability (low spiking threshold, $\theta_2$) ensures stable attractors, leading to persistent spontaneous replay of one stored pattern, with $m \approx 1$ and minimal fluctuations.
• Low excitability (high $\theta_2$) results in attractor destabilization, with $m \approx 0$, and minimal correlation with stored templates.
• Critical excitability levels ($\theta_2$ near a critical value) induce instability in attractors such that noise triggers brief, intermittent replays of the stored patterns—demonstrating scale-free, phase transition behaviors.

The phase transition is marked by maximized fluctuations in $m$: $$\Delta^2(m) = N [\langle |q(t,T)|^2 \rangle - \langle |q(t,T)| \rangle^2]$$, signifying a regime where the system is maximally sensitive, generating spontaneous repetitions as avalanches.

2. Neural Avalanches and Scale-Free Repetitions

At the critical point between stable replay and non-replay, the system exhibits robust neural avalanches, defined as bursts of spiking activity separated by silent gaps. Avalanche size ($s$) and duration ($T$) follow power-law distributions—$P(s) \sim s^{-\beta}$ with $\beta \approx 1.55$ and $P(T) \sim T^{-\alpha}$ with $\alpha \approx 1.63$. The size-duration scaling $\langle s \rangle(T) \sim T^k$ with $k \approx 1.14$ aligns these exponents with experimental findings. This critical avalanche regime manifests only in the intermediate zone, confirming that spontaneous repetition is an emergent property of critical network dynamics rather than a product of stable attractors or noise-driven patterns in subcritical/supercritical regimes.

3. Mechanistic Role of Noise and Network Plasticity

Noise is not a mere source of randomization—it facilitates transitions between dynamical regimes and sustains homeostasis near criticality (Ikeda et al., 16 Feb 2025). Spiking neural network simulations reveal that baseline noise-driven spontaneous activity can transition a network disrupted by repetitive stimulation back to a self-organized critical state, reflected in the restoration of criticality indices ($A_{Cr}$) and EI balance. Mathematically, criticality is determined by the deviation of avalanche size distributions from power law, $$A_{Cr} = \{A_{upper} ~\text{if}~|A_{upper}| \geq |A_{lower}|; ~A_{lower}~\text{otherwise}\}$$. Spontaneous firing and spike-timing-dependent plasticity (STDP), implemented via asymmetric windows such as:

$$F_E(t) = \begin{cases} A_E \exp(-t/\tau_E), & t \geq 0 \ -A_E B_E \exp(t/\tau_E), & t < 0 \end{cases}$$

enable dynamic EI adjustment, prolong fading memory traces, and maintain optimal computational performance—all essential for the persistence and recurrence of internal patterns.

4. Replay, Memory Stabilization, and Topological Suppression

Spontaneous repetition processes extend to the stabilization and consolidation of internal representations in cognitive maps. Hippocampal place cell replays during rest—endogenous, noise-triggered reactivations of prior trajectories—are modeled as sequences of coactivity simplexes injected into decaying networks (Babichev et al., 2018). Without replays, rapid turnover of cell assemblies produces fragmentation and spurious topological fluctuations (elevated Betti numbers $b_0$, $b_1$). Replay events cyclically rejuvenate decayed connections, restoring connectivity (with $b_0 = 1$ for map unity) and suppressing topological defects, as measured by persistent homology. The temporal organization (frequency, compression, randomness) of replay sequences is essential for optimal suppression of such fluctuations and for bridging transient synaptic events with stable spatial memory.

5. Adaptive Feedback and Repetition in Behavioral Sequences

In sensorimotor systems, spontaneous repetition is shaped by adaptive feedback loops. Songbirds produce repeated syllable sequences via positive auditory-motor feedback, with each repetition inducing short-term synaptic depression, driving the system from an initial high repeat probability to a gradual transition, thus preventing indefinite perseveration (Wittenbach et al., 2015). The feedback decay is captured as $A(n) = a_0 \exp(-nT/\tau)$, with $Pr(n) = 1 - \frac{c}{1 + ab^n}$ describing the non-Markovian repeat distribution. Experimental manipulations, such as deafening, confirm the essential role of feedback in sustaining repetition, directly linking adaptive sensory feedback mechanisms with spontaneous behavioral repetition distributions.

6. Cognitive and Computational Perspectives

Spontaneous repetition is fundamental to human pattern recognition—not only at the neural but also at the algorithmic level. Computational cognitive models represent repetition via hierarchical templates, utilizing combinators (e.g., $Rep~e~m~[e]$ in template programs) and weighted deduction systems to infer compressed generative processes (Ren et al., 14 Apr 2025). The minimal description length principle favors representations that factor out repeated subcomputations, suggesting mental representations may encode patterns as recursive, variable-free subroutines. These models provide a unified account for repetition in music, action plans, and language, offering a formal framework for the abstraction and generalization of repeated relational structures.

7. Implications and Broader Significance

The synthesis of spontaneous repetition-related processes across neural, behavioral, and computational systems reveals several convergent themes:

• Networks poised near criticality—or undergoing appropriate noise-driven homeostatic mechanisms—produce intermittent and scale-free repetitions, fundamentally linked to optimal information processing and memory consolidation.
• Feedback adaptation and sensory loop dynamics regulate the timing, frequency, and distribution of repetitive motor actions, shaping the structure of behavioral sequences.
• Computational models and network analyses demonstrate that spontaneous repetition is not a trivial byproduct of noise, but an emergent, regulated property with constructive functional roles.
• These findings shed light on the substrate of memory, the origin of neural avalanches, the architecture of behavioral patterns, and the cognitive representation of complex hierarchical relations.

Contemporary research continues to dissect the precise parameters governing transitions between non-repetitive and repetitive regimes, highlighting the significance of excitability, plasticity, topological integrity, and adaptive feedback in maintaining the balance between persistence and flexibility in biological and artificial systems. Spontaneous repetition is best understood as an emergent property at the intersection of noise, critical dynamics, adaptive feedback, and hierarchical representation.