Cognitive Degradation Lifecycle

• Cognitive degradation lifecycle is defined by the progressive decline in neural processing as persistent Hebbian learning disrupts self-organized criticality.
• Simulation studies reveal that increasing memory overlap and reduced retrieval quality signal a shift from optimal, flexible neural dynamics to rigid, sub-critical states.
• Modeling frameworks using integrate-and-fire networks with dynamic synapses quantify degradation through metrics like retrieval quality (m) and deviation from power-law avalanche behavior (A_y).

The cognitive degradation lifecycle encompasses the temporal sequence and underlying mechanisms by which cognitive processing capacity deteriorates in both biological neural systems and computational analogs. Contemporary research situates cognitive degradation as emerging from the interplay of neural connectivity, learning history, resource depletion, structural damage, and the disruption of critical dynamics in neural circuits. The following sections synthesize fundamental principles, computational and biological mechanisms, modeling strategies, numerical findings, and implications grounded in (Dasgupta, 2014).

1. Principles of Hebbian Learning and Self-Organized Criticality

Cognitive performance in biological systems can be described through the dual principles of associative (Hebbian) learning and self-organized criticality (SOC). Hebbian plasticity encodes memories in synaptic weights according to the correlation of firing patterns, formalized as: $$w_{ij} = \frac{1}{N}\sum_{k=1}^{P} x_i^{(k)} x_j^{(k)}$$ where $x_i^{(k)}$ are components of pattern $k$ across $N$ neurons and $P$ is the number of stored patterns. Modifications, such as biasing for correlated patterns, enhance associative memory capacity.

Crucially, the integration with SOC is accomplished by introducing dynamic synapses as per the Tsodyks-Markram model. Here, synaptic efficacy is dynamically modulated by resource depletion and recovery processes: $$\frac{dJ_{ij}}{dt} = (W_{ij} - J_{ij}) - W_{ij} J_{ij}\, \delta(t - t_{\text{spike}})$$ where $W_{ij}$ is the Hebbian-learned "baseline" and $J_{ij}$ its instantaneous value. The network is thereby regulated toward a critical regime, evidenced by neuronal "avalanche" events exhibiting power-law size distributions—a haLLMark of optimal dynamic range and information processing. Hebbian memory encoding and criticality-maintenance via dynamic synapses instantiate a balance between stability and flexibility.

2. Mechanisms of Cognitive Aging and Degradation

Several biological factors are implicated in cognitive aging: loss of connectivity, increased intrinsic noise, and white matter degeneration. The model described contends that a longer learning history—prolonged, cumulative Hebbian synaptic modification—plays a central role in disrupting the emergent criticality needed for optimal cognitive operation.

Continuous encoding and reinforcement cause stored patterns to overlap increasingly, reducing pattern separation and yielding attractor rigidification in the network’s energy landscape. This restricts the neural substrate's ability to represent and process novel stimuli efficiently. The attractor structure transitions from flexible and critical early in life to rigid and sub-critical with age, mirroring a decline in fluid intelligence while sparing crystallized knowledge.

3. Longer Learning History as a Driver of Degradation

The theoretical and simulation results reinforce the hypothesis that the degradation of cognitive performance is, in part, explained by the persistent overwrite of network synaptic structure due to extended Hebbian learning. With each new pattern or association encoded, the overlap among representations increases, degrading the network's criticality and information processing capacity.

Formally, pattern overlap is measured by the retrieval quality parameter: $m = \langle \xi_i S_i \rangle$ where $\xi_i$ is the stored component and $S_i$ the retrieved activity. As memories accumulate, $m$ diminishes, signaling impaired pattern retrieval and generalization. The simulation results indicate that as learning history lengthens, the mean squared deviation metric $A_y$—which quantifies the departure from power-law avalanche behavior—also increases, marking the loss of critical dynamics.

4. Modeling Framework and Mechanistic Insights

The studied system consists of integrate-and-fire neuronal networks, equipped with:

• Modified Hopfield associative memory with Hebbian weights optimal for correlated/bias patterns.
• Tsodyks–Markram dynamic synapses, capturing activity-dependent depression and facilitation via kinetic equations:

$$\frac{dx}{dt} = \frac{z}{T_{\text{rec}}} - U_{\text{SE}} x \delta(t-t_{\text{spike}})$$

where $x$ is the fraction of available resources.

• Homeostatic regulation, driving synaptic weights toward an ideal critical value:

$$W_{ij} = W_{ij} + k(a - W_{ij}) \delta(t-t_{\text{spike}})$$

with $k$ a small constant and $a$ the target connectivity required for criticality.

This hybrid framework enables examination of how protracted learning impacts the network’s ability to remain at or near criticality, relating directly to observed degradation phenomena.

5. Simulation Outcomes: Disruption of Criticality

Simulation studies reveal several regimes:

• For moderate and orthogonally encoded patterns, the network preserves power-law avalanche size distributions indicative of critical behavior.
• In the regime of multiple, randomly overlapping memory patterns, repeated Hebbian learning induces deviation from the power-law, manifest as a structured avalanche distribution (quantified by $A_y$) and increased pattern overlap.
• Quality of retrieval, measured by $m$, falls as memory load (number and overlap of stored patterns) increases, and the attractor landscape becomes distorted, compromising stable and flexible switching between patterns.

These findings demonstrate that as cognitive load from learning expands, the neural dynamics progressively shift from optimal criticality to a degraded, subcritical state associated with cognitive aging.

6. Implications for the Lifecycle of Cognitive Degradation

The examined framework posits that the lifecycle of cognitive degradation is mathematically and computationally emergent from the tension between Hebbian encoding and the constraints of self-organized criticality. Initially, efficient learning and criticality maximize information processing; as learning accumulates, the repeated modification of synaptic structure erodes criticality, leading to diminished neural flexibility and impaired processing.

This links age-related cognitive decline—in particular, fluid intelligence losses—to quantifiable properties such as:

• Decreased pattern separation (increased overlap),
• Disappearance of optimal power-law avalanche behavior,
• Lower retrieval quality (reduced $m$).

Key measures such as the mean squared deviation from power-law scaling ($A_y$) and retrieval overlap afford direct, simulation-based correlates of the theoretical model. The results suggest that interventions that slow or regulate the rate of extended learning or foster homeostatic plasticity may preserve brain criticality and mitigate functional degradation over the lifespan.

7. Summary Table: Mapping Model Features to Degradation Lifecycle

Biological/Computational Property	Model/Symbol	Effect on Degradation Lifecycle
Hebbian learning (memory encoding)	$w_{ij}$, $W_{ij}$	Increases pattern overlap, advances aging
Dynamic synapses, SOC	$J_{ij}$, Eq. (3.3)	Maintains criticality, opposes aging
Homeostatic adjustment	Eq. (3.6)	Stabilizes, can delay degradation
Pattern overlap / retrieval quality	$m = \langle \xi_i S_i\rangle$	Declines as degradation advances
Avalanche scaling deviation	$A_y$	Rises with prolonged learning

In summary, the cognitive degradation lifecycle is fundamentally governed by the antagonistic effects of memory encoding through Hebbian plasticity and the maintenance of neural criticality via dynamic synaptic processes. As associative learning accumulates, overlaps among memories rigidify the attractor landscape, criticality is lost, and cognitive capacity to flexibly process novel stimuli is diminished, providing a quantitative and mechanistic account for the cognitive declines observed with aging.