By name: plasticity-network-framework description: "Network-based operationalization of plasticity as the ratio between system size and connectivity strength. Links structure to dynamical regimes (plastic vs rigid). Use for: complex systems analysis, brain plasticity quantification, neural network rigidity, ecosystem resilience, state space accessibility." license: Complete terms in LICENSE.txt metadata: arxiv_id: "2603.25180" published: "2026-03-14" authors: "Author(s) from arXiv metadata" tags: [plasticity, complex-systems, network-structure, dynamical-regimes, brain-resilience, neural-plasticity]
Quantifying Plasticity: Network-Based Framework
Paper: "Quantifying plasticity: a network-based framework linking structure to dynamical regimes" (arXiv:2603.25180) Core Insight: Plasticity operationalized as
system size / connectivity strength
Core Problem
Plasticity is a fundamental property of complex systems (brain, organisms, ecosystems), but typically remains a descriptive concept inferred retrospectively from observed outcomes. This paper provides a quantitative operational definition linking network structure to dynamical regimes.
Framework
Plasticity Definition
Plasticity = System Size / Connectivity Strength
Where:
- System Size (N): Number of elements → determines state space dimensionality
- Connectivity Strength (C): Coupling among elements → determines state coupling
Two Dynamical Regimes
| Regime | Plasticity | System Size | Connectivity | Behavior |
|---|---|---|---|---|
| High Plasticity | High (N/C >> 1) | Large | Weak | Many accessible states, flexible responses |
| Low Plasticity (Rigid) | Low (N/C << 1) | Small | Strong | Locked states, constrained dynamics |
Mechanism
System Size → Dimensionality
- More elements = larger state space (2^N possible configurations for binary elements)
- High dimensionality enables diverse dynamical trajectories
Connectivity → Coupling
- Stronger connections = tighter state coupling
- High connectivity locks system into restricted state trajectories
Ratio N/C → Plasticity
- Large N / weak C = flexible system (many reachable states)
- Small N / strong C = rigid system (state locking)
Applications
Brain Plasticity
- Developmental plasticity: Young brains (high N, weak C) → high flexibility
- Adult rigidity: Mature brains (moderate N, strong C) → stable but less adaptable
- Pathology: Stroke/injury → changes N/C ratio → altered plasticity
Neural Networks
- Overparameterized models: High N, moderate C → high plasticity (good for learning)
- Compact models: Low N, strong C → rigidity (stable but limited adaptation)
- Training dynamics: Plasticity affects optimization landscape
Ecosystems
- Biodiversity (N): More species → larger state space
- Interaction strength (C): Strong trophic links → tighter coupling
- Resilience: High plasticity ecosystems adapt to disturbances
Reusable Patterns
Pattern 1: Plasticity Assessment
Given complex system with N elements and connectivity matrix:
1. Compute connectivity strength C (average coupling strength)
2. Calculate plasticity ratio = N / C
3. Classify regime:
- Ratio > threshold_high → plastic system
- Ratio < threshold_low → rigid system
- Intermediate → mixed behavior
Pattern 2: State Space Accessibility
For system with plasticity ratio:
1. High plasticity: Explore broad state space (good for exploration)
2. Low plasticity: Narrow state space (good for stability)
3. Trade-off: Balance flexibility vs robustness
Pattern 3: Intervention Design
To modify plasticity:
- Increase system size N (add elements, increase dimensionality)
- Decrease connectivity C (loosen coupling, increase independence)
- Or both simultaneously
Quantification Methods
Connectivity Strength Metrics
- Average coupling: Mean interaction strength
- Network density: Fraction of connected pairs
- Weighted connectivity: Sum of edge weights / N
- Spectral measure: Largest eigenvalue of adjacency matrix
System Size Metrics
- Number of nodes: Direct count of elements
- Effective dimensionality: PCA on state vectors
- Configuration entropy: log2(N) for binary elements
Comparison with Existing Concepts
| Concept | Focus | Quantification | Network Basis |
|---|---|---|---|
| Structural plasticity | Synapse formation/deletion | Yes (synapse count) | Partial |
| Functional plasticity | Activity changes | Yes (signal metrics) | No |
| This framework | Structure-dynamics link | Yes (N/C ratio) | Full |
Pitfalls
- Size vs connectivity trade-off: Increasing N often increases C → plasticity may not change monotonically
- Network topology ignored: Ratio N/C assumes uniform connectivity → misses heterogeneous structure effects
- Dynamics oversimplified: State space dimensionality depends on element dynamics, not just count
- Time-scale neglected: Plasticity evolves over time → static ratio ignores temporal dynamics
Related Skills
- [[effective-plasticity]] - Network-based framework for plasticity quantification
- [[structural-plasticity-growth-stability]] - Analysis of structural plasticity in neural networks
- [[neural-manifold-dynamics-learning]] - Neural manifold learning dynamics
- [[synaptic-weight-distributions-plasticity-geometry]] - Synaptic weight distributions and plasticity geometry
Activation
plasticity quantification, complex systems, network structure, dynamical regimes, brain resilience, neural rigidity, state space, connectivity strength, system dimensionality, ecosystem stability, N/C ratio