Random matrix theory of sparse neuronal networks with heterogeneous timescales

arXiv:2512.12767 · q-bio.NC, cond-mat.dis-nn, cs.LG, hep-th, math.PR · Submitted 2025-12-14 · Read on arXiv

q-bio.NC, cond-mat.dis-nn, cs.LG, hep-th, math.PR

Submitted: 2025-12-14

Updated: 2026-09-14

Comments: v2: slightly expanded, accepted for publication

Journal ref: SciPost Phys. 21 (2026) 065

DOI: 10.21468/SciPostPhys.21.3.065

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Sparsity — 18× in this paper · explained in 4 episodes
• Core — 17× in this paper · explained in 2 episodes
• Decoupling — 5× in this paper · explained in 2 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Fine-Tuning — 3× in this paper · explained in 5 episodes
• Spectral Geometry — 3× in this paper · explained in 2 episodes
• Phase Transitions — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Continual Learning — 1× in this paper · explained in 2 episodes
• Cooperation — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Inverse Participation Ratio (IPR) — 1× in this paper · explained in 2 episodes
• Modularity — 1× in this paper · explained in 9 episodes
• Pruning — 1× in this paper · explained in 4 episodes
• Quantization — 1× in this paper · explained in 12 episodes

Sources

• Stability Criteria for Complex Ecosystems
• Heterogeneity of Interaction Strengths and Its Consequences on Ecological Systems
• Emergence of robust memory manifolds
• Dynamical phase transitions in quantum reservoir computing
• Dissipation alters modes of information encoding in small quantum reservoirs near criticality
• Hierarchy of chaotic dynamics in random modular networks
• Could Living Cells Use Phase Transitions to Process Information?
• Soft Modes as a Predictive Framework for Low Dimensional Biological Systems across Scales
• Optimal interplay between synaptic strengths and network structure enhances activity fluctuations and information propagation in hierarchical modular networks
• Spectral Theory of Sparse Non-Hermitian Random Matrices
• Random matrices with row constraints and eigenvalue distributions of graph Laplacians
• Hammerstein equations for sparse random matrices
• Statistical field theory of random graphs with prescribed degrees
• Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
• Density of states correlations in L'evy Rosenzweig-Porter model via supersymmetry approach
• Universality and individuality in neural dynamics across large populations of recurrent networks
• Limits on the computational expressivity of non-equilibrium biophysical processes
• Temporal pattern recognition through analog molecular computation
• Reverse engineering recurrent networks for sentiment classification reveals line attractor dynamics
• Attractor and integrator networks in the brain

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