Random matrix theory of sparse neuronal networks with heterogeneous timescales
Not on the map. Why?
Abstract (arXiv)
Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation slows and diversifies inhibitory timescales, leading to improved task performance that is attributed to emergent marginally stable equilibria [PNAS 122 (2025) e2316745122]. Yet the link between trained network characteristics and their roles in shaping desirable dynamical landscapes remains unexplored. Here, we investigate the Jacobian matrices describing the dynamics near these equilibria and show that they are sparse, non-Hermitian rectangular-block matrices modified by heterogeneous synaptic decay timescales and activation-function gains. We specify a random matrix ensemble that faithfully captures the spectra of trained Jacobian matrices, arising from the inhibitory core - excitatory periphery network motif (pruned E weights, broadly distributed I weights) observed post-training. An analytic theory of this ensemble is developed using statistical field theory methods: a Hermitized resolvent representation of the spectral density is processed with a supersymmetry-based treatment in the style of Fyodorov and Mirlin. In this manner, an analytic description of the spectral edge is obtained, relating statistical parameters of the Jacobians (sparsity, weight variances, E/I ratio, and the distributions of timescales and gains) to near-critical features of the equilibria essential for robust working memory computation.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 11 of its 79 references that are in the map. First posted on arXiv 14 Dec 2025.
Builds on
11 of 79 references.
References · 11
- 2021Gradient Descent on Neural Networks Typically Occurs at the Edge of Stabilitycited by 427
- 2019Universality and individuality in neural dynamics across large populations of recurrent networkscited by 61
- 2021Attractor and integrator networks in the braincited by 61
- 2019Reverse engineering recurrent networks for sentiment classification reveals line attractor dynamicscited by 39
- 2021Emergence of robust memory manifoldscited by 4
- 2022Spectrum of non-Hermitian deep-Hebbian neural networkscited by 4
- 2024Dissipation alters modes of information encoding in small quantum reservoirs near criticalitycited by 3
- 2018From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behaviorcited by 1
- 2019Optimal interplay between synaptic strengths and network structure enhances activity fluctuations and information propagation in hierarchical modular networkscited by 1
- 2024Excitation-inhibition balance controls information encoding in neural populationscited by 1
- 2024Hierarchy of chaotic dynamics in random modular networkscited by 1
Built on by
Not cited yet.