Speaker
Description
Recurrent Neural Networks provide versatile models for studying dynamics in neural circuits (Barak, 2017). While numerical simulations can reproduce complex neural phenomena, analytical approaches are needed to uncover their underlying mechanisms. Dynamical Mean Field Theory (DMFT) has provided such a framework for large random networks, allowing the derivation of statistical descriptions of neural activity under simplifying assumptions (Sompolinsky et al., 1988). These assumptions typically include homogeneous connectivity statistics, which limit the ability to capture biologically relevant structural variability.
Here, we extend DMFT to heterogeneous network architectures by introducing heterogeneous Dynamical Mean Field Theory (hDMFT) (Park et al., 2024). This framework incorporates arbitrary degree distributions while preserving a tractable Gaussian effective description. We show that degree heterogeneity induces neuron-dependent dynamical properties and shapes the phase diagram of recurrent networks by enhancing dynamical instability compared to homogeneous architectures.
When partial symmetry is introduced to account for reciprocal connectivity (Song et al., 2005) or learning-induced structure (Clark and Abbott, 2024), hDMFT predicts the emergence of neuron-dependent effective self-interactions whose strength scales with neuronal degree. This mechanism produces a broad distribution of intrinsic timescales, with highly connected neurons exhibiting slower dynamics. The theoretical prediction that neuronal timescales correlate with in-degree is supported by analysis of the MICrONS dataset (Functional connectomics spanning multiple areas of mouse visual cortex, 2025), which combines structural connectivity with neural recordings.
The hDMFT framework provides an analytical link between structural heterogeneity and emergent network dynamics, including phase transitions, collective activity, and response properties. These results establish how connectivity statistics can shape the functional diversity and computational capabilities of large-scale recurrent neural systems.
| Preferred Presentation | No specific preference |
|---|