Paper List

Journal: ArXiv Preprint
Published: Unknown
Theoretical NeuroscienceMachine Learning

Competition, stability, and functionality in excitatory-inhibitory neural circuits

Università degli Studi di Padova | University of California at San Diego | Rice University | University of California at Santa Barbara

Simone Betteti, William Retnaraj, Alexander Davydov, Jorge Cortés, Francesco Bullo
Figure
Figure
Figure
Figure
Figure

The 30-Second View

IN SHORT: This paper addresses the core challenge of extending interpretable energy-based frameworks to biologically realistic asymmetric neural networks, where traditional symmetric weight assumptions break down.

Innovation (TL;DR)

  • Methodology Introduces a game-theoretic interpretation where each neuron acts as a selfish agent minimizing its own energy, with collective dynamics reaching Nash equilibria rather than global energy minima.
  • Methodology Extends the proximal gradient dynamics framework to asymmetric firing rate networks, defining neuron-specific interaction costs {E_int^i(x,u_i)} and activation costs {E_act^i(x_i)}.
  • Theory Bridges energy-based models with network stability theory (Lyapunov diagonal stability) to analyze regulation and balancing in excitatory-inhibitory circuits.

Key conclusions

  • Asymmetric neural networks can be reformulated as noncooperative games where Nash equilibria correspond to stable network states, providing interpretability without global energy functions.
  • The Wilson-Cowan model reveals that excitatory self-connection weight w_EE serves as a principal switch governing transitions between cooperative and antagonistic dynamical regimes.
  • Lateral inhibition microcircuits function as contrast enhancers through hierarchical excitation-inhibition interplay, sharpening subtle environmental differences with arbitrary precision.
Background and Gap： Current energy-based models require symmetric synaptic matrices, excluding biologically realistic asymmetric systems like excitatory-inhibitory networks governed by Dale's law, leaving their dynamics conceptually unanchored.

Abstract: Energy-based models have become a central paradigm for understanding computation and stability in both theoretical neuroscience and machine learning. However, the energetic framework typically relies on symmetry in synaptic or weight matrices - a constraint that excludes biologically realistic systems such as excitatory–inhibitory (E–I) networks. When symmetry is relaxed, the classical notion of a global energy landscape fails, leaving the dynamics of asymmetric neural systems conceptually unanchored. In this work, we extend the energetic framework to asymmetric firing rate networks, revealing an underlying game-theoretic structure for the neural dynamics in which each neuron is an agent that seeks to minimize its own energy. In addition, we exploit rigorous stability principles from network theory to study regulation and balancing of neural activity in E-I networks. We combine the novel game-energetic interpretation and the stability results to revisit standard frameworks in theoretical neuroscience, such as the Wilson-Cowan and lateral inhibition models. These insights allow us to study cortical columns of lateral inhibition microcircuits as contrast enhancer - with the ability to selectively sharpen subtle differences in the environment through hierarchical excitation–inhibition interplay. Our results bridge energetic and game-theoretic views of neural computation, offering a pathway toward the systematic engineering of biologically grounded, dynamically stable neural architectures.