Firing rate models in Neuroscience

Graduate course
  Taught at: 2026
  Latin American School on Computational Neuroscience - LASCON, Universidade de São Paulo (USP)

We develop the theory of firing rates, showing how it appears in tonically spiking neurons. We then review some applications of firing rates, such as tuning curves, rate coding, f-I curves, and effective (mean-field) models of neural networks. We review some interesting results obtained from firing rates, such as the Hopfield theory, Wilson-Cowan model applications, and our proposed rate-variance coding scheme.

Bibliography

  1. Gerstner W, Kistler WM, Naud R, Paninski L (2014) Neuronal Dynamics: From single neurons to networks and models of cognition. Cambridge University Press.
  2. Dayan, P. and Abbott, L.F. (2001) Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. The MIT Press.
  3. Izhikevich E.M. (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT press
  4. M Girardi-Schappo, L Maler, A Longtin (2026) Optimal rate-variance coding due to firing threshold adaptation near criticality. arXiv:2509.04106 [q-bio.NC]
  5. D D Caprioti, M Haas, C F Vasconcelos, M Girardi-Schappo (2026) Learning About Learning: A Path from Spin Glasses to Artificial Intelligence. arXiv:2601.07635 [cond-mat.dis-nn]