1. Integrate and Fire Neurons
Michael Phelan

2. Topics History Comparison of Models Applications
“Excitatory Shot Noise” – Droste and Lindner
[1, 2]

3. History First described in 1907 by Louis Lapicque[3]
[4]
First described in 1907 by Louis Lapicque[3]
Without advanced experimental data, estimated neuronal behavior as a simple circuit
Was further developed into the Leaky Integrate-and-Fire Model

4. Circuit Diagrams
[4]
[5]

8. Applications
“Linked Gauss-Diffusion processes for modeling a finite-size neuronal network” – Carfora and Pirozzi 2017[6]
“Double-Barrier Memristive Devices for Unsupervised Learning and Pattern Recognition” – Hansen, et al. 2017[7]
Event-Driven Random Back-Propagation: Enabling Neuromorphic Deep Learning Machines – Neftci, et al. 2017[8]
[7]
[9]
[6]

9. “Exact analytical results for integrate-and-fire neurons driven by excitatory shot noise” [10]
Felix Droste and Benjamin Lindner
June 2017
Humboldt University, Berlin

10. Abstract and Introduction
[12]
[11]
Presynaptic spike (PS) pulses modeled as Gaussian (Diffusion Approximation, DA) fail to predict real firing rate
Vth ~ mV, Average PS ~ 1-2 mV
Individual PS >10 mV
Poisson noise (shot-noise) better models “perfect” LIF Neurons

11. model 𝑓 𝑣 =𝜇, 𝜇−𝑣, 𝜇+ 𝑣 2 The model must apply a Poisson Noise
Time Constant
Weighted Shot Noise
Voltage Function
The model must apply a Poisson Noise
A sufficiently low spike weight value and high spike rate can be approximated as Gaussian
This is not always the case
𝑓 𝑣 values can describe different neuron behavior
dVm(t)/dt
Time Signal
Time of ith Spike
= Ri (Spike Rate)
Spike Weight
𝑓 𝑣 =𝜇, 𝜇−𝑣, 𝜇+ 𝑣 2
PIF
LIF
QIF
EIF

12. Firing Rate Firing rate is defined by multiple variables
Firing rate can be estimated as a function of PS input for Poission distribution better than DA
Over a range of PS weights and firing rates and slope factors this estimate beats DA

13. Coefficient of Variation and other results
CV (SD/Mean) Comparisons for a QIF show DA is close to simulations for Spike Weigh < 1
By a = 10, a massive difference appears
Droste and Lindner’s theory follows the simulation almost exactly
This is true of relationships with CV, power spectrum, and susceptibility

14. Discussion
Claim to have produced a better LIF model than standard PS model
Advantage: Demonstrate the effects of individual and strong PS for realistic modeling
Disadvantage: Does not take inhibitory neuronal input into account
Future Applications: May be applied to recurrent neural nets
[13]
[14]

15. Bibliography
“Biology-Cell Membrane-Transport.” Accessed September 19,
“Pinterest.” Pinterest. Accessed September 19,
Abbott, L. F. “Lapicque’s Introduction of the Integrate-and-Fire Model Neuron (1907).” Brain Research Bulletin 50, no. 5–6 (December 1999): 303–4.
“Louis_Lapicque.jpg (639×1000).” Accessed September 19,
“Biological Neuron Model.” Wikipedia, August 31,
Carfora, M. F., and E. Pirozzi. “Linked Gauss-Diffusion Processes for Modeling a Finite-Size Neuronal Network.” Bio Systems, August 2, doi: /j.biosystems
Hansen, Mirko, Finn Zahari, Martin Ziegler, and Hermann Kohlstedt. “Double-Barrier Memristive Devices for Unsupervised Learning and Pattern Recognition.” Frontiers in Neuroscience 11 (February 28, 2017). doi: /fnins
Neftci, Emre O., Charles Augustine, Somnath Paul, and Georgios Detorakis. “Event-Driven Random Back-Propagation: Enabling Neuromorphic Deep Learning Machines.” Frontiers in Neuroscience 11 (June 21, 2017). doi: /fnins
“Exploring Deep Learning & CNNs.” RSIP Vision, April 27,
Droste, Felix, and Benjamin Lindner. “Exact Analytical Results for Integrate-and- Fire Neurons Driven by Excitatory Shot Noise.” Journal of Computational Neuroscience 43, no. 1 (August 2017): 81–91. doi: /s
“Normal Distribution.” Wikipedia, September 10,
“Poisson Distribution.” Wikipedia, September 17,
Harvard University. Harvard Professor Takes Alzheimer’s Fight Personally, n.d.
“neural_networks_fully_connected_layers_gumgum1.gif (1400×515).” Accessed September 21, onnected_layers_gumgum1.gif?w=700&h=258&zoom=2.

16. Questions?