Integrate and Fire Neurons

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Presentation transcript:

Integrate and Fire Neurons Michael Phelan

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

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

Circuit Diagrams [4] [5]

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]

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

Abstract and Introduction [12] [11] Presynaptic spike (PS) pulses modeled as Gaussian (Diffusion Approximation, DA) fail to predict real firing rate Vth ~ 10-20 mV, Average PS ~ 1-2 mV Individual PS >10 mV Poisson noise (shot-noise) better models “perfect” LIF Neurons

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

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

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

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]

Bibliography “Biology-Cell Membrane-Transport.” Accessed September 19, 2017. http://www.dynamicscience.com.au/tester/solutions1/biology/cell/cellmbntrnspt.html. “Pinterest.” Pinterest. Accessed September 19, 2017. https://www.pinterest.com/pin/493073859187921437/. 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, 2017. https://upload.wikimedia.org/wikipedia/commons/0/0c/Louis_Lapicque.jpg. “Biological Neuron Model.” Wikipedia, August 31, 2017. https://en.wikipedia.org/w/index.php?title=Biological_neuron_model&oldid=798233823. Carfora, M. F., and E. Pirozzi. “Linked Gauss-Diffusion Processes for Modeling a Finite-Size Neuronal Network.” Bio Systems, August 2, 2017. doi:10.1016/j.biosystems.2017.07.009. 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:10.3389/fnins.2017.00091. 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:10.3389/fnins.2017.00324. “Exploring Deep Learning & CNNs.” RSIP Vision, April 27, 2015. http://www.rsipvision.com/exploring-deep-learning/. 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:10.1007/s10827-017-0649-5. “Normal Distribution.” Wikipedia, September 10, 2017. https://en.wikipedia.org/w/index.php?title=Normal_distribution&oldid=799950 766. “Poisson Distribution.” Wikipedia, September 17, 2017. https://en.wikipedia.org/w/index.php?title=Poisson_distribution&oldid=801131 724. Harvard University. Harvard Professor Takes Alzheimer’s Fight Personally, n.d. https://www.youtube.com/watch?v=xQwbsAywZrI. “neural_networks_fully_connected_layers_gumgum1.gif (1400×515).” Accessed September 21, 2017. https://tctechcrunch2011.files.wordpress.com/2017/04/neural_networks_fully_c onnected_layers_gumgum1.gif?w=700&h=258&zoom=2.

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