Laboratory of Computational Neuroscience LCN - Brain Mind - I&C - Life Sciences - EPFL

• Three Video-Lectures per week of about 30 Minutes each over 14 weeks (42 lectures total). Official Course Title is Neural Networks and Biological Modeling

  This course, designed for Physicists and mathematically trained Life Scientists focuses on biological modeling, in particular the dynamics of neurons and learning in neural systems. It consists of four parts:

  • I - Models of Single Neurons;
  • II - Synaptic Changes and Learning
  • III - Noise and the Neural Code
  • IV - Structured Networks: Competition, Decision, Field Equeations
  Video Lectures have two windows - Adjust the view the way you like it: By clicking on the small screen, it becomes big and vice versa

• Week 1. A first simple neuron model.
  Part A - Motivations and the mathematics of a passive membrane (28 min)
  Part B - From the passive membrane to the Leaky Integrate-and-Fire Neuron (43 min)
  Part C - How good are simple models? -- Nonlinear and generalized Integrate-and-Fire Neuron Models (33 min)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch. 1 and Ch. 4.1
• Week 2. The Hodgkin-Huxley Model and Detailed ion-current based neuron models
  Part A - Reversal potential and Hodgkin-Huxley Equations (37 min)
  Part B - Is there a firing threshold in the Hodgkin-Huxley Model? (20 min)
  Part C - Refractoriness, Pulse currents, step current and ramp currents. Molecular basis of ion-current based neuron models (25 min)
  Part D - Dendrites and cable equation (29 min) (material taught in week 7)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch. 2.1 - 2.3
• Week 3. Two-dimensional models and phase plane analysis (Fitzhugh-Nagumo and Morris-Lecar model)
  Part A - From 4 to 2: Simplifying the Hodgkin-Huxley Equations (35 min)
  Part B - The Role of Nullclines: FitzHugh-Nagumo model (31 min)
  Part C - Phase Plane Analysis: Morris-Lecar and FitzHugh-Nagumo model (31 min)
  Reading Spiking Neuron Models (Cambridge Univ. Press) Ch. 3.1 and 3.2
• Week 4: Complements to Two-dimensional models
  Part A - Separation of time scales; Type I and Type II Models: bifurcation patterns (40 min)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch. 3.3

• Week 4. Synaptic Plasticity and Long-term potentiation
  Part B - Hebbian Learning and Long-Term Potentation (LTP) of Synapses; BCM Model (35 min)
  Part C - Functional Consequences of Hebbian Learning: Development of Receptive Fields (17 min)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch. 10.1 and 10.2 as well as Ch. 11.1.4.
• Week 5. Networks of Neurons and Associative Memory (Hopfield Model)
  Part A - Associative Memory and Classification by Similarity; Model of (Anti-)Ferromagnet (28 min)
  Part B - Storing several patterns: Hopfield model (27 min)
  Part C - Memory Capacity (26 min)
  Reading: A Short Introduction to the Hopfield model (Lecture Notes by W. Gerstner, in French)
  Here is a simple demo of the Hopfield model
• Week 6: Introduction to Reinforcement Learning
  Part A - Reward-based learning: Behavior, Conditioning and Synaptic Changes (28 min)
  Part B - Rat Navigation and Reinforcement Learning Theory (36 min)
  Part C - Continuous state space and eligibility traces (19 min)
  Reading: Reinforcement Learning (MIT Press) by R. Sutton and A. Barto

• Week 7: Hand-out of miniproject and more on topics of week 2,5, and 6.
  Part A - Reward-based learning: Eligibility Traces and Application to Morris Water Maze (31 min)
  Part B - Detailed neuron models: Dendrites and cable equation (29 min)
  Part C - Handout of Miniprojects (23 min)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch. 2.4 and 2.5

• Week 8: Variability of Spike trains, noise and the neural code
  Part A - Variability of Spike trains: Rates, Timing, Noise, and the Poisson Process (40 min)
  Part B - Noise in a passive membrane (20 min)
  Part C - Noise in Integrate-and-Fire models: Escape Noise, Renewal Models, and Stochastic Spike Arrival (27 min)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch 5.1-5.3, 5.5, and Ch. 5.6
• Week 9: Noisy neurons and coding: variance, autocorrelation, and stochastic resonance
  Part A - Variability of Spike trains: Rates, Timing, Noise, and the Poisson Process (41 min)
  Part B - Langevin equation and Ornstein-Uhlenbeck process (12 min)
  Part C - Comparison of Noise Models; Neural Codes and Stochastic Resonance (29 min)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch 5.5, 5.7-5.9
• Week 10. Populations of Neurons and Fokker-Planck equation
  Part A - Membrane potential distribution in a homogeneous population (42 min)
  Part B - Flux across a reference potential and Fokker Planck equation (27 min)
  Part C - Threshold and reset (24 min)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch 5.5 and Ch 6.1-6.2
• Week 11. Population Rate models and Coding --- Reverse correlations, PSTH and rapid transients
  Part A - Forward correlation, PSTH, and population response for spiking neurons Reverse correlation as optimal stimulus.. (25 min)
  Part B - Reverse correlation as linear filter. (32 min)
  Part C - Transient population response: Poisson neuron vs. spiking neurons (41 min)
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch. 7
and Ch. 6.3

• Week 12. Spatially Extended Networks and Field Equations
  Part A - Single population - population rate equation. (35 min) - Look also at the slides
  Part B - From a single population to spatially coupled populations: field equations (52 min) - Look also at the slides
  Part C - Bump formation and application to head direction cells; edge enhancement (19 min) - Look also at the slides
  Reading: Spiking Neuron Models (Cambridge Univ. Press) Ch. 6.4 and Ch. 6.5 as well as Ch. 9.1
• Week 13. Perception, Decision, and Competition in Connected Populations
  Part A - Motion Perception and Decisions in Cortex; Theory of Decision Dynamics (44 min)
  Part B - Analysis of Decision Dynamics in two dimensions (13 min)
  Part C - Decision dynamics in connected populations; decisions and free will (22 min)
  Reading: X.J. Wang, Probabilistic Decision Making by Slow Reverberation in Cortical Circuits, NEURON 36:955-968 (2002)
• Week 14. Population Dynamics and Associative Memory
  Part A - Review of Associative Memories and Mean-Field Theory. (44 min)
  Part B - Multiple patterns (29 min)
  Part C - Associative Memory and Population Dynamics of Spiking Neurons (28 min)
  Reading: Hertz, Krogh, Palmer, Introduction to the Theory of Neural Computation (Addison Wesley, 1991) Chapter 2.5; as well as W. Gerstner and J. L. van Hemmen, Associative Memory in a Network of Spiking Neurons, NETWORK 2: 139-164

• Spiking Neuron Models by W. Gerstner and W. Kistler (Cambridge Univ. Press).
• Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press).
• Reinforcement Learning: an Introduction by R. Sutton and A. Barto (MIT Press)

Exercises.
Attention. Paper and Pencil Exercises are integrated in the lectures. For example a Monday session from 10h15 to 13h00 can be structured as 35 minutes course + 10 minutes exercise + break + 25 minutes course + 20 minutes exercise + break + 20 minutes course + 15 minutes exercise. The Python based exercises and demos are after the lectures.