Course 2025-2026 a.y.

20882 - COMPUTATIONAL NEUROSCIENCES

Department of Computing Sciences

Course taught in English
31
AI (6 credits - I sem. - OBS  |  ING-INF/06)
Course Director:
NICOLAS BRUNEL

Classes: 31 (I sem.)
Instructors:
Class 31: NICOLAS BRUNEL


Suggested background knowledge

Linear algebra Ordinary differential equations Probability theory and stochastic processes

Mission & Content Summary

MISSION

The goal of the course is to teach students about models and methods in computational and theoretical neuroscience. It will address the following questions: How do neurons, the basic units of our brains, work? How are neurons interconnected together to form complex networks? How do networks of neurons encode sensory information, and how is that information decoded to form estimates of sensory variables, or to generate motor actions? How is information from our senses stored in memory in brain networks? How do brains learn to perform complex computations, based on current sensory information and information stored in memory? It will present mathematical models of brain systems at various spatial and temporal scales, whose goals are that provide tentative answers to these questions. It will also present theoretical and computational methods that can be used to investigate these models. It will explore the biophysics of single neurons and synapses, the architecture and dynamics of networks, and how networks encode and store information they receive from the external world. A typical course will start by a presentation of relevant experimental data; It will then present basic models, and the main results obtained with such models; and finally, it will present an example in which models have been used successfully to shed light on the mechanisms of operations of brain systems. No background in neuroscience is necessary to follow this course.

CONTENT SUMMARY

1.     Neurons

  • Introduction to neuronal biophysics
  • The Hodgkin-Huxley model for action potential generation
  • 2D models: The geometry of action potential generation
  • Dendrites and axons: Cable theory and compartmental models
  • Simplified spiking neuron models: Integrate-and-fire and generalizations
  • Response of neurons to stochastic inputs

2.     Synapses

  • Introduction to synapses and basic models of synaptic transmission
  • Short-term synaptic plasticity 
  • Long-term synaptic plasticity

3.     Networks: Architectures and Dynamics

  • Introduction to brain networks at various scales and basic network models
  • Dynamics of networks of binary neurons
  • Dynamics of networks of rate units
  • Dynamics of networks of spiking neurons

 

4.     Population rate models

  • Reductions of networks of spiking neurons to rate models
  • Dynamics of excitatory-inhibitory networks
  • The ring model

5.     Coding

  • Phenomenological models of how single neurons encode sensory stimuli
  • Quantifying information transmitted by neurons: Shannon and Fisher information
  • Population coding

6.     Plasticity and learning

  • Unsupervised learning
  • Models of development of visual cortex
  • Supervised learning
  • Reinforcement learning

7.     Memory

  • Associative memory models: The Hopfield model
  • More realistic versions of the Hopfield model
  • Models of storage and retrieval of sequences

 

8.     Computing

  • Emergence and amplification of selectivity in sensory systems
  • Deep network models of the visual stream
  • Representation of space and navigation: The hippocampal formation
  • Models of working memory
  • Models of decision making

Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Have a basic knowledge of neuroscience.
  • Be familiar with standard theoretical models in the field, from neurons to networks.
  • Understand the methods by which mathematical models in neuroscience are analyzed.

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Apply mathematical tools to analyze simplified neuron and network models.
  • Perform numerical simulations of various types of neuron and network models, how they learn and compute

Teaching methods

  • Lectures
  • Practical Exercises
  • Collaborative Works / Assignments

DETAILS

Practical exercises: Every week, a few exercises will be given to students. These exercises will consist either in numerical simulations of specific models, or pen-and-paper calculations related to models described in the course. The exercises will allow students to deepen their knowledge and to prepare themselves for the final written exam.

Collaborative works/assignments: In the second part of the course, pairs of students will be asked to study a paper from the literature, and to present this paper during the exam week.


Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
     x
  • Collaborative Works / Assignment (report, exercise, presentation, project work etc.)
 x    

ATTENDING AND NOT ATTENDING STUDENTS

Assessment will be done using a final written exam (50%) and a project presentation (50%)


Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

Slides of the lectures will be made available before the lectures on blackboard. Some of the lectures will use material from the following textbooks:

  • Dayan and Abbott, ``Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems'' (MIT Press, 2001)
  • Ermentrout and Terman, ``Mathematical Foundations of Neuroscience'' (Springer, 2010)
  • Gerstner, Kistler, Naud and Paninski ``Neuronal Dynamics: From single neurons to networks and models of cognition'' (Cambridge U. Press, 2014)
  • Hertz, Krogh, and Palmer, ``Introduction to the Theory of Neural Computation'' (Addison-Wesley, 1991 - now from: Perseus Book Group and Westview Press

The relevant chapters will be available on blackboard.

Last change 05/06/2025 12:50