Academic year 2023-2024


Theoretical Neuroscience

Master in Cognitive Science (Cogmaster)

ENS-PSL, EHESS & Université Paris Cité

Coordinators: Jonas Ranft & Jean-Pierre Nadal

Teaching assistant: Esther Poniatowski (PhD student, DEC, ENS)


Instructors: Boris Barbour (IBENS, ENS), Brice Bathellier (Paris-Saclay Institute of Neuroscience), Yves Boubenec (DEC, ENS), Alex Cayco Gajic (DEC, ENS), Mehdi Khamassi  (ISIR, SU), Srdjan Ostojic (DEC, ENS), Gianluigi Mongillo (Vision Institute), Jean-Pierre Nadal (Dep. of Physics, ENS & CAMS, EHESS), Jonas Ranft (Biol Dept, ENS), Michael Zugaro (CIRB, Collège de France).




Level: Level 2 (level 1- depending on the student: check the prerequisites!)

Major(s): Modeling

Semestre: S1/S3

ECTS : 6

Validation: oral presentation (work done in binome based on an article) & written exam

Prerequisites: good knowledge and practice in maths, Python basics (see below)

Course taught in: English

Code: COGSCI 318


Number of hours:  24h CM + 15h TD + validation: oral presentation & written exam

Dates: from September 21 to January 18 (exam session included),

on Thursdays, Lectures 1:30pm-3:30pm, TDs 3:45pm-5pm.

[updated Oct 4:] No lecture on Nov. 2, 9 and 30, Dec. 28 and Jan. 4.

Location: First lecture at the Biology Department of the ENS, 46 rue dUlm, room 306.
Then: 28 Sept room 316, 5 Oct room 306, 12 Oct room 306, 19 Oct room 316, 26 Oct room 316, 16 Nov room 306, 23 Nov room 306. Next lectures: TBA

Website: for registered students, course material will be on the moodle site of Université Paris Cité, and on a github site for the TDs.


The course is open to students of all disciplines. Attendance is limited to 25 students, with mandatory registration.


1a. Course description (English)

This course is an advanced introduction to theoretical and computational neuroscience. It introduces quantitative approaches to central questions in neuroscience: What functions and computations does the brain accomplish? By which mechanisms?  The scope of the course is threefold. First, to present a number of questions for which a quantitative approach is relevant. Second, to introduce mathematical tools necessary to the study of these questions, as well as to the study of similar questions in related fields (psychophysics, computer science, biophysics,...). Third, and maybe most importantly, to discuss concrete examples relevant to brain function in which one can make progress through modelling. Questions and examples that will be discussed include: How do neurons code inputs to the brain? Is ‘function’ carried out by single neurons or by groups of neurons? How can one model the learning and storage of memories? How does the brain generate outputs such as motor outputs?

1b. Description du cours (Français)

Ce cours est une introduction avancée aux neurosciences théoriques et neurosciences computationnelles. Il présente des approches quantitatives sur des questions centrales en neurosciences : Quelles sont les fonctions et les calculs que le cerveau accomplit ? Par quels mécanismes ?  L’objectif du cours est triple. Premièrement, présenter un certain nombre de questions pour lesquelles une approche quantitative est pertinente. Deuxièmement, introduire les outils mathématiques nécessaires à l'étude de ces questions, ainsi qu'à l'étude de questions similaires dans des domaines connexes (psychophysique, informatique, biophysique,...). Troisièmement, et c'est peut-être le plus important, discuter des exemples concrets pertinents au fonctionnement du cerveau pour lesquels on peut faire des progrès grâce à la modélisation. Les questions et les exemples qui seront discutés incluent : Comment les neurones codent-ils les entrées sensorielles ? Une fonction est-elle assurée par des neurones isolés ou par des groupes de neurones ? Comment modéliser la mémoire ? Comment le cerveau génère-t-il des sorties telles que les sorties motrices ?



The course is well suited for both M1 and M2 students, provided the following prerequisites are met.

A good familiarity (knowledge and practice) with elementary mathematics in analysis, linear algebra and probability is mandatory. Some knowledge in neurobiology, and in dynamic systems and statistical mechanics, will be useful but not necessary.

For projects that are part of the TDs (“Travaux Dirigés”) and validation, basic programming knowledge, preferably in Python, is necessary.

Recommended level: Cognitive science, Biology: M2; Mathematics, Physics, Computer science: L3 or M1


2. Learning outcomes

On successful completion of this course, students should have acquired knowledge on:

·         Main modelling approaches in neuroscience, from single neurons to network of neurons

·         Theoretical principles underlying neuronal coding as well some neuronal functions

·         How to perform some mathematical analysis of neuronal dynamics

·         Making numerical simulations of both single neuron and network models

·         Combing theoretical approach, numerical simulations and confrontation with empirical data to obtain insights on various problems

·         Understanding the most recent literature in theoretical and computational neuroscience


3a. Pedagogy, class organization and homework

Each course consists in a presentation by one the instructors, done partly with slides and partly on the blackboard. Part of the lectures are given by a binome, an experimentalist and a theoretician.

All course material (with restricted access to registered students) will be made available through the course website. The access code is provided to students upon registration.


A TD session follows each lecture. Exercises related to the lecture of the previous week are discussed.   The exercises sets are made available in advance on the course website.

It is strongly recommended to try to solve the exercises before the TD session during which they will be discussed.

Part of the TD session is devoted to the preparation of the students’ projects (see Assessment below).


3b. Assessment


3c. Textbook and readings

This course does not have a textbook (and there is no single book covering all the topics covered in the Course). Some parts are original presentations not fully covered by existing monographies.

However, many parts correspond more or less to what can be found in books whose references will be given on the Course website. These books are either freely available online or can be found in local libraries (RISC, ENS, IHP). We especially recommend:

·   P. Dayan and LF Abbott, Theoretical Neuroscience (MIT Press 2nd edition 2005), (A nice overview of the field of computational neuroscience, at a level comparable to that of the course).

·   W. Gerstner, W. M. Kistler, R. Naud and L. Paninski, Neuronal Dynamics - From single neurons to networks and models of cognition, Cambridge University Press 2014,

·  B. Ermentrout and D. Terman, Mathematical Foundations of Neuroscience (Springer, 2010) (A book with detailed mathematical treatments, with a focus on the dynamics of neural activity).

All course material (slides, related papers) will be made available on the course website, with access restricted to registered students. Note however that parts of the lectures will be taught on the blackboard.


4. Course content

The course is organized as a structured set of lectures (not an independent set of lectures), with a program jointly prepared by the instructors. The repartition Lecture # / Instructor is likely to undergo some permutations from one year to the next. The Lectures’ topics are independent of this repartition.


Introduction and basic tools, models and concepts


Lecture 1 - Overview

(Jonas Ranft)


Lecture 2 - Synapses

(Gianluigi Mongillo)


Lecture 3 – Biophysics of Neurons

(Jonas Ranft)


Lecture 4 - Excitatory-Inhibitory Networks

(Srdjan Ostojic)


Lecture 5 - Unsupervised learning & Neural coding

(Jean-Pierre Nadal)


Lecture 6 - Rate models

(Srdjan Ostojic)


Lecture 7 - Supervised learning & Associative memory (feedforward networks & attractor networks)

(Gianluigi Mongillo & Jean-Pierre Nadal)


Lecture 8 - Behavioural learning

(Mehdi Khamassi)


Models of specific cognitive systems.

Each Class is given by a binome Experimentalist & Theoretician.


Lecture 9 - Cerebellum

(Boris Barbour & Alex Cayco Gajic)


Lecture 10 - The Role of the Hippocampus in Navigation

(Michael Zugaro  & Jonas Ranft)


Lecture 11 - Decision making

(Yves Boubenec & Jean-Pierre Nadal)


Lecture 12 – Perceptual systems (vision, audition; application of Deep Learning to the study of the auditory system)

(Brice Bathellier & Srdjan Ostojic)



5. Course policies


General policy


Laptop/phone policy.

The use of labtops is authorized in class for taking notes or to have access to the course web site, and to make the final project presentation. Students must have their labtop for the TDs.

No computer, iPhone or any other digital device is allowed during the written exam (students must bring a watch to know time).


Attendance. Regular attendance of, and punctual arrival at, both lectures and TD are crucial to succeed in this course, and they are mandatory for all students registered for credit. This is important both for your individual success in this course, and for every other students’ success. Keep in mind in particular that, by arriving late, you are jeopardizing your own but also your classmates’ education by disrupting the flow of lectures. Practically speaking, if you are registered for credit then your grade will suffer from poor attendance or recurrent late arrivals. If you are not registered for credit, the same policy applies, though with different consequences: poor attendance or recurrent late arrivals may force us to ask you to stop auditing the course.


Participation. You are strongly encouraged to participate in lectures and in TD. This means asking deep and challenging questions, but also asking simple questions, asking for clarification, saying “I’m just not getting this, please explain it in some new way” or “I’m lost, can you remind me why we’re talking about this?” You can ask questions in French or English at any time.


Contacting the organizer or the TA is the best way to contact us when you have brief questions.


Homework. Projects: Students will work in groups of two or three (depending on the total number of students. Take this opportunity for collaboration with your classmates wisely: working with a classmate who is more comfortable than you on a particular topic can help you understand that topic better; working with a classmate who knows less than you about a particular topic can help you consolidate what you know and force you to reassess fundamental elements of your knowledge.


Academic honesty policy Cheating will not be tolerated and may cost you your grade as well as have deeper repercussions in your academic career. The following is a non-exhaustive list of examples of what counts as cheating in this course: (i) signing on the attendance sheet without attending the class (e.g. signing and leaving, or signing for someone else); (ii) copying the homework write-up or the exam answers of another student, with or without that student’s knowledge; (iii) copying elements of your solutions of exercises from sources in the literature without giving them due credit; (iv) using the same homework to validate two courses.