**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).

Contact: jean-pierre.nadal@phys.ens.fr,
eponiatowski@clipper.ens.psl.eu

**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 ?

**Prerequisites:**

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**

- A final
written exam with exercises similar to those discussed during the TDs
(40%)
- A small
numerical project, based on a paper chosen at the beginning of the year,
done in teams of 2 or 3 students, with an oral presentation (on the paper
and the students’ project). Part of the TD sessions consists in working on
the project. (40%)
- Regular
attendance (prerequisite) and participation in TDs discussions (10%)

**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), http://www.gatsby.ucl.ac.uk/~lmate/biblio/dayanabbott.pdf (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, https://neuronaldynamics.epfl.ch/

·
B. Ermentrout and D. Terman,
*Mathematical Foundations of Neuroscience*
(Springer, 2010) http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.139.7871&rep=rep1&type=pdf (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**

- Attendance is
mandatory and verified. More than 2 justified absences means that students
can no longer validate a course for credit (ECTS).
- Final grades
below 6/20 are eliminatory (i.e. the credits cannot count towards the 30
ECTS necessary to validate a semester).
- There is no
second session (no “rattrapage”).
- The minimal
penalty for plagiarism is the removal of the ECTS from the student’s
course contract.
- Courses are
indivisible: students cannot follow and validate only part of the course
for partial credit.

**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.