Computational Neuroscience: Neural Dynamics

This course lays the foundations for a neurally grounded understanding of the fundamental processes in perception, in cognition, and in motor control, that enable intelligent action in the world. The theoretical perspective is aligned with ideas from embodied and situated cognition, but embraces concepts of neural representation and aims to reach higher cognition. Neural grounding is provided at the level of populations of neurons in the brain that form strongly recurrent neural networks and are ultimately linked to the sensory and motor surfaces.

The theoretical concepts on which the course is based come form dynamical systems theory. These concepts are used to characterize neural processes in strongly recurrent neural networks as neural dynamic systems, in which stable activation states emerge from the connectivity patterns within neural populations. These connectivity patterns imply that neural populations represent low-dimensional features spaces. This leads to neural dynamic fields of activation as the building blocks of neural cognitive architectures. Dynamic instabilities induce change of attractor states from which cognitive functions such as detection, change, or selection decisions, working memory, and sequences of processing stages emerge.

The course partially follows a textbook (Dynamic Thinking—A primer on Dynamic Field Theory, Schöner, Spencer, and the DFT research group. Oxford University Press, 2016), of which chapters will serve as reading material. Exercises will focus on hands-on simulation experiments, but also involve readings and the writing of short essays on interdisciplinary research topics. See www.dynamicfieldtheory.org for some of that material. Tutorials on mathematical concepts are provided, so that training in calculus and differential equations is useful, but not a prerequisite for the course. 

Lecturers

Details

Course type
Lectures
Credits
6 CP
Term
Winter Term 2020/2021
E-Learning
e-learning course available

Dates

Lecture
Takes place every week on Thursday from 14:15 to 16:00 in an online live session in the e-learning course.
First appointment is on 29.10.2020
Last appointment is on 11.02.2021
Exercise
Takes place every week on Thursday from 16:15 to 17:00 in an online live session in the e-learning course.
First appointment is on 29.10.2020
Last appointment is on 11.02.2021

Requirements

This course requires some basic math preparation, typically as covered in two semesters of higher mathematics (functions, differentiation, integration, differential equations, linear algebra). The course does not make extensive use of the underlying mathematical techniques, but uses the mathematical concepts to express scientific ideas. Students without prior training in the relevant mathematics may be able to follow the course, but will have to work harder to familiarize themselves with the concepts.


Exercises

Exercises are organized by Sophie Aerdtker and Dr. Mathis Richter. Details on grading are available in the course rules below.

Literature

The course will be based on selected chapters of a textbook (Dynamic Thinking: A Primer on Dynamic Field Theory by Schöner, G., Spencer, J, and the DFT Research Group, Oxford University Press). The Introduction and the first two chapters are available for download in the course materials below. These and others will also serve as readings for some of the exercises. 

For the mathematical background in dynamical systems an excellent resource is a book that is available online as a free download (thanks to the author's generosity): Edward R. Scheinerman's Invitation to Dynamical Systems.  This book covers both discrete and continuous time dynamical systems, while in the course we will only make use of continuous time dynamical systems formalized as differential equations. 

Teaching Units

Welcome and Introduction
Lecture slides Introduction

Brief introduction to the course 

Video Introduction lecture video
Dynamical systems tutorials

These short tutorials are outside the main syllabus of the lecture course. They serve to provide background to the mathematical concepts used. A resource is the book by Scheinerman cited on the course's homepage. 

Lecture slides Dynamical systems tutorial 1

about the basic concepts of dynamical systems.

Video Dynamical systems tutorial 1 video
Lecture slides Dynamical systems tutorial 2

about numerical solutions of differential equations

Video Dynamical systems tutorial 2 video
Document Code sample

for the numerical solution of differential equations

Lecture slides Dynamical systems tutorial 3

about attractors and instabilities 

Video Dynamical systems tutorial 3

about attractors and bifurcations

Exercises Exercise 1
Reference solution Exercise solution and remarks

This is not a solution as we would have expected it from you but rather a document that explains a possible solution.

Braitenberg vehicles: Embodied nervous systems
Lecture slides Lecture on Braitenberg vehicles
Link A web-simulator for Braitenberg vehicles

provided by Harmen de Weerd, a dutch researcher. 

Video Lecture on Braitenberg vehicles: video
Neural dynamics

Introduction into the foundations of neural dynamic thinking. Chapter 1 of the DFT primer (see background material) is useful reading for this. 

Lecture slides Neural dynamics
Video Neural dynamics
Exercises Neural dynamics
Neural basis of dynamic fields
Lecture slides Neural basis of dynamic fields
Video Neural basis of dynamic fields
Exercises Neural basis of dynamic fields
Dynamic Field Theory: Detections
Lecture slides Detection in DFT
Video Detection in DFT
Exercises Detection in DFT
Dynamic Field Theory: Selection
Lecture slides Selection in DFT
Video Selection in DFT
Exercises Selection in DFT
Document Reading for Exercise 5
Dynamic Field Theory: Memory
Lecture slides Dynamic Field Theory: Memory
Video Dynamic Field Theory: Memory
Exercises Dynamic Field Theory: Memory
Dynamic Field Theory and embodiment

Linking to sensory inputs and linking to motor output, with issues of normalization and coordinate frames 

Lecture slides Dynamic Field Theory and embodiment
Video Dynamic Field Theory and embodiment
Review of the foundations of DFT
Exercises Essay exercise (exercise 7)

This essay exercise reviews the foundations of DFT

Higher-dimensional fields
Lecture slides DFT in higher dimensions
Video DFT in higher dimensions
Intentional systems
Lecture slides Neural dynamic concepts for intentional systems
Video Intentional systems

Documents

Document Rules

for how exerices can be used to obtain bonus points, for passing the exam, and for how the final grade is computed 

The Institut für Neuroinformatik (INI) is a central research unit of the Ruhr-Universität Bochum. We aim to understand the fundamental principles through which organisms generate behavior and cognition while linked to their environments through sensory systems and while acting in those environments through effector systems. Inspired by our insights into such natural cognitive systems, we seek new solutions to problems of information processing in artificial cognitive systems. We draw from a variety of disciplines that include experimental approaches from psychology and neurophysiology as well as theoretical approaches from physics, mathematics, electrical engineering and applied computer science, in particular machine learning, artificial intelligence, and computer vision.

Universitätsstr. 150, Building NB, Room 3/32
D-44801 Bochum, Germany

Tel: (+49) 234 32-28967
Fax: (+49) 234 32-14210