Hauptinhalt

Topinformationen

Study Project: Computing with Spikes (Part I)

8.3073

Dozenten

Beschreibung

Spiking neural networks (SNNs) are models of brain computation in which individual neurons communicate with spikes, just like the brain does. Compared to more successful artificial neural network models (think Deep Nets), SNNs still raise a number of unique and challenging research questions: (i) How do you learn in a neural network when error-backpropagation doesn’t work? (ii) And can you do this with local update (plasticity) rules that use local information only? (iii) How do you learn a neural network or neuron model that uses spikes very efficiently and still finds a good representation of a continuous input stream?. The potential upsides of spiking nets: We can build specialized, neuromorphic hardware for spike-based networks that promises low-latency real-time, low-power and adaptive computation for the next generation of A.I.
In this context, the study project will follow the neuromorphic tradition of building a system that starts with spike-based sensing: An event-based stereo-vision setup with 2 artificial retinas and a stereo audio sensor for which we will implement an artificial cochlea ourselves. Our goal is to put state-of-the-art theories and algorithms for SNN computation to rigorous testing. We will thus challenge ourselves to tackle multi-modal multi-sensor real-time integration of information – an incredibly challenging technical task that our brain is purpose-built for and handles with ease. Step-by-step, we will tackle aspects of this problem in spiking neural network models that range from simple to complex, from “this-works-but-is-not-how-the-brain-does-it” to “this-is-closer-to-the-brain-but-really-hard-to-make-work”.
The project and accompanying interdisciplinary course are primarily aimed at Master students with an interest in one or more of the following themes: modeling networks of dynamical systems (plastic neurons), simulating spiking neural networks, low-level programming and engineering of A.I. systems using unconventional technologies, staying up to date and documenting state-of-the-art research in SNNs, or supporting a potentially quite complex project organisationally.

Weitere Angaben

Ort: 93/E12
Zeiten: Mo. 14:00 - 16:00 (wöchentlich), Do. 10:00 - 12:00 (wöchentlich)
Erster Termin: Donnerstag, 04.04.2024 10:00 - 12:00, Ort: 93/E12
Veranstaltungsart: Studienprojekt (Offizielle Lehrveranstaltungen)

Studienbereiche

Cognitive Science > Master-Programm

Research Areas:

Algebraic geometry 14-XX
K-theory 19-XX
Algebraic topology 55-XX

Publications in MathSciNet

Publications in Zentralblatt

Publications:

Cellularity of hermitian K-theory and Witt-theory (with Markus Spitzweck and Paul Arne Østvær)
On the η-inverted sphere. K-Theory-Proceedings of the International Colloquium
Gigantic random simplicial complexes Link (with Jens Grygierek, Martina Juhnke-Kubitzke, Matthias Reitzner and Tim Römer)
On very effective hermitian K-theory Link (with Alexey Ananyevskiy and Paul Arne Østvær)
The first stable homotopy groups of motivic spheres DOI (with Markus Spitzweck and Paul Arne Østvær)
Vanishing in stable motivic homotopy sheaves (with Kyle Ormsby and Paul Arne Østvær) Link
The multiplicative structure on the graded slices of hermitian K-theory and Witt-theory (with Paul Arne Østvær) Link
Slices of hermitian K–theory and Milnor's conjecture on quadratic forms (with Paul Arne Østvær) Link
Calculus of functors and model categories, II (with Georg Biedermann) Link
The Arone-Goodwillie spectral sequence for Σ∞Ωn and topological realization at odd primes (with Sebastian Buescher, Fabian Hebestreit und Manfred Stelzer) Link
Motivic slices and coloured operads (with Javier Gutierrez, Markus Spitzweck and Paul Arne Østvær) Link
Motivic strict ring models for K-theory (with Markus Spitzweck and Paul Arne Østvær) PDF
Theta characteristics and stable homotopy types of curves DOI
A universality theorem for Voevodsky's algebraic cobordism spectrum (with Ivan Panin and Konstantin Pimenov) Link
On the relation of Voevodsky's algebraic cobordism to Quillen's K-theory DOI (with Ivan Panin and Konstantin Pimenov)
On Voevodsky's algebraic K-theory spectrum BGL (with Ivan Panin and Konstantin Pimenov)
Rigidity in motivic homotopy theory DOI (with Paul Arne Østvær)
Calculus of functors and model categories DOI (with Georg Biedermann and Boris Chorny)
Motivic Homotopy Theory Link (with B.I.Dundas, M.Levine, P.A.Østvær and V.Voevodsky)
Motives and modules over motivic cohomology Link (with Paul Arne Østvær)
Modules over motivic cohomology DOI (with Paul Arne Østvær)
Enriched functors and stable homotopy theory Link (with Bjørn Ian Dundas and Paul Arne Østvær)
Motivic functors Link (with Bjørn Ian Dundas and Paul Arne Østvær)

Preprints and Talks:

Motives, homotopy theory of varieties, and dessins d'enfants PDF
GQT Graduate School PDF

Projekte

DFG-Sachbeihilfe "Algebraic bordism spectra: Computations, filtrations, applications" (DFG-RSF-Antrag mit Alexey Ananyevskiy)
DFG-Sachbeihilfe "Applying motivic filtrations" (mit Marc Levine und Markus Spitzweck) im DFG Schwerpunktprogramm 1786
DFG-Sachbeihilfe "Operads in algebraic geometry and their realizations" (mit Jens Hornbostel,
Markus Spitzweck und Manfred Stelzer) im DFG Schwerpunktprogramm 1786
DFG Sachbeihilfe ``Operad structures in motivic homotopy theory'' im DFG Schwerpunktprogramm 1786 ``Homotopy theory and algebraic geometry'' (mit Markus Spitzweck)
DFG Sachbeihilfe ``Motivic filtrations over Dedekind domains'' im DFG Schwerpunktprogramm 1786 ``Homotopy theory and algebraic geometry'' (mit Marc Levine und Markus Spitzweck)
DFG Graduiertenkolleg 1916 ``Combinatorial structures in geometry''
DFG Sachbeihilfe ``Goodwillie towers, realizations, and E_n-structures''
Graduiertenkolleg ``Combinatorial structures in algebra and topology'' (mit H. Brenner, W. Bruns, T. Römer und R. Vogt)
DFG Sachbeihilfe ``Combinatorial structures in algebra and topology'' (mit H. Brenner, W. Bruns, T. Römer und R. Vogt)

Supervision

PhD

Philip Herrmann: Stable equivariant motivic homotopy theory and motivic Borel cohomology, 2012
Florian Strunk: On motivic spherical bundles, 2013

Master/Diplom

Markus Severitt: Motivic Homotopy Types of Projective Curves, 2006 PDF
Philip Herrmann: Ein Modell für die motivische Homotopiekategorie, 2009
Florian Strunk: Ein Modell für motivische Kohomologie, 2009
Sebastian Büscher: Anwendung der F₂-kohomologischen Goodwillie-Spektralsequenz für iterierte Schleifenraeume, 2010
Fabian Hebestreit: On topological realization at odd primes, 2010
Katharina Lorenz: Darstellung unterschiedlicher mathematischer Rekonstruktionen von Größen, 2012
Jana Brickwedde: Fehlvorstellungen zum Grenzwertbegriff, 2015
Lena-Christin Müller: Penrose-Parkettierungen und ihre Eigenschaften, 2015
Larissa Bauland: Der Satz von Seifert-van Kampen und einige seiner Anwendungen, 2018
Nikolaus Krause: Eine algebraische Einfuehrung in die Milnor-Witt K-Theorie, 2019

Bachelor

Ein Spezialfall des letzten Satzes von Fermat, 2010
Transzendente Zahlen, 2010
Zur Gruppe des Rubik-Wuerfels, 2011
Einige Betrachtungen zum letzten Satz von Fermat, 2012
Die Involution auf algebraischer K-Theorie, 2012
Platonische und Archimedische Körper, 2012
Klassifikation regulärer Polyeder, 2013
Grundbegriffe der Trigonometrie und ihrer Umsetzung in der gymnasialen Sekundarstufe I, 2014
Die Riemann’sche Zetafunktion und der Primzahlsatz, 2014
Konstruktion der klassischen Zahlbereiche, 2014
Eigenschaften und spezielle Werte der Riemann'schen Zetafunktion, 2015
Das quadratische Reziprozitätsgesetz und dessen Bedeutung in der Kryptographie, 2015
Graphen färben, 2015
Klassifikation und Visualisierung von Koniken, 2016
Konstruktion von Polygonen mit einem einzigen Schnitt, 2016
Parkettierungen der Ebene durch kongruente konvexe Fuenfecke, 2019
Die klassischen Hopf-Faserbuendel und einige ihrer Eigenschaften, 2019
Einige Anmerkungen mathematischer und historischer Natur zu Fermats Letztem Satz, 2019