Nicolas Berkouk

Post-doctoral researcher - EPFL's Topology and Neuroscience team

Nicolas Berkouk

I am currently a post-doctoral researcher in the Topology and Neuroscience team at EPFL, under the supervision of Kathryn Hess. I was previously funded by Innosuisse, thanks to a collaboration with the Lausanne based start-up Giotto.ai, in order to use topology to investigate explicability of deep learning. I formerly completed my Ph.D. under the supervision of Steve Oudot, entitled Persistence and Sheaves: from Theory to Applications.

In my research, I melt ideas coming from real world applications' challenges with theoretical algebraic topology, in order both to develop innovative tools for machine learning, and to tackle new questions in pure mathematics. I am also collaborating with researchers in social sciences, to study the formation of the field of Explainable AI.

For an overview of my research, you can have a look at my Ph.D. defense:

News

Our paper Singular Value Representation: A New Graph Perspective On Neural Networks with Dan Meller got accepted to AISTAT23! Watch the SVR of a fully connected NN learning to classify the MNIST dataset:

Interested in the interplay between Euler Calculus, Sheaf theory and interleaving distance ? Check my new preprint here.

The PSHT (Persistence, Sheaves and Homotopy Theory) online seminar goes on for another year! For the occasion we developed a brand new website, if you're interested, you will find all the necessary information there.

Upcoming events

Past events

  • December 2022 Interactions between representation theory and topological data analysis workshop, CAS, Oslo. Persistence and the Sheaf-Function Correspondence.
  • November 2022 Chaire Pari Seminar (Paris - France). The field of Explainable AI : designing machines to explain machines ?
  • November 2022 Online workshop on computational persistence. Projected Barcodes and Integral Sheaf Metrics
  • October 2022 ETH Symplectic Geometry Seminar (Zürich - Switzerland), K-theory of constructible sheaves and persistence.
  • July 2022 AI and Health : Interdisciplinary Approaches Colloquium, Lebesgue Center for Mathematics. The field of explainable AI : designing machines to explain machines ?
  • June 2022 ATMCS Conference 2022 (Oxford - UK), Projected Barcodes and Integral Sheaf Metrics.
  • June 2022 Oxford TDA Seminar, Projected Barcodes and Integral Sheaf Metrics.
  • 18th February 2022 COSTECH (UTC - Compiègne) Seminar. The field of Explainable AI : designing machines to explain machines ?
  • 17th February 2022 DataShape (INRIA - France) Seminar, Persformer: A Transformer Architecture for Topological Machine Learning, , joint with Raphael Reinauer.
  • 10th February 2022 AlToGeLiS online Seminar. Persformer: A Transformer Architecture for Topological Machine Learning, joint with Raphael Reinauer.
  • 10th February 2022 STS Lab (UNIL - Lausanne) Seminar. The field of Explainable AI : designing machines to explain machines ?
  • August 2021 Sheaves and Homotopical Methods for Topological Data Analysis, Mini-Symposium as part of the SIAM AG21' conference, Co-organizer with François Petit.
  • July 2021 5th Conference on Geometric Science of Information, Paris, France. Talk: Algebraic Homotopy Interleaving Distance.
  • May 2021 AMLD workshop on AI and Topology, EPFL, Lausanne. Talk: Level-Sets Persistence and Sheaf Theory.
  • April 2021 Workshop on Topological Data Analysis, IMSI, Chicago, US. Talk: Ephemeral Persistence Modules and Disance Comparisons.
  • June 2020 Applied Topology Seminar, EPFL, Lausanne, Switzerland. Talk: Sheaves as Computable and Stable Desciptors of Data.
  • June 2020 AATRN Seminar, online. Talk: Sheaves as Computable and Stable Desciptors of Data, video available here.
  • June 2020 Representation Theory Seminar, Bielefeld University, Bielefeld, Germany. Talk: Derived Methods for Persistence.
  • January 2019 Applied Topology workshop, Kyoto University, Kyoto, Japan. Talk: A Derived Isometry Theorem for Constructible Sheaves Over R.
  • May 2018 Bridging Statistics and Sheaves workshop, IMA, Minneapolis, USA. Poster: A Derived Isometry Theorem for Constructible Sheaves Over R.
  • March 2018 Luxembourg University, Luxembourg. Gave a 10 hours course with Steve Oudot: Theoretical Foundations of Persistence.
  • February 2018 Linking Topology to Algebraic Geometry and Statistics workshop, MPI, Leipzig, Germany. Poster: Computing the convolution distance for constructible sheaves over R.
  • December 2017 Journées de Géométrie Algorithmique, Aussois, France. Talk: Stable resolutions of multi-parameter persistence modules.
  • August 2017 Developing abstract foundations for TDA, Banff Center, Canada. Talk: Stable resolutions of multi-parameter persistence modules , video available here.
  • March 2017 Persistent homology working group, IHP, Paris. Talk: Stable resolutions of multi-parameter persistence modules.