Homepage of Benjamin Matthias Ruppik

Hello and welcome! You have landed on the website of a mathematician who is now working on Topological Deep Learning and Representation Learning in Data Science. My name is Ben Ruppik (he/him) and I hold a Master's degree in Mathematics from the University of Bonn and a PhD in low-dimensional topology from the Max Planck Institute for Mathematics and University of Bonn. Currently, I am part of the Dialog Systems and Machine Learning lab led by Prof. Milica Gašić at Heinrich-Heine-University Düsseldorf, exploring the use of Topological Data Analysis in Natural Language Processing and Task-oriented Dialogue Systems. On this website, you will find some of my projects, publications, and other resources related to my research interests. You are welcome to reach out to me via e-mail or LinkedIn in German or English!

Papers and Preprints

Links to arXiv; ORCID iD icon ORCID; Google Scholar; ResearchGate.

Topological Deep Learning

Close neighbors of the word cheap in a word embedding.

Dialogue Term Extraction using Transfer Learning and Topological Data Analysis

[Renato Vukovic, Michael Heck, Benjamin Matthias Ruppik, Carel van Niekerk, Marcus Zibrowius, Milica Gasic]
We demonstrate that topological features derived from neighborhoods in a word embedding can be used to extract dialogue terms. In particular, the Wasserstein norm and Persistence Image Vectorization of the persistent homology of the neighborhood appear to be generalizable features which are effective in a transfer learning approach.

Proceedings of the 23rd Annual Meeting of the Special Interest Group on Discourse and Dialogue (SIGDIAL 2022), pages 564-581, Edinburgh, UK
doi:10.18653/v1/2022.sigdial-1.53
arXiv:2208.10448

Task-oriented Dialogue Systems

Using ChatGPT for Zero-shot Dialogue State Tracking.

ChatGPT for Zero-shot Dialogue State Tracking: A Solution or an Opportunity?

[Michael Heck, Nurul Lubis, Benjamin Ruppik, Renato Vukovic, Shutong Feng, Christian Geishauser, Hsien-Chin Lin, Carel van Niekerk, Milica Gasic]
Abstract: Recent research on dialogue state tracking (DST) focuses on methods that allow few- and zero-shot transfer to new domains or schemas. However, performance gains heavily depend on aggressive data augmentation and fine-tuning of ever larger language model based architectures. In contrast, general purpose language models, trained on large amounts of diverse data, hold the promise of solving any kind of task without task-specific training. We present preliminary experimental results on the ChatGPT research preview, showing that ChatGPT achieves state-of-the-art performance in zero-shot DST. Despite our findings, we argue that properties inherent to general purpose models limit their ability to replace specialized systems. We further theorize that the in-context learning capabilities of such models will likely become powerful tools to support the development of dedicated and dynamic dialogue state trackers.

Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 936--950, Toronto, Canada
doi:10.18653/v1/2023.acl-short.81
arXiv:2306.01386

Low-dimensional Topology

Schematic of a regular homotopy.

Casson-Whitney Unknotting Numbers of 2-spheres in the 4-sphere

[Jason Joseph, Michael Klug, Benjamin Ruppik, Hannah Schwartz]
Inspired by Schneiderman-Teichner's perspective on Gabai's 4-dimensional light bulb theorem we define the Casson-Whitney unknotting number of knotted 2-spheres in \(S^4\): Since every 2-knot \(K\) in \(S^4\) can be obtained by first performing a number of (trivial) finger moves on the unknot, and in a next step removing the resulting intersection points in pairs via Whitney moves (along possibly complicated discs), we can define \(u_{\textrm{cw}}(K)\) as the minimal number of finger moves needed in such a process to arrive at \(K\). We relate this to the 1-handle stabilization number and look specifically at examples of ribbon 2-knots and twist-spins of classical knotted arcs.

J. Topology 14.4 (2021), 1321-1350
doi:10.1112/topo.12209
arXiv:2007.13244

Finger-Whitney Unknotting Numbers - Part 1 (.pdf, handwritten slides), Finger-Whitney Unknotting Numbers - Part 2 [Michael] (.pdf, handwritten slides)

Diagram of a free resolution over a group ring of products of cyclic groups.

Homotopy classification of 4-manifolds with finite abelian 2-generator fundamental groups

[Daniel Kasprowski, Mark Powell, Benjamin Ruppik]
We show that for an oriented 4-dimensional Poincaré complex with finite fundamental group, whose 2-Sylow subgroup is abelian with at most 2 generators, the homotopy type is determined by its quadratic 2-type.

arXiv:2005.00274

Thesis

Iterated Whitehead double of the dual knot in the Poincare homology sphere

Casson-Whitney unknotting, Deep slice knots and Group trisections of knotted surface type

Advisors: Arunima Ray and Peter Teichner.

PhD thesis published at University of Bonn.

Main new results:
  • An explicit construction of regular homotopies between rim surgeries (which subsumes some of the previous applications to twist-spun knots).
  • A generalization of the fusion number upper bound for the Casson-Whitney number to higher genus ribbon surfaces in the 4-sphere.
  • The stabilization number of Suciu's ribbon 2-knots \(R_{k}\) is equal to 1.
  • The Casson-Whitney distance of the standard unknotted \(\mathbb{RP}^{2}\) and Suciu's associated \(\mathbb{RP}^{2}\)-knots \(R_{k} \# \mathbb{RP}^{2}\) is equal to 1.
  • Partial results of the algebraic Casson-Whitney number of Suciu's knots.
  • The (+1)-trace on the right handed trefoil knot contains infinitely many non-local knots in its boundary which exhibit the difference between shallow topological sliceness and smooth deep sliceness. This is an interplay between Freedman's construction of a topological slice for 3-fold iterated positively clasped Whitehead doubles on the one hand, and the Heegaard-Floer \(\tau\)-invariant giving a smooth obstruction for sliceness in \(\partial X \times [0,1]\).
  • Group trisections of knotted surface type of the trefoil group, which comes from a bridge trisection of Suciu's ribbon 2-knots.

Resources

Activities

Summer Term 2023

Teaching
Talks
Conferences

Winter Term 2022/2023

Teaching
Talks
Conferences

Summer Term 2022

Teaching
Conferences

Winter Term 2021/2022

Talks

Summer Term 2021

Talks
Conferences

Winter Term 2020/2021

Talks
Conferences

Summer Term 2020

Talks
Conferences/Workshops

Winter Term 2019/2020

Talks
Conferences
  • Winter Braids X, Pisa, February 17 - 21, 2020
  • Low-dimensional topology workshop, Regensburg, October 21 - 23, 2019.

Summer Term 2019

Talks
Conferences

Winter Term 2018/2019

Summer Term 2018

  • Material for the rep 'Introduction to Geometry and Topology' in the summer term 2018.

Winter Term 2017/2018

Summer Term 2017

  • Material for the rep 'Introduction to Geometry and Topology' in the summer term 2017.
  • Handout (.pdf) for a talk on the First Lie Theorem.

Summer Term 2016

Other

Links: Github, MathStackExchange