no code implementations • 6 May 2024 • Hinrikus Wolf, Luis Böttcher, Sarra Bouchkati, Philipp Lutat, Jens Breitung, Bastian Jung, Tina Möllemann, Viktor Todosijević, Jan Schiefelbein-Lach, Oliver Pohl, Andreas Ulbig, Martin Grohe
In the course of the energy transition, the expansion of generation and consumption will change, and many of these technologies, such as PV systems, electric cars and heat pumps, will influence the power flow, especially in the distribution grids.
no code implementations • 11 Mar 2024 • Martin Grohe, Eran Rosenbluth
In the first version, a message only depends on the state of the source vertex, whereas in the second version it depends on the states of the source and target vertices.
no code implementations • 3 Feb 2024 • Christopher Morris, Nadav Dym, Haggai Maron, İsmail İlkan Ceylan, Fabrizio Frasca, Ron Levie, Derek Lim, Michael Bronstein, Martin Grohe, Stefanie Jegelka
Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences.
no code implementations • 20 Jan 2024 • Yuval Lev Lubarsky, Jan Tönshoff, Martin Grohe, Benny Kimelfeld
We study the embedding of the tuples of a relational database, where existing techniques are often based on optimization tasks over a collection of random walks from the database.
1 code implementation • 1 Sep 2023 • Jan Tönshoff, Martin Ritzert, Eran Rosenbluth, Martin Grohe
The recent Long-Range Graph Benchmark (LRGB, Dwivedi et al. 2022) introduced a set of graph learning tasks strongly dependent on long-range interaction between vertices.
Ranked #1 on Link Prediction on PCQM-Contact (MRR-ext-filtered metric)
no code implementations • 29 Aug 2023 • Hinrikus Wolf, Luca Oeljeklaus, Pascal Kühner, Martin Grohe
Grohe (PODS 2020) proposed the theoretical foundations for using homomorphism counts in machine learning on graph level as well as node level tasks.
no code implementations • 8 Mar 2023 • Martin Grohe
We prove that the graph queries that can be computed by a polynomial-size bounded-depth family of GNNs are exactly those definable in the guarded fragment GFO+C of first-order logic with counting and with built-in relations.
no code implementations • 22 Feb 2023 • Eran Rosenbluth, Jan Toenshoff, Martin Grohe
We prove that under certain restrictions, every Mean or Max GNN can be approximated by a Sum GNN, but even there, a combination of (Sum, [Mean/Max]) is more expressive than Sum alone.
1 code implementation • 26 Jan 2023 • Christopher Morris, Floris Geerts, Jan Tönshoff, Martin Grohe
Secondly, when an upper bound on the graphs' order is known, we show a tight connection between the number of graphs distinguishable by the $1\text{-}\mathsf{WL}$ and GNNs' VC dimension.
1 code implementation • 22 Aug 2022 • Jan Tönshoff, Berke Kisin, Jakob Lindner, Martin Grohe
We propose a universal Graph Neural Network architecture which can be trained as an end-2-end search heuristic for any Constraint Satisfaction Problem (CSP).
no code implementations • 27 Jul 2022 • Artur M. Schweidtmann, Jan G. Rittig, Jana M. Weber, Martin Grohe, Manuel Dahmen, Kai Leonhard, Alexander Mitsos
We recommend using sum pooling for the prediction of properties that depend on molecular size and compare pooling functions for properties that are molecular size-independent.
no code implementations • 1 Jun 2022 • Jan G. Rittig, Martin Ritzert, Artur M. Schweidtmann, Stefanie Winkler, Jana M. Weber, Philipp Morsch, K. Alexander Heufer, Martin Grohe, Alexander Mitsos, Manuel Dahmen
We propose a modular graph-ML CAMD framework that integrates generative graph-ML models with graph neural networks and optimization, enabling the design of molecules with desired ignition properties in a continuous molecular space.
no code implementations • 14 Apr 2022 • Luis Böttcher, Hinrikus Wolf, Bastian Jung, Philipp Lutat, Marc Trageser, Oliver Pohl, Andreas Ulbig, Martin Grohe
In our approach, we demonstrate the development of a framework that uses graph neural networks to learn the physical constraints of the power flow.
no code implementations • 18 Dec 2021 • Christopher Morris, Yaron Lipman, Haggai Maron, Bastian Rieck, Nils M. Kriege, Martin Grohe, Matthias Fey, Karsten Borgwardt
In recent years, algorithms and neural architectures based on the Weisfeiler--Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data.
no code implementations • 29 Apr 2021 • Martin Grohe
Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs.
1 code implementation • 11 Mar 2021 • Jan Toenshoff, Neta Friedman, Martin Grohe, Benny Kimelfeld
We study the problem of computing an embedding of the tuples of a relational database in a manner that is extensible to dynamic changes of the database.
Knowledge Graphs Databases
no code implementations • 24 Feb 2021 • Steffen van Bergerem, Martin Grohe, Martin Ritzert
We analyse the complexity of learning first-order queries in a model-theoretic framework for supervised learning introduced by (Grohe and Tur\'an, TOCS 2004).
Logic in Computer Science
1 code implementation • 17 Feb 2021 • Jan Tönshoff, Martin Ritzert, Hinrikus Wolf, Martin Grohe
As the theoretical basis for our approach, we prove a theorem stating that the expressiveness of CRaWl is incomparable with that of the Weisfeiler Leman algorithm and hence with graph neural networks.
Ranked #1 on Graph Classification on REDDIT-B
no code implementations • 28 Jan 2021 • Martin Grohe, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Peter Lindner
In (Grohe, Kaminski, Katoen, Lindner; PODS 2020) we extend the declarative probabilistic programming language Generative Datalog, proposed by (B\'ar\'any et al.~2017) for discrete probability distributions, to continuous probability distributions and show that such programs yield generative models of continuous probabilistic databases.
Probabilistic Programming Databases
no code implementations • 28 Dec 2020 • Martin Grohe, Pascal Schweitzer, Daniel Wiebking
The first one states that the order of non-alternating, non-abelian composition factors for automorphism groups of graphs of bounded Hadwiger number is bounded.
Combinatorics Discrete Mathematics Group Theory 05C75, 05C83, 20D60
no code implementations • 2 Nov 2020 • Martin Grohe, Daniel Neuen
We give an overview of recent advances on the graph isomorphism problem.
Data Structures and Algorithms Discrete Mathematics Combinatorics 05C85 F.2.2; G.2.2
1 code implementation • 2 Oct 2020 • Ralph Abboud, İsmail İlkan Ceylan, Martin Grohe, Thomas Lukasiewicz
In this work, we analyze the expressive power of GNNs with RNI, and prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties.
2 code implementations • 20 May 2020 • Tobias Schumacher, Hinrikus Wolf, Martin Ritzert, Florian Lemmerich, Jan Bachmann, Florian Frantzen, Max Klabunde, Martin Grohe, Markus Strohmaier
We systematically evaluate the (in-)stability of state-of-the-art node embedding algorithms due to randomness, i. e., the random variation of their outcomes given identical algorithms and graphs.
no code implementations • 27 Mar 2020 • Martin Grohe
Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures.
1 code implementation • 18 Sep 2019 • Jan Toenshoff, Martin Ritzert, Hinrikus Wolf, Martin Grohe
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems.
1 code implementation • 4 Oct 2018 • Christopher Morris, Martin Ritzert, Matthias Fey, William L. Hamilton, Jan Eric Lenssen, Gaurav Rattan, Martin Grohe
We show that GNNs have the same expressiveness as the $1$-WL in terms of distinguishing non-isomorphic (sub-)graphs.
Ranked #4 on Graph Classification on NCI1
no code implementations • 27 Aug 2017 • Martin Grohe, Christof Löding, Martin Ritzert
We study the classification problems over string data for hypotheses specified by formulas of monadic second-order logic MSO.
no code implementations • 19 Jan 2017 • Martin Grohe, Martin Ritzert
We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure.
no code implementations • 22 Jul 2013 • Martin Grohe, Kristian Kersting, Martin Mladenov, Erkal Selman
We demonstrate empirically that colour refinement can indeed greatly reduce the cost of solving linear programs.