Mathematical Foundations of AI other than Machine Learning (MFAIML)

WASP Winter Conference.

Summary of the 2021 meetings, goals for the cluster in 2022, presentation from Danai about “Geometric combinatorics“.

The recording of the meeting is accessible here.

Preparation for the WASP Winter conference.

Reading and discussion about 2 papers:

•  Simplicial Neural Network 
• Another step towards demistifying DNN

Talk by Felix Rydell, on Algebraic Vision and its connections to ML. Slides

Talk by Amaury Gouverneur, on Introduction about Information Theory and application in ML. Slides

Talk by George Osipov, on Constraint Satisfaction Problems. Slides

Talk by René Mellema, on Chess computers and search as a paradigm for AI. Slides

Introductory talks on various topics.

Initial discussions. Election of cluster leader.

I’m interested in problems with an intrinsic geometric structure. They can be studied by informative topological invariants, which are compact and, in many cases, computable.

Keywords: Applied Topology, Persistence Theory

Publications:

1. Chachólski, W., Jin, A., Scolamiero, M., Tombari, F., Homotopical decompositions of simplicial and Vietoris-Rips complexes, Journal of Applied and Computational Topology (2021), https://doi.org/10.1007/s41468-021-00066-2
2. Chachólski, W., De Gregorio, A., Quercioli, N., Tombari, F., Landscapes of dataset and functoriality of persistent homology, Preprint https://arxiv.org/abs/2002.05972

Affiliation: KTH Royal Institute of Technology

Email: tombari@kth.se

I’m interested in how we can mimic human behaviour on a macro scale by implementing agent behaviours on a smaller (micro) scale in computational tools. I’m currently looking into how we can incorporate social structures, such as norms, conventions, and social practices, into these agent behaviours. In this research, we use tools such as formal logic to describe these structures and how we should implement them.

Keywords: Social simulation, Formal methods, Socially aware AI

Publications:

1. Mellema, R., Jensen, M., & Dignum, F. (2021). Social Rules for Agent Systems. In A. Aler Tubella, S. Cranefield, C. Frantz, F. Meneguzzi, & W. Vasconcelos (Eds.), Coordination, Organizations, Institutions, Norms, and Ethics for Governance of Multi-Agent Systems XIII (Vol. 12298, pp. 175–180). Springer International Publishing. http://link.springer.com/10.1007/978-3-030-72376-7_10
2. Dignum, F., Dignum, V., Davidsson, P. et al. Analysing the Combined Health, Social and Economic Impacts of the Corovanvirus Pandemic Using Agent-Based Social Simulation. Minds & Machines 30, 177–194 (2020). https://doi.org/10.1007/s11023-020-09527-6

Affiliation: Umeå University

Email: rene.mellema@cs.umu.se

My interests are in the combinatorial and algebraic foundations of modern methods in AI.

Keywords: algebraic graph theory, algebraic and geometric combinatorics

Affiliation: KTH Royal Institute of Technology

Email: danaide@kth.se

I’m interested in discrete probability, particularly random graphs and combinatorial optimisation problems on random graphs, and algorithmic properties of such problems. Methods from statistical physics have shown themselves to be useful in this area, so my interests fall in the intersection between discrete probability, computer science, and statistical mechanics.

Keywords: random graphs, probability theory

Affiliation: Uppsala University

Email: vilhelm.agdur@math.uu.se

My research concerns constraint satisfaction problems over infinite domains. This is a general formalism that captures many computational problems arising in different fields, e.g., in spatial and temporal reasoning relevant to AI. I am particularly interested in algorithms and lower bounds for NP-hard constraint satisfaction problems.

Keywords: Theoretical computer science, Constraint satisfaction

Publications:

1. Jonsson, Peter; Lagerkvist, Victor; Osipov, George;  Acyclic Orders, Partition Schemes and CSPs: Unified Hardness Proofs and Improved Algorithms, Artificial Intelligence, 103505, 2021, Elsevier
2. Dabrowski, Konrad K; Jonsson, Peter; Ordyniak, Sebastian; Osipov, George; Disjunctive Temporal Problems under Structural Restrictions, Proc. 35th AAAI Conference on Artificial Intelligence (AAAI-2021), to appear, 2021
3. Dabrowski, Konrad K; Jonsson, Peter; Ordyniak, Sebastian; Osipov, George; Solving Infinite-Domain CSPs Using the Patchwork Property, Proc. 35th AAAI Conference on Artificial Intelligence (AAAI-2021), to appear, 2021
4. Dabrowski, Konrad K; Jonsson, Peter; Ordyniak, Sebastian; Osipov, George; Fine-Grained Complexity of Temporal Problems, Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning, 17, 1, 284-293, 2020

Affiliation: Linköping University

Email: george.osipov@liu.se

I aim to build connections between AI and algebraic geometry. 

Keywords: Algebraic geometry, algebraic statistics, machine learning. 

Affiliation: KTH Royal Institute of Technology

Email: felixry@kth.se

Information theory  and Machine learning.

Particularly, I am interested in the problem of generalization of learning algorithms. I am always interested in talking about other topics within Information Theory and Machine Learning, so do not hesitate to contact me for a discussion.

Keywords: Generalization error, information-theoretic bounds, stochastic gradient Langevin dynamics

Affiliation: KTH Royal Institute of Technology

Email: amauryg@kth.se

My current research focusses on trying to prove tight upper and lower bounds on the complexity of equality CSPs, to achieve a dichotomy result between tractable and intractable nature of equality constraints.

Keywords: Complexity Theory, Parameterized Algorithms, Constraint Satisfaction Problems

Affilitation: Linköping University

Email: abhijat.sharma@liu.se

My research interests lie in geometric and enumerative combinatorics and their applications to artificial intelligence.

Keywords: Polytope theory, discrete geometry, enumerative combinatorics

Affilitation: KTH Royal Institute of Technology

Email: aryaman@kth.se