3 Search Results for "Ahvonen, Veeti"

Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.3
Foundations of Graph Neural Networks (A Logician’s View) (Invited Paper)

Authors: Egor V. Kostylev

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Graph Neural Networks (GNNs) are a family of neural architectures that are naturally suited to learning functions on graphs. They are now used in a wide range of applications. It has been observed that GNNs share many similarities with classical computer science (CS) formalisms, such as the Weisfeiler-Leman graph isomorphism test, bisimulation, and logic. Most notably, both GNNs and these formalisms deal with functions on graphs and graph-like structures. This observation opens up an opportunity to compare GNN architectures with these formalisms in terms of different kinds of expressibility, thus positioning these architectures within the well-established landscape of theoretical CS. This, in turn, helps us better understand the fundamental capabilities and limitations of various GNN architectures, enabling more informed choices about which architecture to use - if any at all. In these lecture notes, I give an introduction to the state-of-the-art foundations of GNNs - specifically, our current understanding of their expressibility in terms of the classical formalisms, considering several notions of expressive power.
Cite as

Egor V. Kostylev. Foundations of Graph Neural Networks (A Logician’s View) (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kostylev:OASIcs.RW.2024/2025.3,
  author =	{Kostylev, Egor V.},
  title =	{{Foundations of Graph Neural Networks (A Logician’s View)}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{3:1--3:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.3},
  URN =		{urn:nbn:de:0030-drops-250486},
  doi =		{10.4230/OASIcs.RW.2024/2025.3},
  annote =	{Keywords: Graph Neural Networks, Expressivity, Logic}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.9
Descriptive Complexity for Neural Networks via Boolean Networks

Authors: Veeti Ahvonen, Damian Heiman, and Antti Kuusisto

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
We investigate the descriptive complexity of a class of neural networks with unrestricted topologies and piecewise polynomial activation functions. We consider the general scenario where the running time is unlimited and floating-point numbers are used for simulating reals. We characterize these neural networks with a rule-based logic for Boolean networks. In particular, we show that the sizes of the neural networks and the corresponding Boolean rule formulae are polynomially related. In fact, in the direction from Boolean rules to neural networks, the blow-up is only linear. We also analyze the delays in running times due to the translations. In the translation from neural networks to Boolean rules, the time delay is polylogarithmic in the neural network size and linear in time. In the converse translation, the time delay is linear in both factors. We also obtain translations between the rule-based logic for Boolean networks, the diamond-free fragment of modal substitution calculus and a class of recursive Boolean circuits where the number of input and output gates match.
Cite as

Veeti Ahvonen, Damian Heiman, and Antti Kuusisto. Descriptive Complexity for Neural Networks via Boolean Networks. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ahvonen_et_al:LIPIcs.CSL.2024.9,
  author =	{Ahvonen, Veeti and Heiman, Damian and Kuusisto, Antti},
  title =	{{Descriptive Complexity for Neural Networks via Boolean Networks}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{9:1--9:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.9},
  URN =		{urn:nbn:de:0030-drops-196528},
  doi =		{10.4230/LIPIcs.CSL.2024.9},
  annote =	{Keywords: Descriptive complexity, neural networks, Boolean networks, floating-point arithmetic, logic}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.9
Descriptive Complexity for Distributed Computing with Circuits

Authors: Veeti Ahvonen, Damian Heiman, Lauri Hella, and Antti Kuusisto

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
We consider distributed algorithms in the realistic scenario where distributed message passing is operated by circuits. We show that within this setting, modal substitution calculus MSC precisely captures the expressive power of circuits. The result is established via constructing translations that are highly efficient in relation to size. We also observe that the coloring algorithm based on Cole-Vishkin can be specified by logarithmic size programs (and thus also logarithmic size circuits) in the bounded-degree scenario.
Cite as

Veeti Ahvonen, Damian Heiman, Lauri Hella, and Antti Kuusisto. Descriptive Complexity for Distributed Computing with Circuits. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ahvonen_et_al:LIPIcs.MFCS.2023.9,
  author =	{Ahvonen, Veeti and Heiman, Damian and Hella, Lauri and Kuusisto, Antti},
  title =	{{Descriptive Complexity for Distributed Computing with Circuits}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.9},
  URN =		{urn:nbn:de:0030-drops-185433},
  doi =		{10.4230/LIPIcs.MFCS.2023.9},
  annote =	{Keywords: Descriptive complexity, distributed computing, logic, graph coloring}
}
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