6 papers
Neural networks as fuzzy logic formulas
Damian Heiman, Antti Kuusisto, Esko Turunen
Neural networks are a fundamental aspect of modern artificial intelligence, playing a key role in various important machine learning architectures including transformers and graph…
Cross-Attention and Encoder-Decoder Transformers: A Logical Characterization
Veeti Ahvonen, Damian Heiman, Antti Kuusisto +2
We give a novel logical characterization of encoder-decoder transformers, the foundational architecture for LLMs that also sees use in various settings that benefit from cross-atte…
Expressive Power of Graph Transformers via Logic
Veeti Ahvonen, Maurice Funk, Damian Heiman +2
Transformers are the basis of modern large language models, but relatively little is known about their precise expressive power on graphs. We study the expressive power of graph tr…
Graph neural networks and MSO
Veeti Ahvonen, Damian Heiman, Antti Kuusisto
We give an alternative proof for the existing result that recurrent graph neural networks working with reals have the same expressive power in restriction to monadic second-order l…
Descriptive complexity for neural networks via Boolean networks
Veeti Ahvonen, Damian Heiman, Antti Kuusisto
We investigate the expressive power of neural networks from the point of view of descriptive complexity. We study neural networks that use floating-point numbers and piecewise poly…
Logical Characterizations of Recurrent Graph Neural Networks with Reals and Floats
Veeti Ahvonen, Damian Heiman, Antti Kuusisto +1
In pioneering work from 2019, Barceló and coauthors identified logics that precisely match the expressive power of constant iteration-depth graph neural networks (GNNs) relative t…