The paper introduces recurrent Graph Neural Networks (GNNs) that use set-based aggregation and establishes conditions that can be verified directly from the network weights. It proves a two‑directional equivalence between these networks and the Boolean closure of reachability and safety properties, corresponding to the fragment BΣ◦₁ of the modal μ‑calculus. This equivalence allows for verifiable symbolic explanations of networks that satisfy the identified conditions, without relying on counting logic or external halting signals.
By Blai Bonet
arXiv:2606. 20325v1 Announce Type: new Abstract: Classical approximation theorems ask for a new neural network whenever the target accuracy is improved.
By Valentin Abadie, Clemens Hutter, Helmut B\"olcskei
arXiv:2605. 06384v3 Announce Type: replace-cross Abstract: We introduce MinMax Recurrent Neural Cascades (MinMax RNCs), a class of recurrent neural networks built from a novel form of recurrence over the MinMax algebra.
By Alessandro Ronca
Deep neural networks are widely believed to derive their expressive power from their ability to form \textbf{hierarchical representations}, capturing progressively more abstract and compositional features across layers. In language modeling, \textbf{transformers} have emerged as the dominant architecture, with early layers capturing local syntactic patterns and later layers encoding more complex clause-level dependencies.
arXiv:2511. 14953v2 Announce Type: replace-cross Abstract: Discrete structures are currently second-class in differentiable programming.
By Joey Velez-Ginorio, Nada Amin, Konrad Kording, Steve Zdancewic
arXiv:2603. 03612v3 Announce Type: replace Abstract: The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability.
By William Merrill, Hongjian Jiang, Yanhong Li, Anthony Lin, Ashish Sabharwal