The paper introduces MACCHIATO, a training algorithm that builds a ReLU‑MLP from partial truth‑table data while simultaneously constructing an explicit Boolean circuit over AND, OR, and XOR gates that certifies the network’s computation. The method iteratively projects residuals onto low‑dimensional Boolean classes, compiles the resulting circuit into a ReLU‑MLP, and uses logic minimization and influence‑based variable selection to achieve a six‑layer network with provable truth‑table error bounds. Experiments on synthetic random‑junta tasks show that these certified networks outperform Adam‑trained MLPs in data‑sparse or projection‑aligned regimes and complete faster than flat ESPRESSO in certain settings.
By Hrad Ghoukasian, Anastasis Kratsios
arXiv:2606. 17882v1 Announce Type: new Abstract: Bridges between graph neural networks (GNNs) and logical formalisms have been established by fixing architectural choices, such as the types of aggregation, combination, and activation functions.
By Przemys{\l}aw Andrzej Wa{\l}\k{e}ga, Bernardo Cuenca Grau
arXiv:2608. 12617v1 Announce Type: new Abstract: We prove that, on finite simple undirected graphs equipped with a single Boolean node feature, the Boolean queries expressible in $\Sigma$-MPLang, for any collection $\Sigma$ of eventually constant activation functions and with arbitrary real coefficients, form a strict subclass of the Boolean queries expressible in ReLU-MPLang.
By Pablo Barcel\'o, Floris Geerts, Matthias Lanzinger, Klara Pakhomenko, Jan Van den Bussche
arXiv:2602.17493v2 Announce Type: replace-cross
Abstract: We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly $\pm 1$, and the resulting mod...
By Veit Elser, Manish Krishan Lal
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
Baobab compiles an OWL 2 DL (ΣROIQ) ontology with a finite ABox into a Sentential Decision Diagram (SDD), saturating a propositional core and instantiating remaining DL features over the active domain. The resulting evidence‑conditioned weighted model count trains a perception network to recognize real images under partial ABox supervision, enabling a CNN to recover latent ontology concepts that an independent perception would miss. When supervision allows multiple ontology‑consistent completions, Baobab’s mixture indexed by query justifications represents the calibrated posterior, achieving Bayes‑optimal performance on a real‑image MNIST task where single‑WMC and learned mixtures fail, thereby characterizing and mitigating reasoning shortcuts in a non‑Horn description logic.
By Olga Mashkova, Asaad Mohammedsaleh, Fernando Zhapa-Camacho, Robert Hoehndorf
arXiv:2602. 03970v3 Announce Type: replace-cross Abstract: We study the statistical behavior of reasoning probes in a stylized model of iterative computation inspired by neural algorithmic reasoning.
By Anastasis Kratsios, Giulia Livieri, A. Martina Neuman
The paper introduces a flexible symbolic framework that efficiently computes logical explanations for deep neural networks by parameterizing explanations with internal neuron activations and leveraging general-purpose logical engines like SMT solvers. Unlike previous methods that rely on specialized verifiers or are limited to individual input features, this approach is not restricted in shape and can scale to deep architectures. Experiments on image recognition and medical benchmarks demonstrate improved computational efficiency and the ability to explain networks that were previously intractable for logic-based methods.
By Tom\'a\v{s} Kol\'arik, Faezeh Labbaf, Fabrizio Leopardi, Grigory Fedyukovich, Michael Wand, Natasha Sharygina
arXiv:2602. 07400v2 Announce Type: replace Abstract: Gradient-based LUT- and logic-gate-based neural networks (LUTNet, LogicNets, DiffLogic, PolyLUT, NeuraLUT, WARP-LUT, DWN, LILogicNet, LightLUT) replace multiply-accumulate arithmetic with Boolean lookups.
By Simon B\"uhrer, Andreas Plesner, Aczel Till, Roger Wattenhofer
arXiv:2609.13636v1 Announce Type: cross
Abstract: Privacy-preserving inference via Torus Fully Homomorphic Encryption (TFHE) provides strong protection for sensitive data in outsourced deep learning...
By Mahmoud Y. M. Yassin, Mahmoud AbdelHafeez Sayed, Mostafa Taha
arXiv:2605. 20919v3 Announce Type: replace-cross Abstract: Sutra is a typed, purely functional programming language whose compiled forward pass is a PyTorch neural network.
By Emma Leonhart
arXiv:2608. 11136v1 Announce Type: new Abstract: Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning.
By Davide Rinaldi, Luciano Serafini