The paper presents an interactive probabilistically checkable proof (PCP) protocol that allows a polynomial‑time verifier to check the approximate consistency of a probabilistic predictor defined by two circuits, P and Q. By evaluating these circuits at a few points and querying a proof oracle that encodes a witnessing probability distribution, the verifier can confirm that the predictor’s many conditional‑probability claims are self‑consistent. The authors also establish that the problem of verifying l₂‑approximate consistency for explicit probabilistic claims lies in NP, with certificates of size O(mn + log B), and show how to eliminate dependence on the input bit‑precision B through a small additive gap.
By Orr Paradise, Oliver Richardson, Yoshua Bengio, Shafi Goldwasser
arXiv:2608. 16565v1 Announce Type: new Abstract: This cumulative habilitation thesis studies probabilistic circuits (PCs) as a powerful and tractable framework for reasoning and learning under uncertainty in artificial intelligence (AI).
By Robert Peharz
arXiv:2608. 11181v1 Announce Type: cross Abstract: When a probabilistic predictor answers many conditional-probability queries, are its answers self-consistent, and can this be verified in polynomial time?
By Orr Paradise, Oliver Richardson, Yoshua Bengio, Shafi Goldwasser
arXiv:2609. 19077v1 Announce Type: cross Abstract: Formal explainability provides mathematically grounded justifications for individual predictions.
By Frederic Koriche, Jean-Marie Lagniez, Chi Tran
arXiv:2607. 06407v1 Announce Type: new Abstract: The XAI community has studied a wide range of queries and scores for explaining predictions of ML models.
By Marcelo Arenas, Pablo Barcel\'o, Diego Bustamante, Jose Caraball, Mar\'ia Alejandra Schild, Bernardo Subercaseaux
arXiv:2603. 25414v4 Announce Type: replace-cross Abstract: A prevailing assumption in machine learning is that model correctness must be enforced after the fact.
By Houston Haynes
arXiv:2602. 00511v3 Announce Type: replace Abstract: We introduce \emph{Partition of Unity Neural Networks} (PUNNs), a neural-network architecture for multiclass classification based on the classical mathematical notion of a partition of unity.
By Akram Aldroubi
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. 19366v1 Announce Type: cross Abstract: Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain.
By Haizi Yu, Lav R. Varshney
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
arXiv:2608. 13018v1 Announce Type: new Abstract: Standard probabilistic logic programming frameworks typically rely on grounding logic programs into discrete propositional representations.
By Costin B\u{a}dic\u{a}, Amelia B\u{a}dic\u{a}
arXiv:2608. 09117v1 Announce Type: new Abstract: Probabilistic Circuits (PCs) are tractable generative models whose internal nodes encode a hierarchy of probabilistic sum- maries over different variable scopes.
By Bhumika K, Vidhya S, Narayanan C Krishnan