arXiv:2608.31120v1 Announce Type: new
Abstract: The motivation for this paper is the investigation of the trade-offs implicit in probabilistic models used in machine learning. Models are often used t...
By Guy Emerson
arXiv:2607. 13073v1 Announce Type: new Abstract: Neuro-symbolic AI based on $IFOL_B$ is a way to combine neural learning and symbolic reasoning to overcome limitations of purely neural systems (like lack of interpretability and logical structure) with formal logical machinery for self-reference.
By Zoran Majkic
arXiv:2606. 00102v1 Announce Type: new Abstract: Over the centuries, probability theory has grown from the calculus of games of chance into a central framework for reasoning under uncertainty.
By Jean-Louis Le Mou\"el, Vincent Courtillot, Dominique Gibert, Vladimir Kossobokov, Jean-Baptiste Boul\'e, Pierpaolo Zuddas, Fernando Lopes, Pa\"ikan Marccagi, Alexis Maineult
arXiv:2608. 12325v1 Announce Type: new Abstract: Autonomous reasoning is among the most scientifically and economically motivating topics in AI today.
By Rachel Lawrence, Jacqueline Maasch
The paper introduces a new Monte Carlo algorithm for approximate counting of Disjunctive Normal Form (DNF) formulas, featuring an adaptive stopping rule and short‑circuit evaluation. It achieves PAC learning bounds and is asymptotically more efficient than existing methods, including classical Monte Carlo, hashing‑based, and neural‑network approaches. Experiments demonstrate that the algorithm outperforms prior techniques by orders of magnitude and scales to problems with millions of variables.
By Paul Burkhardt, David G. Harris, Kevin T Schmitt
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