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
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. 31845v1 Announce Type: cross Abstract: A transformer's feed-forward (FFN) sublayer materializes the distinctions attention gathers, yet gives no account of what it computes.
By Mark Oskin
The paper introduces DODR, a deterministic operator‑driven reasoning architecture that models reasoning as graph computations in a high‑dimensional linear‑algebraic space, replacing token‑level sampling with matrix operations. Reasoning states are snapshot vectors of semantic units, and three trainable matrix operators—deduction, induction, and abduction—implement Peirce’s inference types. Experiments on 503 records demonstrate near‑perfect deduction, high generalization for induction, and significant gains for abduction, while the design guarantees zero hallucination and supports continual learning.
By Weicai Huang (Beijing MQPat Technologies, Co., Ltd.)
The paper argues that Large Language Models (LLMs) do not function as Solomonoff induction estimators because their training objectives—cross‑entropy, negative log‑likelihood, and next‑token prediction—optimize fit to a supplied conditional distribution rather than a program‑weighted universal mixture. It further contends that additional computation alone does not transform these models into optimal predictors without external hyper‑parameter or architectural changes. The authors suggest that neurosymbolic machine learning, exemplified by models such as Fable and Astra, represents a shift toward symbolic model synthesis, moving beyond purely statistical LLMs.
By Hector Zenil, Abicumaran Uthamacumaran, Luan Ozelim
Whether large language models perform genuine algorithmic reasoning or mere pattern completion is hard to test, because most benchmarks lack a ground truth for correct inductive inference. We introduce F-ICL, an in-context-learning benchmark that supplies one exactly.
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:2608. 01575v1 Announce Type: new Abstract: Whether large language models perform genuine algorithmic reasoning or mere pattern completion is hard to test, because most benchmarks lack a ground truth for correct inductive inference.
By Hector Zenil, Luan Ozelim
arXiv:2607. 15107v1 Announce Type: new Abstract: This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor through quotient sketches lifted to the tangent category setting.
By Sridhar Mahadevan
arXiv:2601.05280v4 Announce Type: replace-cross
Abstract: On the one hand, the question of whether Large Language Models (LLMs) are Solomonoff induction estimators has become an explicit question at...
By Hector Zenil, Abicumaran Uthamacumaran, Luan Ozelim
arXiv:2608. 10420v1 Announce Type: new Abstract: Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts.
By Xin Xu
arXiv:2606. 17886v1 Announce Type: new Abstract: Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs.
By Mikhail Krasnov, Carolina Fortuna, Bla\v{z} Bertalani\v{c}