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.
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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).
arXiv:2609.09855v1 Announce Type: new Abstract: Although probabilistic statements are ubiquitous, foundational disagreements persist about their understanding, as exemplified by debates between Bayes...
arXiv:2607. 04505v1 Announce Type: new Abstract: We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction.
arXiv:2501. 05844v4 Announce Type: replace Abstract: Causal Learning has emerged as a major theme of research in statistics and machine learning in recent years, promising computational techniques to reveal ``true'' causality.
We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction. The most prolific reservoir of such patterns is the natural world, whose physical laws and biological systems have undergone billions of years of ``pre-computation'' and already exhibit surprisingly innovative solutions.
The paper introduces a computational model that encodes symbolic knowledge as mental programs combining natural language and source code, and uses LLM-guided Bayesian learning to sequentially infer these programs. It demonstrates that this approach satisfies data‑efficiency, uncertainty handling, and flexibility, reproducing human inductive learning and active inquiry behaviors such as anchoring and garden‑pathing. In contrast, pure LLMs and classic Bayesian models either fail the task, do not match human behavior, or require prohibitive computational resources.