arXiv:2608. 05015v1 Announce Type: cross Abstract: Representation theorems in decision theory establish that behavior satisfies certain axioms if and only if it can be rationalized by a well-defined objective.
arXiv:2606. 28572v1 Announce Type: cross Abstract: The axiom of choice has divided the foundations of mathematics for over a century, but the distinction between classical and constructive proofs has remained a philosophical and methodological one.
arXiv:2606. 00291v1 Announce Type: cross Abstract: In RLHF, each training example contains a prompt $x$ and two candidate responses $y,y'$, and annotators provide pairwise preferences between these responses.
arXiv:2606. 14688v1 Announce Type: cross Abstract: AI systems coupled to proof assistants now generate formal mathematics at scale, and the gap between what a checker can verify and what a mathematician would value has become the binding constraint.
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:2606. 22974v2 Announce Type: replace Abstract: Recent work on preference elicitation in large language models (LLMs) has demonstrated that, when given a series of choices between two outcomes, LLMs reveal a coherent, model-specific utility structure.
arXiv:2306.00636v3 Announce Type: replace-cross Abstract: Many fairness criteria constrain the policy or choice of predictors, which can have unwanted consequences, in particular, when optimizing the...
The paper investigates how an informed adversary can influence the optimal signal in a constrained signalling channel. It finds that the adversary‑robust optimum aligns with the salience pole on most items, differing only on a small subset where the salience‑to‑Bayes coordinate is undefined. The study demonstrates that as the adversary’s persuasion budget increases, the optimal signal shifts from a posterior‑maximizing to a margin‑maximizing strategy, and provides a diagnostic check for evaluating adversary‑awareness.
The paper introduces GUARD, a neuro‑symbolic system that autoformalizes argumentative material by completing missing premises (guards) before formal verification. It uses large language models to generate candidate guards, Isabelle/HOL to verify them, and a contrastive test to ensure the proof depends on the original premises and does not over‑generalize. Experiments on Debatepedia and ARCT show that GUARD improves verified‑faithful scores by over 30 points and reduces leakage by about 20 points compared to prior LLM‑driven theorem proving methods.
The paper introduces a decision‑theoretic framework that elicits both probability judgments and decisions from large language models (LLMs) to test whether their reported beliefs are consistent with their actions. It shows that this framework yields empirically testable conditions without assuming a specific utility function. In clinical diagnosis simulations, the authors find that while LLMs’ reported beliefs are not perfect reflections of the information in their decisions, the discrepancies are small for the strongest models.
arXiv:2603. 05175v2 Announce Type: replace Abstract: The rapid proliferation of AI applications has intensified debate on effective regulation of these black-box services.
arXiv:2608. 11243v1 Announce Type: new Abstract: We argue that a single structural fact organizes a wide range of phenomena in contemporary AI safety: a semantic safety constraint (e.
arXiv:2606. 28639v2 Announce Type: replace-cross Abstract: We establish the mathematical limits of AGI safety in two forms: verifying a fixed system, and verifying that a certified safety property persists once the system self-modifies.