Navigating the Conceptual Multiverse

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Existing approaches either require expensive labelled supervision with inconsistent cross-task performance or aggregate scores from multiple sources by simple aggregations, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We formalise this as a coupled scoring problem among disparate, frozen verifiers, interpretable as a coordination game with a unique closed-form equilibrium where agreement signals valid steps while disagreement reveals instability. Towards this end, we propose a training-free domain-agnostic step-wise verification approach we call VERDICT: VERification via Disagreement-Informed Coupled Thresholding. To our knowledge, VERDICT is the first training-free verifier that makes the structure of cross-modal disagreement explicit and actionable. It computes consensus scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, \method consistently improves over the base model by up to +5.95%, and performs competitively with domain-specific critics that demand extensive supervision, demonstrating that cross-modal agreement provides robust verification signals without task-specific adaptation and Training-Free Verification

Large language models have improved rapidly on tasks with verifiable answers, such as mathematics and programming. Much less is known about their ability to reason about what we call conceptual questions: questions for which no ground truth is realistically accessible and no widely accepted resolution methodology exists, but on which progress can still be made by debating arguments. Most philosophical questions are of this kind, as are central components of questions in AI safety, decision theory, and social choice. Our approach is based on the view that while bottom-line conclusions on such questions are hard to evaluate, individual contextualized arguments can be evaluated far more reliably. We therefore introduce a dataset of 951 argumentative critiques of 442 position texts, spanning topics from AI safety and decision theory to ethics and politics, with 1,458 ratings by six expert raters along dimensions including centrality, strength, correctness, and clarity. We propose two scoring functions and benchmark a range of models. Performance tracks general capability rankings.

Large language models increasingly tackle hard reasoning problems by spending more test-time compute, yet the dominant strategy remains naive repeated sampling: draw many independent solutions and hope one is correct. Because such sampling explores only through local decoding noise, it tends to produce many near duplicate attempts rather than genuinely different ideas. We ask whether exploration can instead be steered at a semantic level, by first sampling problem specific concepts, hints, or strategies and then conditioning answer generation on them. We refine this into a simple, more exploratory procedure that emits many diverse concepts in a single trajectory, and evaluate it on hard problems where repeated sampling struggles. We then go a step further and make concept generation trainable: a small concept generator is optimized with reinforcement learning so that its concepts maximize the downstream success of a larger, frozen answer generator. On hard mathematical reasoning problems, the trained concept generator substantially improves the answer generator's pass@k over naive repeated sampling at the same answer generation allocation, surpasses concepts drawn from much larger untuned models, and transfers to answer generators it was never trained against, including a model from a different family. A small model can thus be trained into an effective, reusable search policy for a much larger one.