arXiv:2410.16431v3 Announce Type: replace Abstract: The semantic similarity between sample expressions measures the distance between their latent 'meaning'. These meanings are themselves typically represented by textual expressions. We propose a novel approach whereby the semantic similarity among textual expressions is based not on other expressions they can be rephrased as, but rather based on the imagery they evoke. While this is not possible with humans, generative models allow us to easily visualize and compare generated images, or their distribution, evoked by a textual prompt. Therefore, we characterize the semantic similarity between two textual expressions simply as the distance between image distributions they induce, or 'conjure.' We show that by choosing the Jeffreys divergence between the reverse-time diffusion stochastic differential equations (SDEs) induced by each textual expression, this can be directly computed via Monte-Carlo sampling. Our method contributes a novel perspective on semantic similarity that not only aligns with human-annotated scores, but also opens up new avenues for the evaluation of text-conditioned generative models while offering better interpretability of their learnt representations.

arXiv:2510.12066v2 Announce Type: replace Abstract: We describe AI agents as stochastic dynamical systems and frame the problem of learning to reason as in transductive inference: Rather than approximating the distribution of past data as in classical induction, the objective is to capture its algorithmic structure so as to reduce the time needed to solve new tasks. In this view, information from past experience serves not only to reduce a model's uncertainty - as in Shannon's classical theory - but to reduce the computational effort required to find solutions to unforeseen tasks. Working in the verifiable setting, where a checker or reward function is available, we establish three main results. First, we show that the optimal speed-up on a new task is tightly related to the algorithmic information it shares with the training data, yielding a theoretical justification for the power-law scaling empirically observed in reasoning models. Second, while the compression view of learning, rooted in Occam's Razor, favors simplicity, we show that transductive inference yields its greatest benefits precisely when the data-generating mechanism is most complex. Third, we identify a possible failure mode of naive scaling: in the limit of unbounded model size and compute, models with access to a reward signal can behave as savants - brute-forcing solutions without acquiring transferable reasoning strategies. Accordingly, we argue that a critical quantity to optimize when scaling reasoning models is time, whose role in learning has remained largely unexplored.

arXiv:2511.07833v2 Announce Type: replace-cross Abstract: Reinforcement Learning with Verifiable Rewards(RLVR) has emerged as a powerful framework for enhancing the reasoning capabilities of large language models (LLMs). However, existing approaches such as Group Relative Policy Optimization (GRPO) and its variants, while effective on reasoning benchmarks, struggle with agentic tasks that require iterative decision-making. We introduce MURPHY, a multi-turn RLVR framework that incorporates execution feedback directly into training, extending GRPO to optimize over multi-turn trajectories where models iteratively refine solutions. MURPHY combines a feedback conditioned rollout tree with trajectory-level credit assignment, and uses pruning to reduce the cost of multi-turn optimization. Evaluations on code generation benchmarks with two model families show that MURPHY consistently improves multi-iteration performance, achieving up to an 8% absolute gain in pass@1 over compute-matched GRPO baselines, and outperforming the prior leading method that incorporates multi-turn execution feedback.