arXiv:2510.09782v2 Announce Type: replace Abstract: We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our findings indicate that training solely via next-token prediction can lead LLMs to internalize logical invariants as higher-order geometry in representation space, challenging the ``stochastic parrot'' argument. Experiments across Qwen and LLaMA model families further suggest the presence of a general, possibly universal, representational law underlying machine understanding and human linguistic regularities, largely independent of specific training recipes or model architectures. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomena, offering a new lens for interpretability and formal analysis of LLMs' behavior.

arXiv:2602.07801v2 Announce Type: replace-cross Abstract: In long-video understanding, conventional uniform frame sampling often fails to capture key visual evidence, leading to degraded performance and increased hallucinations. To address this, recent agentic thinking-with-videos paradigms have emerged, adopting a localize-clip-answer pipeline in which the model actively identifies relevant video segments, performs dense sampling within those clips, and then produces answers. However, existing methods remain inefficient, suffer from weak localization, and adhere to rigid workflows. To solve these issues, we propose VideoTemp-o3, a unified agentic thinking-with-videos framework that jointly models video grounding and question answering. VideoTemp-o3 exhibits strong localization capability, supports on-demand clipping, and can refine inaccurate localizations. Specifically, in the supervised fine-tuning stage, we design a unified masking mechanism that encourages exploration while preventing noise. For reinforcement learning, we introduce dedicated rewards to mitigate reward hacking. Besides, from the data perspective, we develop an effective pipeline to construct high-quality long video grounded QA data, along with a corresponding benchmark for systematic evaluation across various video durations. Experimental results demonstrate that our method achieves remarkable performance on both long video understanding and grounding.