Purging the Gray Zone: Latent-Geometric Denoising for Precise Knowledge Boundary Awareness

Large language models (LLMs) often exhibit hallucinations due to their inability to accurately perceive their own knowledge boundaries. Existing abstention fine-tuning methods typically partition datasets directly based on response accuracy, causing models to suffer from severe label noise near the decision boundaries and consequently exhibit high rates of abstentions or hallucinations. This paper adopts a latent space representation perspective, revealing a "gray zone" near the decision hyperplane where internal belief ambiguity constitutes the core performance bottleneck. Based on this insight, we propose the **GeoDe** (**Geo**metric **De**noising) framework for abstention fine-tuning. This method constructs a truth hyperplane using linear probes and performs "geometric denoising" by employing geometric distance as a confidence signal for abstention decisions. This approach filters out ambiguous boundary samples while retaining high-fidelity signals for fine-tuning. Experiments across multiple models (Llama3, Qwen3) and benchmark datasets (TriviaQA, NQ, SciQ, SimpleQA) demonstrate that GeoDe significantly enhances model truthfulness and demonstrates strong generalization in out-of-distribution (OOD) scenarios. Code is available at https://github.com/Notbesidemoon/GeoDe.

Thinking in Dynamics: How Multimodal Large Language Models Perceive, Track, and Reason Dynamics in Physical 4D World

Humans inhabit a physical 4D world where geometric structure and semantic content evolve over time, constituting a dynamic 4D reality (spatial with temporal dimension). While current Multimodal Large Language Models (MLLMs) excel in static visual understanding, can they also be adept at "thinking in dynamics", i.e., perceive, track and reason about spatio-temporal dynamics in evolving scenes? To systematically assess their spatio-temporal reasoning and localized dynamics perception capabilities, we introduce Dyn-Bench, a large-scale benchmark built from diverse real-world and synthetic video datasets, enabling robust and scalable evaluation of spatio-temporal understanding. Through multi-stage filtering from massive 2D and 4D data sources, Dyn-Bench provides a high-quality collection of dynamic scenes, comprising 1k videos, 7k visual question answering (VQA) pairs, and 3k dynamic object grounding pairs. We probe general, spatial and region-level MLLMs to express how they think in dynamics both linguistically and visually, and find that existing models cannot simultaneously maintain strong performance in both spatio-temporal reasoning and dynamic object grounding, often producing inconsistent interpretations of motion and interaction. Notably, conventional prompting strategies (e.g., chain-of-thought or caption-based hints) provide limited improvement, whereas structured integration approaches, including Mask-Guided Fusion and Spatio-Temporal Textual Cognitive Map (ST-TCM), significantly enhance MLLMs' dynamics perception and spatio-temporal reasoning in the physical 4D world. Code and benchmark are available at https://dyn-bench.github.io/.