arXiv:2603.04277v1 Announce Type: cross Abstract: Autonomous aerial robots operating in GPS-denied or communication-degraded environments frequently lose access to camera metadata and telemetry, leaving onboard perception systems unable to recover the absolute metric scale of the scene. As LLM/VLM-based planners are increasingly adopted as high-level agents for embodied systems, their ability to reason about physical dimensions becomes safety-critical -- yet our experiments show that five state-of-the-art VLMs suffer from spatial scale hallucinations, with median area estimation errors exceeding 50%. We propose VANGUARD, a lightweight, deterministic Geometric Perception Skill designed as a callable tool that any LLM-based agent can invoke to recover Ground Sample Distance (GSD) from ubiquitous environmental anchors: small vehicles detected via oriented bounding boxes, whose modal pixel length is robustly estimated through kernel density estimation and converted to GSD using a pre-calibrated reference length. The tool returns both a GSD estimate and a composite confidence score, enabling the calling agent to autonomously decide whether to trust the measurement or fall back to alternative strategies. On the DOTA~v1.5 benchmark, VANGUARD achieves 6.87% median GSD error on 306~images. Integrated with SAM-based segmentation for downstream area measurement, the pipeline yields 19.7% median error on a 100-entry benchmark -- with 2.6x lower category dependence and 4x fewer catastrophic failures than the best VLM baseline -- demonstrating that equipping agents with deterministic geometric tools is essential for safe autonomous spatial reasoning.

arXiv:2602.13498v1 Announce Type: cross Abstract: Muon-style optimizers leverage Newton-Schulz (NS) iterations to orthogonalize updates, yielding update geometries that often outperform Adam-series methods. However, this orthogonalization discards magnitude information, rendering training sensitive to step-size hyperparameters and vulnerable to high-energy bursts. To mitigate this, we introduce TrasMuon (\textbf{T}rust \textbf{R}egion \textbf{A}daptive \textbf{S}caling \textbf{Muon}). TrasMuon preserves the near-isometric geometry of Muon while stabilizing magnitudes through (i) global RMS calibration and (ii) energy-based trust-region clipping. We demonstrate that while reintroducing adaptive scaling improves optimization efficiency, it typically exacerbates instability due to high-energy outliers. TrasMuon addresses this by defining a trust region based on relative energy ratios, confining updates to a stable zone. Empirical experiments on vision and language models demonstrate that TrasMuon converges faster than baselines. Furthermore, experiments without warmup stages confirm TrasMuon's superior stability and robustness.

arXiv:2410.15756v3 Announce Type: replace-cross Abstract: Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation. The primary obstacle lies in the severe lack of data-there is much fewer proofs than code snippets for Large Language Models (LLMs) to train upon. In this paper, we introduce SAFE, a framework that overcomes the lack of human-written proofs to enable automated proof generation of Rust code. SAFE establishes a self-evolving cycle where data synthesis and fine-tuning collaborate to enhance the model capability, leveraging the definitive power of a symbolic verifier in telling correct proofs from incorrect ones. SAFE also re-purposes the large number of synthesized incorrect proofs to train the self-debugging capability of the fine-tuned models, empowering them to fix incorrect proofs based on the verifier's feedback. SAFE demonstrates superior efficiency and precision compared to GPT-4o. Through tens of thousands of synthesized proofs and the self-debugging mechanism, we improve the capability of open-source models, initially unacquainted with formal verification, to automatically write proofs for Rust code. This advancement leads to a significant improvement in performance, achieving a 52.52% accuracy rate in a benchmark crafted by human experts, a significant leap over GPT-4o's performance of 14.39%.