arXiv:2603.22362v1 Announce Type: cross Abstract: Full-waveform inversion (FWI) estimates physical parameters in the wave equation from limited measurements and has been widely applied in geophysical exploration, medical imaging, and non-destructive testing. Conventional FWI methods are limited by their notorious sensitivity to the accuracy of the initial models. Recent progress in continuous representation FWI (CR-FWI) demonstrates that representing parameter models with a coordinate-based neural network, such as implicit neural representation (INR), can mitigate the dependence on initial models. However, its underlying mechanism remains unclear, and INR-based FWI shows slower high-frequency convergence. In this work, we investigate the general CR-FWI framework and develop a unified theoretical understanding by extending the neural tangent kernel (NTK) for FWI to establish a wave-based NTK framework. Unlike standard NTK, our analysis reveals that wave-based NTK is not constant, both at initialization and during training, due to the inherent nonlinearity of FWI. We further show that the eigenvalue decay behavior of the wave-based NTK can explain why CR-FWI alleviates the dependency on initial models and shows slower high-frequency convergence. Building on these insights, we propose several CR-FWI methods with tailored eigenvalue decay properties for FWI, including a novel hybrid representation combining INR and multi-resolution grid (termed IG-FWI) that achieves a more balanced trade-off between robustness and high-frequency convergence rate. Applications in geophysical exploration on Marmousi, 2D SEG/EAGE Salt and Overthrust, 2004 BP model, and the more realistic 2014 Chevron models show the superior performance of our proposed methods compared to conventional FWI and existing INR-based FWI methods.

arXiv:2602.02050v3 Announce Type: replace Abstract: Tool-using agents based on Large Language Models (LLMs) excel in tasks such as mathematical reasoning and multi-hop question answering. However, in long trajectories, agents often trigger excessive and low-quality tool calls, increasing latency and degrading inference performance, making managing tool-use behavior challenging. In this work, we conduct entropy-based pilot experiments and observe a strong positive correlation between entropy reduction and high-quality tool calls. Building on this finding, we propose using entropy reduction as a supervisory signal and design two reward strategies to address the differing needs of optimizing tool-use behavior. Sparse outcome rewards provide coarse, trajectory-level guidance to improve efficiency, while dense process rewards offer fine-grained supervision to enhance performance. Experiments across diverse domains show that both reward designs improve tool-use behavior: the former reduces tool calls by 72.07% compared to the average of baselines, while the latter improves performance by 22.27%. These results position entropy reduction as a key mechanism for enhancing tool-use behavior, enabling agents to be more adaptive in real-world applications.

arXiv:2512.03454v3 Announce Type: replace-cross Abstract: Interpreting natural-language commands to localize target objects is critical for autonomous driving (AD). Existing visual grounding (VG) methods for autonomous vehicles (AVs) typically struggle with ambiguous, context-dependent instructions, as they lack reasoning over 3D spatial relations and anticipated scene evolution. Grounded in the principles of world models, we propose ThinkDeeper, a framework that reasons about future spatial states before making grounding decisions. At its core is a Spatial-Aware World Model (SA-WM) that learns to reason ahead by distilling the current scene into a command-aware latent state and rolling out a sequence of future latent states, providing forward-looking cues for disambiguation. Complementing this, a hypergraph-guided decoder then hierarchically fuses these states with the multimodal input, capturing higher-order spatial dependencies for robust localization. In addition, we present DrivePilot, a multi-source VG dataset in AD, featuring semantic annotations generated by a Retrieval-Augmented Generation (RAG) and Chain-of-Thought (CoT)-prompted LLM pipeline. Extensive evaluations on six benchmarks, ThinkDeeper ranks #1 on the Talk2Car leaderboard and surpasses state-of-the-art baselines on DrivePilot, MoCAD, and RefCOCO/+/g benchmarks. Notably, it shows strong robustness and efficiency in challenging scenes (long-text, multi-agent, ambiguity) and retains superior performance even when trained on 50% of the data.