CLOSER-VLN: Closed-Loop Self-Verified Retrieval-Augmented Reasoning for Aerial Vision-Language Navigation

Vision-language navigation (VLN) has recently advanced with large language and multimodal models, enabling agents to follow natural-language instructions in unseen environments without training a task-specific navigation policy. However, most existing VLN methods relying on large models still adopt an open-loop decision-execution approach, where candidate actions are generated from instructions and observations but are rarely verified or corrected before execution. This causes critical issues in aerial VLN, where minor errors in intermediate actions may quickly accumulate into large trajectory deviations and lead to target loss. To address this issue, we propose Closed-loop Self-verified Retrieval-augmented Reasoning (CLOSER), a training-policy-free method that sequentially performs action reasoning, reliability verification, targeted retrieval, and action correction in a closed-loop manner before executing concrete actions. We instantiate the CLOSER in aerial VLN tasks and develop a CLOSER-VLN framework, which is composed of three components: a hierarchical reasoner for generating candidate actions based on available information, a multidimensional action verifier for assessing the reliability of actions generated by the reasoner, and a verification-triggered multimodal retriever for retrieving targeted exemplars from a memory bank only when verification fails. We conduct experimental evaluations on the CityNav benchmark, where CLOSER-VLN achieves 32.01% SR and 21.28% SPL on the test-unseen split, confirming the effectiveness of closed-loop reasoning.

TheoremGraph: Bridging Formal and Informal Mathematics

Mathematical knowledge is organized around statements and their dependencies, but this structure is exposed unevenly: informal papers cite mostly at the document level, while formal libraries record fine-grained dependencies over a much smaller body of mathematics. We introduce TheoremGraph, a unified statement-level dependency graph spanning both informal and formal mathematics. On the informal side, we parse 11.7M theorem-like environments from mathematics arXiv and recover 18.3M candidate directed dependencies, each labeled by the extractor that proposed it so downstream users can trade coverage for precision. On the formal side, we release LeanGraph, a Lean 4 elaborator-level extractor producing 388,105 declaration nodes and 11.3M typed edges across 25 Lean projects. We bridge the two graphs by embedding generated natural-language slogans into a shared semantic space, linking related statements across papers and across the informal/formal divide; an LLM judge affirms 47,952 such matches above a 0.8 cosine floor, with the judge-acceptance rate rising from 48% across the floor to 87% in the >=0.9 tier. On formal concept retrieval, our name-and-signature representation with graph expansion comes within 0.5pp of LeanSearch v2's reranked Recall@10 (0.775 vs. 0.780) without an LM reranker. We release the dataset, extractors, HTTP API, and MCP interface as infrastructure for mathematical search, attribution, and retrieval-augmented reasoning, available at theoremsearch.com and huggingface.co/datasets/uw-math-ai/theorem-matching.

From Verdict to Process: Agentic Reinforcement Learning for Multi-Stage Fact Verification

Recent approaches combining Large Language Models (LLMs) with retrieval-augmented reasoning have shown promise for automated fact verification. To process complex claims, these verification pipelines typically execute multi-stage workflows that coordinate tightly coupled modules, including claim decomposition, evidence gathering, and verdict prediction. However, existing methods optimize individual stages in isolation or rely on fixed heuristics, which limits adaptive coordination among stages and can lead to suboptimal outcomes. In this work, we propose ProFact, an agentic reinforcement learning framework for end-to-end optimization of multi-stage fact verification trajectories. ProFact trains a unified policy to coordinate claim decomposition, evidence seeking, answer generation, and verdict prediction. To address the sparse and delayed supervision provided by final veracity labels, ProFact introduces process-aware rewards that provide stage-level learning signals throughout the verification process. Empirical evaluation shows that ProFact consistently outperforms strong baselines in both verification performance and inference efficiency. These results highlight the effectiveness of process-aware trajectory optimization for multi-stage fact verification.