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Junsheng Wang, Tiantian Gong, Yeyun Wu, Liyan Zhang 0001

Domain-adaptive hashing enhances discriminative hash representations by transferring knowledge from a label-rich source domain to a label-scarce target domain. It has attracted significant attention due to its ability to enable efficient cross-domain retrieval without requiring target domain labels. However, existing methods generally assume that source domain labels are completely accurate. In practice, labels obtained via web crawling or crowdsourcing often contain varying degrees of noise, which hampers semantic alignment and aggravates domain shift. To tackle these issues, we propose a novel method termed Evidential Learning and Progressive Alignment (ELPA) for domain-adaptive hashing. This method comprises two key modules: the Uncertainty-aware Noise Separation (UNS) and the Progressive Cross-domain Alignment (PCA). In the UNS, we exploit the belief and uncertainty masses obtained from the evidential learning model and utilize the posterior probabilities of a Gaussian Mixture Model to effectively distinguish clean samples from noisy ones. In PCA, we introduce a progressive partial optimal transport mechanism that prioritizes pseudo-label generation for well-aligned target samples, thereby gradually achieving class-level and global-level cross-domain alignment. Extensive experiments across multiple benchmark datasets with various noise ratios demonstrate that ELPA consistently surpasses existing state-of-the-art methods, exhibiting superior robustness and generalization capability.

Xiaoxi Li 0005, Wenxiang Jiao, Jiarui Jin, Guanting Dong 0001, Jiajie Jin, Yinuo Wang, Hao Wang 0049, Yutao Zhu 0001, Ji-Rong Wen, Yuan Lu 等

Large reasoning models have demonstrated strong problem-solving abilities, yet real-world tasks often require external tools and long-horizon interactions. Existing agent frameworks typically follow predefined workflows, which limit autonomous and global task completion. In this paper, we introduce DeepAgent, an end-to-end deep reasoning agent that performs autonomous thinking, tool discovery, and action execution within a single, coherent reasoning process. To manage long-horizon interactions, we introduce an autonomous memory folding mechanism that compresses past interactions into structured episodic, working, and tool memories, reducing error accumulation while preserving critical information. To teach general-purpose tool use efficiently and stably, we develop an end-to-end reinforcement learning strategy, namely ToolPO, that leverages LLM-simulated APIs and applies tool-call advantage attribution to assign fine-grained credit to the tool invocation tokens. Extensive experiments on eight benchmarks, including general tool-use tasks (ToolBench, API-Bank, TMDB, Spotify, ToolHop) and downstream applications (ALFWorld, WebShop, GAIA, HLE), demonstrate that DeepAgent consistently outperforms baselines across both labeled-tool and open-set tool retrieval scenarios. The code and demo are available at https://github.com/RUC-NLPIR/DeepAgent.

Jihao Zhao, Daixuan Li, Pengfei Li, Shuaishuai Zu, Biao Qin, Hongyan Liu 0002

The effectiveness upper bound of retrieval-augmented generation (RAG) is fundamentally constrained by the semantic integrity and information granularity of text chunks in its knowledge base. Moreover, domain documents are characterized by dense terminology and strong contextual dependencies, which exacerbate the semantic fragmentation of text chunks, thereby making it difficult to efficiently utilize their key information. To address these challenges, this paper proposes QChunker, which restructures the RAG paradigm from retrieval-augmentation to understanding-retrieval-augmentation. Firstly, QChunker models the text chunking as a composite task of text segmentation and knowledge completion to ensure the logical coherence and integrity of text chunks. Drawing inspiration from Hal Gregersen's ''Questions Are the Answer'' theory, we design a multi-agent debate framework comprising four specialized components: a question outline generator, text segmenter, integrity reviewer, and knowledge completer. This framework operates on the principle that questions serve as catalysts for profound insights. Through this pipeline, we successfully construct a high-quality dataset of 45K entries and transfer this capability to small language models. Additionally, to handle long evaluation chains and low efficiency in existing chunking evaluation methods, which overly rely on downstream QA tasks, we introduce a novel direct evaluation metric, ChunkScore. Both theoretical and experimental validations demonstrate that ChunkScore can directly and efficiently discriminate the quality of text chunks. Furthermore, during the text segmentation phase, we utilize document outlines for multi-path sampling to generate multiple candidate chunks and select the optimal solution employing ChunkScore. Extensive experimental results across four heterogeneous domains exhibit that QChunker effectively resolves aforementioned issues by providing RAG with more logically coherent and information-rich text chunks. Notably, this study also establishes a small-domain QA dataset concerning hazardous chemical safety, which fully reveals the significant value of RAG in specialized domains and the generalization capability of the QChunker framework.

Xingyuan Zeng, Zuohan Wu, Yue Wang 0012, Chen Zhang 0013, Quanming Yao, Libin Zheng 0001, Jian Yin 0001

Owing to their unprecedented comprehension capabilities, large language models (LLMs) have become indispensable components of modern web search engines. From a technical perspective, this integration represents retrieval-augmented generation (RAG), which enhances LLMs by grounding them in external knowledge base. A prevalent technical approach in this context is graph-based RAG (G-RAG). However, current G-RAG methodologies frequently underutilize graph topology, predominantly focusing on low-order structures or pre-computed static communities. This limitation affects their effectiveness in addressing dynamic and complex queries. Thus, we propose DA-RAG, which leverages attributed community search (ACS) to dynamically extract relevant subgraphs based on the queried question. DA-RAG captures high-order graph structures, allowing for the retrieval of self-complementary knowledge. Furthermore, DA-RAG is equipped with a chunk-layer oriented graph index, which facilitates efficient multi-granularity retrieval while significantly reducing both computational and economic costs. We evaluate DA-RAG on multiple datasets, demonstrating that it outperforms existing RAG methods by up to 40% in head-to-head comparisons across four metrics while reducing index construction time and token overhead by up to 37% and 41%, respectively.

Jin Cheng 0008, Xiangxiang Dai, Ningning Ding, John C. S. Lui, Jianwei Huang 0001

Proximity graphs are the state-of-the-art solution for approximate nearest neighbor (ANN) search, supporting applications such as Web search and retrieval-augmented generation (RAG). Sustaining long-term performance requires adaptive pruning as data and query workloads evolve. However, existing approaches are largely static and uniform. Adaptive pruning faces three key challenges: temporal drift in data and query distributions, spatial heterogeneity across graph regions, and costly feedback due to graph-level evaluations. We present BANCO, a bandit-based framework for adaptive proximity graph pruning. BANCO unifies diverse pruning strategies within a common decision space and optimizes them via a drift-aware batched bandit algorithm. It addresses temporal drift through drift-aware updates, captures spatial heterogeneity using contextual features for region-specific pruning, and reduces evaluation costs through batched feedback aggregation. We establish a dynamic regret bound with sublinear loss and polynomial computational complexity. Extensive experiments on four real-world datasets demonstrate that BANCO helps maintain long-term ANN search efficiency and accuracy under evolving data and workloads.

Jiasheng Xu, Mingda Li, Yongqiang Tang, Peijie Wang, Wensheng Zhang 0002

Large Language Models (LLMs) have demonstrated strong capabilities in web search and reasoning. However, their dependence on static training corpora makes them prone to factual errors and knowledge gaps. Retrieval-Augmented Generation (RAG) addresses this limitation by incorporating external knowledge sources, especially structured Knowledge Graphs (KGs), which provide explicit semantics and efficient retrieval. Existing KG-based RAG approaches, however, generally assume that anchor entities are accessible to initiate graph traversal, which limits their robustness in open-world settings where accurate linking between the user query and the KG entity is unreliable. To overcome this limitation, we propose AnchorRAG, a novel multi-agent collaboration framework for open-world RAG without the predefined anchor entities. Specifically, a predictor agent dynamically identifies candidate anchor entities by aligning user query terms with KG nodes and initializes independent retriever agents to conduct parallel multi-hop explorations from each candidate. Then a supervisor agent formulates the iterative retrieval strategy for these retriever agents and synthesizes the resulting knowledge paths to generate the final answer. This multi-agent collaboration framework improves retrieval robustness and mitigates the impact of ambiguous or erroneous anchors. Extensive experiments on four public benchmarks demonstrate that AnchorRAG significantly outperforms existing baselines and establishes new state-of-the-art results on the real-world reasoning tasks.

Senlei Zhang, Tongjun Shi, Dandan Song 0005, Luan Zhang, Shuhao Zhang 0001, Xiaofei Liao, Hai Jin 0001

Retrieval-Augmented Generation (RAG) enhances Large Language Models (LLMs) by leveraging external knowledge, where retrieval accuracy directly affects generation quality. However, dense retrievers, commonly employed in RAG, suffer degraded performance in evolving corpora where new documents arrive continuously and distribution shifts accumulate over time. In such settings, continually updating retrievers is crucial, yet conventional retraining is computationally expensive and often impractical. To address this challenge, we propose FlowRAG, a lightweight and effective method for continual retriever adaptation in evolving corpora. FlowRAG augments the encoder with Layer-wise Prompt Embeddings and introduces a Cross-Layer Fusion mechanism to capture hierarchical semantic representations. In addition, a novel Generator-Guided Loss aligns retriever scores and intermediate representations with the LLM's generation likelihoods, encouraging retrieval decisions that are both semantically relevant and beneficial for generation. Experiments on datasets spanning four domains demonstrate that FlowRAG, which updates only about 0.64% of the total model parameters, consistently outperforms strong baselines in retrieval accuracy, generation quality, and robustness to forgetting in non-stationary settings.

Yi Sun, Jinyu Xu 0001, Qing Xie 0002, Jiachen Li 0002, Yanchun Ma, Yongjian Liu

Composed Image Retrieval (CIR) aims to retrieve a target image from a query composed of a reference image and modification text. Recent training-free zero-shot methods often employ Multimodal Large Language Models (MLLMs) with Chain-of-Thought (CoT) to compose a target image description for retrieval. However, due to the fuzzy matching nature of ZS-CIR, the generated description is prone to semantic bias relative to the target image. We propose SDR-CIR, a training-free Semantic Debias Ranking method based on CoT reasoning. First, Selective CoT guides the MLLM to extract visual content relevant to the modification text during image understanding, thereby reducing visual noise at the source. We then introduce a Semantic Debias Ranking with two steps, Anchor and Debias, to mitigate semantic bias. In the Anchor step, we fuse reference image features with target description features to reinforce useful semantics and supplement omitted cues. In the Debias step, we explicitly model the visual semantic contribution of the reference image to the description and incorporate it into the similarity score as a penalty term. By supplementing omitted cues while suppressing redundancy, SDR-CIR mitigates semantic bias and improves retrieval performance. Experiments on three standard CIR benchmarks show that SDR-CIR achieves state-of-the-art results among one-stage methods while maintaining high efficiency. The code is publicly available at https://github.com/suny105/SDR-CIR.

Ruikun Luo, Zixiao Feng, Lin Gu 0002, Xiaoyu Xia 0001

Multimodal Retrieval-Augmented Generation (MM-RAG) extends the capabilities of Large Language Models (LLMs) by incorporating external image-text knowledge bases to handle various tasks. However, MM-RAG systems in open environments are highly vulnerable to retrieval poisoning attacks, i.e., adversaries can inject malicious image-text pairs that are retrieved and dominate the generation process, leading to incorrect or harmful outputs. Due to the unique challenges of image-text fusion and cross-modal interference, existing defenses for text-based RAG cannot be directly applied to multimodal scenarios. In this paper, we propose IRAG, the first robust defense framework specifically designed for MM-RAG. The core of IRAG lies in its hazard separation. This structured defense isolates potential contamination sources by leveraging redundancy and consensus, enhancing system robustness and ensuring reliable outputs even when portions of retrieved content are compromised. Extensive experiments conducted under the MMQA and WebQA and the BQI and ROTI poisoning schemes demonstrate that IRAG consistently restores system reliability: the normal answer accuracy improves by 15–30% (restoring it to pre-poisoning levels), while the poisoned answer rate is reduced to below 7%.

Guanting Dong 0001, Licheng Bao, Zhongyuan Wang 0006, Kangzhi Zhao, Xiaoxi Li 0005, Jiajie Jin, Jinghan Yang, Hangyu Mao, Fuzheng Zhang, Kun Gai 等

Recently, Agentic Reinforcement Learning (Agentic RL) has made significant progress in incentivizing the multi-turn, long-horizon tool-use capabilities of web agents. While mainstream agentic RL algorithms autonomously explore high-uncertainty tool-call steps under the guidance of entropy, excessive reliance on such signals leads to the training collapse. In this paper, we delve into the challenges caused by entropy and propose the Agentic Entropy-Balanced Policy Optimization (AEPO), an agentic RL algorithm designed to balance entropy in both the rollout and policy update phases. AEPO comprises two core components: (1) a dynamic entropy-balanced rollout mechanism that adaptively allocates global and branch sampling budget through entropy pre-monitoring, while imposing a branch penalty on consecutive high-entropy tool-call steps to prevent over-branching issues; and (2) Entropy-Balanced Policy Optimization that inserts a stop-gradient operation into the high-entropy clipping term to preserve and properly rescale gradients on high-entropy tokens, while incorporating entropy-aware advantage estimation to prioritize learning on high-uncertainty tokens. Results across 14 challenging datasets show that AEPO consistently outperforms 7 mainstream RL algorithms. Further analysis reveals that AEPO improves rollout sampling diversity while maintaining stable policy entropy, facilitating scalable training of general web agents. The code is available at https://github.com/RUC-NLPIR/ARPO.

Haiyan Wu, Chenchen Wang, Chaoqun Sun, Chengxiong Lu, Zhiqiang Zhang 0010, Yanhong Chen

Retrieval-Augmented Generation (RAG) effectively mitigates hallucinations and knowledge gaps in Large Language Models (LLMs) for knowledge-intensive tasks by incorporating external web-based knowledge. However, when integrating diverse yet potentially conflicting web-sourced information, RAG systems are prone to knowledge conflicts that manifest as incorrect or inconsistent model behaviors, ultimately leading to unreliable responses. To address this challenge, this paper proposes Conflict-Aware RAG, a general training framework that leverages the model's inherent conflict-sensing capability to build a more robust RAG system via phased optimization. At the core of this framework lies ConScore, a conflict signal that quantifies the model's awareness of potential knowledge conflicts by comparing generative probabilities across distinct knowledge sources. This signal then guides both the construction of training data and a multi-stage optimization workflow: In the Supervised Fine-Tuning (SFT) stage, conflict features are employed to select representative distracting documents, laying the groundwork for core RAG capabilities; in the Direct Preference Optimization (DPO) stage, high-quality preference pairs are constructed using the conflict signal to boost the model's robustness against distracting knowledge; and in the Reranking stage, conflict confidence and information gain are integrated to synergistically optimize the collaboration mechanism between the retriever and LLM. Experiments on six knowledge-intensive question answering (QA) datasets demonstrate that Conflict-Aware RAG significantly outperforms mainstream baselines. Further ablation studies and quantitative analyses validate the method's stability and generalization, laying the foundation for robust RAG systems.

Xuri Ge, Chunhao Wang, Xindi Wang 0001, Zheyun Qin, Zhumin Chen, Xin Xin 0003

Composed Image Retrieval (CIR) aims to retrieve target images based on a reference image and modified texts. However, existing methods often struggle to extract the correct semantic cues from the reference image that best reflect the user's intent under textual modification prompts, resulting in interference from irrelevant visual noise. In this paper, we propose a novel Multi-level Vision Selection by Multi-modal Chain-of-Thought Reasoning (MCoT-MVS) for CIR, integrating attention-aware multi-level vision features guided by reasoning cues from a multi-modal large language model (MLLM). Specifically, we leverage an MLLM to perform chain-of-thought reasoning on the multimodal composed input, generating the retained, removed, and target-inferred texts. These textual cues subsequently guide two reference visual attention selection modules to selectively extract discriminative patch-level and instance-level semantics from the reference image. Finally, to effectively fuse these multi-granular visual cues with the modified text and the imagined target description, we design a weighted hierarchical combination module to align the composed query with target images in a unified embedding space. Extensive experiments on two CIR benchmarks, namely CIRR and FashionIQ, demonstrate that our approach consistently outperforms existing methods and achieves new state-of-the-art performance. Code and trained models are publicly released at https://github.com/JJJJerry/WWW2026-MCoT-MVS.

Jun Yang, Yuhan Bai, Dandan Song 0005, Zhijing Wu 0001, Yuhang Tian 0002

The rapid spread of misinformation on social media has underscored the importance of automatic fact-checking. Existing fact-checking pipelines typically rely on multi-stage frameworks involving evidence retrieval and claim verification. However, these methods face two major challenges: (1) the retrieval process often introduces noisy evidence, which compromises the reliability of the final veracity prediction; and (2) the verification models may overlook critical factual details, resulting in hallucinated conclusions. To address these issues, we propose a fact-checking framework SLED with Self-supervised denoising evidence retrieval and LLM-Enhanced Debate-based verification. In the retrieval stage, SLED leverage trained verifier to assess credibility and necessity of retrieved evidence, enabling the elimination of noisy evidence. In the verification stage, SLED prompts the LLM to generate dual-perspective reasoning and simulates a multi-agent debate, followed by distillation into a lightweight model for final veracity prediction. Experiments on CHEF and HOVER datasets demonstrate that SLED achieves the state-of-the-art results in complex fact verification scenarios.

Abdur-Rahman Ibrahim Sayyid-Ali, Daanish Uddin Khan, Naveed Anwar Bhatti

Large language model (LLM) based answer engines offer real-time, conversational answers but raise concerns about scalability and web sustainability. Unlike traditional search that serves results from cached indices, these systems fetch pages anew for each query, creating redundant network traffic. We present the first measurement-driven study of commercial LLM answer engines, combining automated client-side tracing and controlled server-side audits. Analyzing ChatGPT and Claude across 1,000 queries, we find that both operate as meta-search layers heavily reliant on existing indices, fetching top-ranked pages with minimal caching. A human-equivalent cost model shows their per-query network footprint far exceeds that of human searchers, varying sharply by architecture. These results reveal the infrastructural burden of real-time fetching and motivate cooperative efficiency measures like shared caches, transparent retrieval standards, and publisher controls such as llms.txt, to make AI-augmented search more sustainable.

Zhongyu Yang, Wei Pang 0001, Yingfang Yuan

Retrieval is being redefined by agentic AI, demanding multimodal reasoning beyond conventional similarity-based paradigms. Composed Image Retrieval (CIR) exemplifies this shift as each query combines a reference image with textual modifications, requiring compositional understanding across modalities. While embedding-based CIR methods have achieved progress, they remain narrow in perspective, capturing limited cross-modal cues and lacking semantic reasoning. To address these limitations, we introduce XR, a training-free multi-agent framework that reframes retrieval as a progressively coordinated reasoning process. It orchestrates three specialized types of agents: imagination agents synthesize target representations through cross-modal generation, similarity agents perform coarse filtering via hybrid matching, and question agents verify factual consistency through targeted reasoning for fine filtering. Through progressive multi-agent coordination, XR iteratively refines retrieval to meet both semantic and visual query constraints, achieving up to a 38% gain over strong training-free and training-based baselines on FashionIQ, CIRR, and CIRCO, while ablations show each agent is essential. Code is available: https://01yzzyu.github.io/xr.github.io/.

Jinwei Su, Qizhen Lan, Yinghui Xia, Lifan Sun, Weiyou Tian, Tianyu Shi 0003, Lewei He

Large Language Model (LLM)-based agentic systems have shown strong capabilities across various tasks. However, existing multi-agent frameworks often rely on static or task-level workflows, which either over-process simple queries or underperform on complex ones, while also neglecting the efficiency-performance trade-offs across heterogeneous LLMs. To address these limitations, we propose Difficulty-Aware Agentic Orchestration (DAAO), which can dynamically generate query-specific multi-agent workflows guided by predicted query difficulty. DAAO comprises three interdependent modules: a variational autoencoder (VAE) for difficulty estimation, a modular operator allocator, and a cost- and performance-aware LLM router. A self-adjusting policy updates difficulty estimates based on workflow success, enabling simpler workflows for easy queries and more complex strategies for harder ones. Experiments on six benchmarks demonstrate that DAAO surpasses prior multi-agent systems in both accuracy and inference efficiency, validating its effectiveness for adaptive, difficulty-aware reasoning. Our code is open-sourced at https://github.com/AutoAgents-ai/DAAO

Wenlin Zhang 0001, Kuicai Dong, Junyi Li 0001, Yingyi Zhang 0001, Xiaopeng Li 0014, Pengyue Jia, Yi Wen 0001, Derong Xu, Maolin Wang 0001, Yichao Wang 0002 等

Deep search agents, which autonomously iterate through multi-turn web-based reasoning, represent a promising paradigm for complex information-seeking tasks. However, current agents suffer from critical inefficiency: they conduct excessive searches as they cannot accurately judge when to stop searching and start answering. This stems from outcome-centric training that prioritize final results over the search process itself. We identify the root cause as misaligned decision boundaries, the threshold determining when accumulated information suffices to answer. This causes over-search (redundant searching despite sufficient knowledge) and under-search (premature termination yielding incorrect answers). To address these errors, we propose a comprehensive framework comprising two key components. First, we introduce causal intervention-based diagnosis that identifies boundary errors by comparing factual and counterfactual trajectories at each decision point. Second, we develop Decision Boundary Alignment for Deep Search agents (DAS), which constructs preference datasets from causal feedback and aligns policies via preference optimization. Experiments on public datasets demonstrate that decision boundary errors are pervasive across state-of-the-art agents. Our DAS method effectively calibrates these boundaries, mitigating both over-search and under-search to achieve substantial gains in accuracy and efficiency. Our code and data are publicly available at: https://github.com/Applied-Machine-Learning-Lab/WWW2026_DAS.

Shunliang Fu, Yanxin Zhang, Yixin Xiang, Xiaoyu Du 0002, Jinhui Tang 0001

Existing multimodal document question-answering (QA) systems predominantly rely on flat semantic retrieval, representing documents as a set of disconnected text chunks and largely neglecting their intrinsic hierarchical and relational structures. Such flattening disrupts logical and spatial dependencies—such as section organization, figure-text correspondence, and cross-reference relations—that humans naturally exploit for comprehension. To address this limitation, we introduce a document-level structural Document MAP (DMAP), which explicitly encodes both hierarchical organization and inter-element relationships within multimodal documents. Specifically, we design a Structured-Semantic Understanding Agent to construct DMAP by organizing textual content together with figures, tables, charts, etc into a human-aligned hierarchical schema that captures both semantic and layout dependencies. Building upon this representation, a Reflective Reasoning Agent performs structure-aware and evidence-driven reasoning, dynamically assessing the sufficiency of retrieved context and iteratively refining answers through targeted interactions with DMAP. Extensive experiments on MMDocQA benchmarks demonstrate that DMAP yields document-specific structural representations aligned with human interpretive patterns, substantially enhancing retrieval precision, reasoning consistency, and multimodal comprehension over conventional RAG-based approaches. Code is available at https://github.com/Forlorin/DMAP

Xingyu Ma, Xin Tian, Lingxiang Wu, Xuepeng Wang, Xueming Tang, Jinqiao Wang

Text-to-SQL technology converts natural language queries into SQL statements for database retrieval. Recent advances in large language models (LLMs) have improved Text-to-SQL performance, but generated SQL often contains semantic or syntax errors that degrade user experience and system stability. Existing SQL error detection methods are costly, lack interpretability, and do not support error labeling. To overcome these issues, we propose SQL-Checker a specialized model for Text-to-SQL error detection. We first analyze common error factors in Text-to-SQL, and we design a novel data synthesis framework based on these error factors. This framework simulates error factors to construct a basic error SQL data, and then using an error analysis template to distill high-quality SQL error analysis data from large-scale models. For complex errors, a self-guided iterative distillation strategy further enhances data quality. SQL-Checker is then trained on this distilled dataset. Additionally, we refine SQL error labeling and, integrate error label recognition into the detection task, enabling macro-level cause analysis. Experiments show SQL-Checker achieves state-of-the-art results on multiple error detection datasets. Incorporating SQL-Checker into the Text-to-SQL pipeline also improves execution accuracy.

Jiadong Xie 0002, Jeffrey Liang, Siyi Teng, Jeffrey Xu Yu, Yingfan Liu

Approximate nearest neighbor (ANN) searches are commonly employed in various machine learning applications, such as recommendation systems, but traditional ANN searches typically involve only a single reference vector in a query. To broaden the capabilities of ANN search and support multi-reference-vector queries, thereby enabling a wider range of machine learning applications, we introduce all/any-k ANN search. They aim to find vectors that are similar to all or any of the multi-reference vectors in a query, respectively. To effectively and efficiently support all/any-k ANN search, we first propose distance metrics to evaluate the ranking of vectors among those in the dataset for exact all/any-k NN. Building on this, we introduce search algorithms and prove they can search according to the proposed distance metrics on graph indexes designed for traditional ANN. Additionally, we further introduce two-stage search algorithms for all/any-k ANN search to further enhance their search performance. We conduct extensive experiments on real-world datasets to validate the efficiency and effectiveness of our proposed algorithms compared to existing approaches.