XMC-AGENT : Dynamic Navigation over Scalable Hierarchical Index for Incremental Extreme Multi-label Classification (2024)

Abstract: The eXtreme Multi-label Classification (XMC) aims to accurately assign a large number of labels to instances, presenting challenges in learning, managing, and predicting across a vast and rapidly growing set of labels. Traditional XMC methods, such as one-vs-all and treebased methods struggle with the increasing set of labels due to their static label assumptions, while embedding-based methods face difficulties with complex mapping relationships due to their late-interaction paradigm. In this paper, we propose a large language model (LLM) powered agent framework for extreme multilabel classification – XMC-AGENT, which can effectively learn, manage and predict an extremely large and dynamically increasing set of labels. Specifically, XMC-AGENT models the extreme multi-label classification task as a dynamic navigation problem, employing a scalable hierarchical label index to effectively manage the unified label space. Additionally, we design two algorithms to enhance the dynamic navigation capabilities of XMC-AGENT: a selfconstruction algorithm for building the scalable hierarchical index, and an iterative feedback learning algorithm for adjusting the agent to specific tasks. Experiments demonstrate that XMC-AGENT achieves the state-of-the-art performance on three datasets.

heading: 1 Introduction
text: The eXtreme Multi-label Classification (XMC) task aims to classify instances to relevant labels from an extremely large label candidate space (Bhatia et al., 2015; Bengio et al., 2019; Prabhu et al., 2018). XMC is a widely used technique in many realworld applications, such as assigning appropriate
∗Corresponding authors.
tags to products in e-commerce platforms (Medini et al., 2019; Chang et al., 2021), recommending of interest in recommendation systems (McAuley and Leskovec, 2013), and facilitating search queries auto-completion in search engines (Agrawal et al., 2013; Yadav et al., 2021).
Unfortunately, due to the extensive and dynamic growth of the label candidates, XMC is a very challenging task. In real-world XMC problems, the number of potential labels often ranges from tens of thousands to millions (Song et al., 2020). Such a large output space poses significant challenges for modeling, learning, and computing the mapping from instances to large-scale labels, i.e., the scalability problem. For instance, it is difficult to
5659
directly learn the mapping from headsets (instance) in Figure 1 to xbox and glasses (labels), and computing all instance-label pairs will result in a high computation cost. Furthermore, the label set in real-world XMC scenarios is often dynamically changing and rapidly growing. The evolving labels further raise the challenge of efficient integration of new labels without the necessity for extensive retraining.
Current eXtreme Multi-Label Classification methods are mainly tree-based (Khandagale et al., 2019; Majzoubi and Choromanska, 2020; Zhang et al., 2021; Yu et al., 2022; Kharbanda et al., 2022) and embedding-based approaches (Gupta et al., 2021; Dahiya et al., 2021; Mittal et al., 2021a; Xu et al., 2023; Gupta et al., 2023; Chien et al., 2023). Tree-based approaches organize the labels as a fixed and static label tree, classify instances from root to leaf nodes and gradually narrow down the label candidates. These approaches, while addressing the challenge posed by large-scale label sets, struggle with dynamically growing label sets due to the utilization of prefixed, static label indices. Embedding-based approaches, on the other hand, predict labels by mapping labels and instances into the same vector space and selecting labels based on their vector similarities. However, due to the lack of fine-grained interaction between instances and labels, issues arise when dealing with complex mapping relationships. Moreover, to effectively integrate new labels, a process of re-training or continual training is necessary. However, the extensive label space and large volumes of data make retraining resource-intensive, and continuous learning can result in severe catastrophic forgetting, degrading previously acquired label knowledge.
In this paper, we propose an agent-based framework for extreme multi-label classification – XMCAGENT, which can effectively learn, manage, and predict the extremely large and dynamically increasing set of labels by leveraging LLMs-powered agents. Specifically, XMC-AGENT models the extreme multi-label classification task as a dynamic navigation problem (i.e., the model searches through the label space to locate the labels corresponding to the instance), and employs a scalable hierarchical label index to effectively manage the extensive label space via transforming them into a tree-like label index. In this way XMC-AGENT can uniformly manage both existing labels and future labels and seamlessly integrate future labels
by inserting them at suitable positions in the tree as they emerge, leveraging their connections and associations with existing labels, thereby avoiding disruption of existing structures and the need for extensive retraining. By leveraging the capabilities of LLMs for dynamic navigation within a structured label space, XMC-AGENT offers a novel and effective solution for addressing the scalability and adaptability challenges of XMC.
Given the XMC-AGENT framework, we propose a self-construction algorithm for scalable hierarchical label building and a self-correction algorithm for the general navigational capabilities of LLMs. Specifically, the self-construction algorithm autonomously transforms the large label set into a structured hierarchical index by adopting a selfquestioning strategy, i.e., the XMC-AGENT determines comparison relations between labels and recursively merges these relations to build the structured label index. In this way, the self-construction algorithm enables the seamless integration of newly emerged labels. Furthermore, we propose a selfcorrection algorithm, which dynamically obtains feedback signals from previous incorrect navigation trajectories and iteratively adjusts its navigation capability on specific tasks.
Generally, our main contributions are:
• We propose an LLM-powered agent framework named XMC-AGENT. By modeling the XMC problem as a navigation task within the label space, XMC-AGENT can naturally handle the incremental XMC problem and achieve state-of-the-art performance on three standard datasets.
• We design a scalable hierarchical label index construction algorithm named selfconstruction. By discovering the associative relationships between labels, self-construction enables the seamless integration of newly emerged labels into an existing label index.
• We design an iterative feedback learning algorithm named self-correction, which leverages the navigation trajectory as feedback to effectively align general navigation capability with specific classification scenarios.

heading: 2 Methodology
text: Let X and Y represent the sets of input instances and labels respectively, and { Y0,Y1, · · · ,Yk} represent the acquired labels at different time. For
Iterative Feedback Learning
Input: It's a Man's Man's Field… (Labels: Pop, Rock)
Dynamic Semantic Navigation
Let me search the Index
Compare input with: Dance and Music Choose: Both
Compare input with shortlist. The answers are Latin Dance and Pop
MusicDance
Latin Dance⟡ Samba⟡ Rock⟡ Guitar⟡ Pop⟡
Clothing Arts Sports
a) b) c)
Scalable Hierarchical Indexing
Generate Centers
Sampling Samples
Partition Labels
Refine Partition
Clothing Sports
CreationsArts
Clothing SportsArts
6K Labels
Sports Creations Arts Clothing
Detected Path While Navigation
Undetected Path While Navigation
Root Arts (Hit)
Music (Hit)
Pop⟡ (Hit)
Rock⟡ (Miss)
Latin Dance⟡ (Error)
Guitar⟡Clothing Activewear⟡ [Random Sample]
Samba⟡ Dance (Error)
Detected but Irrelevant
Undetected but RelevantUndetected and Irrelevant
Various Feedback
Compare input with: Clothing, Arts and Sports Choose: Arts
Figure 2: Illustrations of our proposed LLM-powered agent framework. a) Modeling the extreme multi-label classification task as a dynamic navigation problem, and utilizing a two-stage navigation strategy to seek optimal results over a semantic hierarchical label index1. b) Employing a self-construction algorithm to build a scalable hierarchical label index by adopting a self-questioning strategy. c) Employing a self-correction algorithm to enhance the general navigational capabilities by iteratively learning feedback signals from previous navigation trajectories.
simplicity, we consider a two-stage incremental setting in this paper, which means Y = Y0 ∪ Y1.
We bring XMC-AGENT to confront the challenges encountered in addressing the incremental XMC, which is achieved by: (1) Constructing a scalable hierarchical label index using LLMs. (2) Employing iterative feedback learning to effectively adjust LLMs with specific tasks.

heading: 2.1 Extreme Multi-label Classification as Dynamic Navigation
text: The essence of multi-label classification lies in searching for multiple relevant labels from the label space, which leads to increased difficulty in directly solving the problem (i.e., one-vs-all approaches) with the increase of the set of labels. Considering this, we propose XMC-AGENT to simplify the problem by incorporating the interrelationships between labels to construct a label index I, which consists of a specialized center c along with multiple sub-indices, denoted as I ≡ (c, {Ii}), and employing an LLM-powered agent to navigate over the index for the optimal results. The main idea of dynamic navigation is illustrated in Figure 2.a.
Specifically, we employ a two-stage navigation strategy to seek the optimal results over the hierarchical index. In the first stage, a breadth-first search
1Tags with superscript ⋄ represent the actual labels, while the others represent centers generated during the construction.
is employed to generate a shortlist via the comparison of the instances and centers in the index. The breadth-first search stops when traversing the entire index or reaching a certain number of terminal index (i.e., reaching Dance and Music in Figure 2. b). The shortlist is composed of the union of all labels from the reached terminal index (i.e., [ Latin Dance, Samba, Rock, Guitar, Pop ]). In the second stage, XMC-AGENT selects labels relevant to the instance from the shortlist and outputs them based on the relevance (i.e., XMC-AGENT assign Latin Dance and Pop to the instance, and regard the former as more relevant).

heading: 2.2 Scalable Hierarchical Index Building via Self-construction
text: To adapt the navigation strategy (comparison among the instance and centers), we adopt a compare-based (Schultz and Joachims, 2003; Haghiri et al., 2017; Emamjomeh-Zadeh and Kempe, 2018; Ghoshdastidar et al., 2019) index building approach; instead of using explicit similarity computations to form a hierarchical label index. Specifically, we utilize LLMs to determine comparison relations between labels and recursively merge these relations to build the structured label index.
Algorithm 1 Hierarchical Label Indexing of selfconstruction Input: Label partition p = (c,Y), Task description T Output: Hierarchical label index I
1: if should stop then ▷ Pre-defined stop criteria 2: return p 3: end if 4: repeat 5: Ŷ ← Sample(Y) ▷ Sample a subset labels to represent Y 6: C ← GenCenters(T, Ŷ) ▷ Generate sub-index centers according to Ŷ 7: for li ∈ Y do ▷ Assign each label to relevant centers 8: Ci ← AssignCenter(li, C) 9: end for 10: P ← Partition({(li, Ci)}|Y0|i=1 ) ▷ Create sub-partitions according to the
assignment 11: P† ← V alidation(P) 12: until P† ̸= ∅ 13: for pi ∈ P† do ▷ Recursive execution 14: Ii ← QuickCluster(pi, T ) ▷ Algorithm 1 15: end for 16: I ←Merge(c, {Ii}|P †| i=1 ) ▷ Algorithm 2 17: return I

heading: 2.2.1 Compare-based Hierarchical Indexing
text: Considering the label set Y0 in Figure 2.b, we initially regard it as a partition p⋆ = (root,Y0) and sample a subset Ŷ as representations from p⋆. Then, a collection of sub-index centers (e.g., Sports, Creations, Clothing and Arts ) can be generated based on Ŷ , using the following prompt :
Which centers are relevant to the provided product category?
To get the partition of Y0, each label li ∈ Y0 is compared with C, assigning li to relevant centers Ci, using the following prompt :
Look through the provided labels of product categories and give a set of cluster centers.
This process generate k + 1 partitions eventually, denoted as P = {p1, · · · , pk, pother}. The first k partitions correspond to the k centers and their assigned labels, while the last partition pother, encompasses labels irrelevant to all centers in C.
We additionally apply a post-refinement to address potential issues existing in the obtained partition (i.e., there is a significant overlap between
Algorithm 2 Merge Operation of self-construction Input: Sub-index set {Ii}, Predecessor center c Output: Hierarchical label index I
1: Init: Sc ← [ ] ▷ Successors of c 2: for Ii ∈ {Ii} do 3: if Ii is other then ▷ The index for a group of labels
assigned to center other 4: Add successors of Ii to Sc 5: else 6: Add Ii to Sc 7: end if 8: end for 9: return (c, Sc)
Algorithm 3 Scalable Label Integration of selfconstruction Input: Hierarchical label index I, New Labels Y ′ , Task de-
scription T Output: Extended Index I
1: for li ∈ Y ′
do 2: Pi ← Search(I, li) ▷ Compare li with centers in I in a top-down manner 3: for pij ∈ Pi do 4: pij ← (cij ,Yij ∪ {li}) ▷ Insert li to partition pij 5: if pij should split then ▷ Pre-defined criteria 6: Iij ← QuickCluster(pij , T ) ▷ Algorithm1 7: pij ← Iij ▷ Replace pij with new index 8: end if 9: end for
10: end for 11: return I
partition Arts and Creations in Figure 2.a, retaining both would result in the waste of resources), as C is generated from a subset of Y0.
We recursively execute the above process for each partition until the stopping criteria are satisfied (i.e., the number of labels within the partition is less than a pre-defined threshold). One noteworthy benefit of using the recursive strategy is that as the recursion depth increases, the label similarities within an obtained partition also increase. This in turn leads to the increase in the specificity of the sub-index center’s representation (i.e., Clothing -> Athletic Apparel -> Running Apparel).
As mentioned before, the partition process also generates non-semantic centers, denoted as pother, which block the information circulation over the index. To address this issue, we establish direct connections between the successors and predecessors of these centers, thereby eliminating their impact on the semantic index. The details of the indexbuilding process are shown in Algorithm 1.

heading: 2.2.2 Integration of Scalable Indexing
text: To incorporate new labels into an existing index, we propose an InsertSort like algorithm. We use an example to illustrate the main idea in Figure 3. For each new label, XMC-AGENT recursively compares it with the centers of the sub-index and assigns it to relevant sub-indices until reaching the terminal index. Once the labels within a terminal index surpassing the pre-defined threshold, we use Algorithm 1 to directly generate fine-grained subindices for the terminal index.

heading: 2.3 Agent Adaption via Iterative Feedback Learning
text: To adjust the mapping relationship between instances and labels for a specific application, one approach is to add summarized mapping rules to the context of LLMs. However, due to the inherent challenge of having extensive labels, the summarized rules are incapable of covering all annotated data, which gives rise to inconsistency between classification results and user intent.
Different from using summarized decision criteria, we propose an approach to utilize feedback to inform the navigation process of LLMs. Giving an input instance, LLMs would give several predictions using the self-constructed index, which consists of two distinct label types: Hit representing labels both detected and relevant, like Pop in Figure 2, and Error representing labels detected but
2Polonaise is a dance of Polish origin. Polonaise dance greatly influenced European ballrooms, folk music, and European classical music.
irrelevant, indicating inconsistency, like Latin Dance in Figure 2. Additionally, there exist labels which are relevant but remain undetected in the search process, denoted as Miss, also indicating inconsistency, like Rock in Figure 2. Furthermore, based on the three types of labels, we also mark the centers along their search paths with the corresponding type. For example, Arts is on the search path of Pop, and Dance is on the search path of Latin Dance, thus they are marked as Hit and Error respectively.
Self-Feedback by Deductive Reasoning To provide feedback using deductive reasoning, we utilize the decision criteria provided by the LLMs themselves for both the two types of inconsistent labels (Error and Miss). For example, in Figure 2, XMCAGENT leverages the self-generated decision criteria for the inconsistent label Rock (Miss) as a feedback signal to adjust its navigational capability.
Contrastive-Feedback by Inductive Reasoning To provide feedback using inductive reasoning, we create a shortlist by randomly sampling the three types of labels along with irrelevant labels without detection, akin to the navigation process, and the expected response are all relevant labels in the list.
When a sufficient amount of feedback, i.e., Figure 4, is collected, we engage in the refinement of LLMs iteratively to align the navigation capability using the feedback data.

heading: 3 Experimental Setting

heading: 3.1 Datasets and Evaluation
text: We evaluate our method on the following datasets: AmazonCat-13K (McAuley and Leskovec, 2013)
in product tagging domain, LF-Amazon-131K (McAuley and Leskovec, 2013) in the recommendation domain and LF-WikiSeeAlso-320K in the wiki-page tagging domain, where 13K, 131K and 320K indicate the total label size. All datasets are available in the extreme classification repository (Bhatia et al., 2016). To evaluate the ability of various methods in an incremental setting, we randomly split the labels into two parts. The statistics of the processed datasets (notated with superscript) are listed in Table 1.
We consider two evaluation setups: Incremental Performance (Inc) and Overall Performance (Overall). The former focus on classification results only on Y1 and the latter focus on both Y0 and Y1. We evaluate the models’ performance with Precision@k and Recall@k, where k ∈ {1, 3, 5, 10}, which are two commonly-used evaluation metrics in XMC (Xiong et al., 2022; Aggarwal et al., 2023).

heading: 3.2 Baselines
text: We compare our method with the following baselines. 1) BM25 conducts a nearest neighbor retrieval using TF-IDF features. 2) TAS-B (Hofstätter et al., 2021) ranks labels based on the similarity with the instance by Faiss (Johnson et al., 2019). 3) MACLR (Xiong et al., 2022) leverages the raw text and self-training with pseudo positive pairs to improve the extreme zero-shot capacity. 4) SemSup-XC (Aggarwal et al., 2023) use webcollected semantic descriptions to represent labels and facilitate generalization by using a combination of semantic and lexical similarity. 5) ICXML (Zhu and Zamani, 2023) propose three demonstration selection approaches to create in-context learning prompts for gpt-3.5-turbo to generate approximate labels, then using TAS-B mapping these approximate labels to labels set and get final reranking results by gpt-3.5-turbo. 6) Linear Search To assess the efficacy of directly employing LLMs for XMC, we traverse all labels using
both zero-shot and few-shot approaches, sorting the labels based on the output logits. Considering the scale of the label sets, we only conducted experiments on AmazonCat-13K†.

heading: 4 Results and Analysis

heading: 4.1 Main results
text: In all experiments, we choose Vicuna-13B-v1.5 (Zheng et al., 2023) as the base LLM. The experimental results over three datasets, as presented in Table 2, reveal that:

heading: 1) XMC-AGENT exhibits a noteworthy improvement in addressing incremental XMC problem.
text: Compared with previous methods, our classification as a navigation approach demonstrates an improved capability in handling new labels on three datasets of different scales. Simultaneously, our approach achieves optimal performance under the overall setup, exemplifying a commendable balance between utility and generalization.

heading: 2) XMC-AGENT enhances its dynamic naviga-
text: tion capability by integrating the proposed components. Compared with the Linear Search results on AmazonCat-13K†, our approach achieves an acceptable time cost while exhibiting superior navigation performance under both setups (i.e., 9.3% P@1 improvement in Inc and 45.9% P@1 improvement in Overall), which indicates the effectiveness of the proposed components.

heading: 3) XMC-AGENT demonstrates a stable perfor-
text: mance across various application scenarios. In our experiments, we found that previous methods have varying applicability across scenarios. For instance, TAS-B exhibits a better performance in scenarios with longer label length (e.g., LF-Amazon131K† and LF-WikiSeeAlso-320K†), ICXML performs better in cases where the mapping relationship between instances and labels is complex (e.g., LF-WikiSeeAlso†), and SemSup-XC demonstrates better capabilities in scenarios where the mapping relationship is more direct (e.g., AmazonCat-13K† and LF-Amazon-131K†). Our approach, which utilizes an LLM to uniformly manage the label space and learn mapping relationships from feedback rather than integrating them into embedding, enables effective handling of various applications.

heading: 4.2 Analysis
text: To understand the impact of various key components on the results, we conduct ablation studies on
the key components of XMC-AGENT and further provide qualitative analysis of the performance of previous methods with continual fine-tuning.

heading: 4.2.1 Ablating the Label Index
text: To investigate the impact of label index on the final performance, we replaced the index used in XMCAGENT with two alternative methods. The first one uses K-Means to recursively partition the label set (with k=16) as mentioned in PECOS (Yu et al., 2022). The second one employs Faiss (Johnson et al., 2019) as a retriever, to identify the Top 500 similar labels with the instances as a shortlist. Both the two approaches use TAS-B as the text embedder. From results presented in Table 3, we can observe that :
1) Replacing with K-Means results in significant performance degradation. This is partly due to the cascading error propagation in the index, as each label only appears once in the K-Means index. Additionally, to navigate over the index, each cluster requires a description as representation. However, due to the limitations of LLMs’ context window and long-text processing capabilities, the generated descriptions cannot fully cover labels within the cluster, resulting in the inability to find relevant
labels based on the center during navigation. 2) Replacing with a shortlist is more effective than K-Means, but still inferior to our approach. This is due to the retrieval method can only detect a fixed portion of relevant labels (as shown in Figure 5, even at R@3000, only 60%-70% of the relevant labels can be detected), thereby restricting the exploration space for subsequent feedback learning.

heading: 4.2.2 Ablating Feedback Learning
text: To investigate the influence of the feedback mechanisms, we separately employ one at a time. From the results presented in Table 3, we can observe that both mechanisms contribute to the final per-
formance, but the emphasis on the improvements differs between the two mechanisms. Employing feedback based on inductive reasoning solely leads to a greater improvement in recall. while solely employing feedback based on deductive reasoning leads to a greater improvement in precision.
This discrepancy arises from the inherent nature of the feedback signals in the two mechanisms. When using deductive reasoning, the feedback signal originates from the self-correction of the inconsistent label, thereby enhancing the discriminatory ability for one specific label. While using inductive reasoning, the signal comes from the exploration of random candidates, leading to an improvement in the discriminatory ability for overall labels.
Additionally, we assess the impact of iteratively employing the feedback mechanism, as illustrated in Figure 6. Across three rounds of iteration, both metrics on the two datasets exhibit an improvement, suggesting the proposed feedback learning mechanism possesses robust stability and generalization.

heading: 4.2.3 Effect of Continual Fine-tuning
text: As the baselines are not designed for incremental XMC problems, we conduct continual fine-tuning (CFT) on the model trained with Y0 using additional labels to assess their adaptability in dealing with new labels. The corresponding results are shown in Table 4. It can be observed that the model’s classification ability for new labels significantly improved after CFT. However, the overall performance across the entire labels does not show improvement, suggesting the forgetting of the capabilities learned by previous methods on a fixed label set.

heading: 5 Related Works
text: Previous research on XMC can be divided into two settings: full label coverage (Prabhu et al., 2018; Mittal et al., 2021b,a; Kharbanda et al., 2022; Yu et al., 2022) and weak label coverage (Gupta et al., 2021; Dahiya et al., 2021; Xiong et al., 2022; Gupta et al., 2023), the difference is whether supporting predictions for newly added labels during inference.
A prevalent approach for addressing weak label coverage entails the utilization of a bi-encoder to map labels and instances into the same vector space. SiameseXML (Dahiya et al., 2021) generalizes existing Siamese Networks (Chen et al., 2020) by combining Siamese architectures with per-label extreme classifiers. MACLR (Xiong et al., 2022) constructs label and input text encoders by training a pseudo label-input annotation data through a twostage process. SemSup-XC (Aggarwal et al., 2023) uses web information to augment label semantics and calculates the similarity between label and input from both semantic and lexicon perspectives.
Unlike previous approaches that transformed the classification task into an end-to-end generation task (Simig et al., 2022) or utilized the in-context learning ability of LLMs to generate approximate labels(Chang et al., 2018; Tay et al., 2022; Kishore et al., 2023; Wang et al., 2023), we model XMC as an LLM-Agent dynamic navigation task(Kishore et al., 2023; Wang et al., 2023), allowing for better handling the dynamically growing extensive labels.

heading: 6 Conclusion
text: In this paper, we propose XMC-AGENT to address the challenge of dynamically expanding label set in extreme multi-label classification. This framework utilizes a self-constructed label index for effective management of the extensive labels. And incorporates an iterative feedback learning mechanism to adjust general navigational capabilities to a specific task. The results on three standard datasets indicate that our approach effectively enhances the classification performance in incremental settings.
Limitations
We identify two limitations in our work that necessitates further investigation. Firstly, we only employ Vicuna-13B-v1.5 as the base model of XMCAGENT, the impact of using different LLMs on the final performance requires further detailed research. Additionally, we only explore extreme multi-label text classification problem with XMC-AGENT, future works can extend the approach presented in this paper to other domains, like the extreme multilabel image classification problem.

heading: 7 Acknowledge
text: We sincerely thank all anonymous reviewers for their insightful comments and valuable suggestions. This research work is supported by the National Natural Science Foundation of China under Grants no. 62306303, no. 62122077 and no. 62106251. This work is supported by Ant Group Research Fund.

heading: A Experiment Details
text: The deductive and inductive data used across each iteration of feedback learning is list in Table 5, with a distribution ratio of approximately 1:1. When using feedback data to adjust Vicuna-13B-v1.5, we set epoch to 1, learning rate to 2e-5 with no warmup and batch size to 256 using FSDP (Zhao et al., 2023). All the experiments are implemented on NVIDIA A100-80GB GPU clusters.

heading: B Ablating the Navigation Policy
text: To investigate the impact of navigation policy on the results, we experiment with multiple combinations of strategies on AmazonCat-13K†. Due to the second-stage navigation strategy adopting an end-to-end approach to sequentially generate relevant labels from the shortlist, we only experiment with the first-stage strategy. We evaluate the effectiveness of the navigation policy from two aspects: 1) The recall of the first stage, denoted as Recall, where a higher proportion of relevant labels in the shortlist obtained in the first stage implies a smaller performance loss in subsequent processing. 2)The number of labels in the obtained shortlist, denoted as Size, where a higher number of labels in the shortlist leads to higher subsequent processing costs.
We employed two distinct navigation policies: 1) Breadth-First Search (BFS): This policy explores the label index in a breadth-first manner, employing a queue to store upcoming sub-indices for search initiation upon detection of a terminal index during any iteration, and continuing until completion of the process. 2) Depth-First Search (DFS): This policy explores the index in a depth-first manner, utilizing a stack to retain the next sub-indices for search initiation upon detection of a terminal index during any iteration. And we terminate the navigation process upon detecting 20 terminal indices.
When navigating over the label index, we employ two different methods to represent the subindex currently being compared: 1) Only utilizing the description center of the sub-index currently being confronted (i.e., Dance, Music or Sports). 2) Providing a series of descriptions centers traversed from the root to the current sub-index, denoted as ancestor aug, i.e., [ Root -> Arts -> Dance ].
From the results in Table 6 we can observe that compared with retrieved top 300 similar labels using Faiss, employing a breadth-first manner nav-
igation policy achieved a higher recall rate while retrieving fewer labels. Furthermore, despite the additional information offered by ancestor augmentation, it does not enhance the recall rate of navigation results. This phenomenon is attributed to the information from common ancestors enhancing the similarity between different sub-indexes, thus diminishing their distinctiveness.

heading: C Full results for Linear Search
text: Considering the scale of the label set, we traverse all tags in AmazonCat-13K† in a point-wise manner, sorting the labels based on the output logits. We conducted experiments using both zero-shot and few-shot (k=1, 3, 5) approaches. When using the few-shot approach, for each label, we randomly select k instances related to that label from the training set to construct demonstrations. We then employ the large language models to determine the relevance between the label and the input instance, and we rank all labels based on the logits of the response. The full results are present in Table 7 and the comparison results with the previous method and XMC-AGENT are shown in Figure 7. From the results, it can be observed that employing LLMs in a point-wise manner has achieved comparable recall rates to the previous method, with slightly lower precision rates. However, the Linear Search approach incurs high time costs due to the need to traverse all labels for each instance. XMC-AGENT improves search speed by constructing a scalable
hierarchical label index and employing feedback learning to adjust the navigational capability, which simultaneously enhances precision.

heading: D Full results for ablation study
text: The full results for ablation study are present in Table 8 and Table 9.

heading: Future Work
text: Additionally, we only explore extreme multi-label text classification problem with XMC-AGENT, future works can extend the approach presented in this paper to other domains, like the extreme multilabel image classification problem