Fine-grained Representation Research Articles

Dual intent view contrastive learning for knowledge aware recommender systems

Knowledge-aware recommendation systems often face challenges owing to sparse supervision signals and redundant entity relations, which can diminish the advantages of utilizing knowledge graphs for enhancing recommendation performance. To tackle these challenges, we propose a novel recommendation model named Dual-Intent-View Contrastive Learning network (DIVCL), inspired by recent advancements in contrastive and intent learning. DIVCL employs a dual-view representation learning approach using Graph Neural Networks (GNNs), consisting of two distinct views: a local view based on the user-item interaction graph and a global view based on the user-item-entity knowledge graph. To further enhance learning, a set of intents are integrated into each user-item interaction as a separate class of nodes, fulfilling three crucial roles in the GNN learning process: (1) providing fine-grained representations of user-item interaction features, (2) acting as evaluators for filtering relevant relations in the knowledge graph, and (3) participating in contrastive learning to strengthen the model’s ability to handle sparse signals and redundant relations. Experimental results on three benchmark datasets demonstrate that DIVCL outperforms state-of-the-art models, showcasing its superior performance. The implementation is available at: https://github.com/yzxx667/DIVCL.

A multimodal similarity-aware and knowledge-driven pre-training approach for reliable pneumoconiosis diagnosis

Background Pneumoconiosis staging is challenging due to the low clarity of X-ray images and the small, diffuse nature of the lesions. Additionally, the scarcity of annotated data makes it difficult to develop accurate staging models. Although clinical text reports provide valuable contextual information, existing works primarily focus on designing multimodal image-text contrastive learning tasks, neglecting the high similarity of pneumoconiosis imaging representations. This results in inadequate extraction of fine-grained multimodal information and underutilization of domain knowledge, limiting their application in medical tasks. Objective The study aims to address the limitations of current multimodal methods by proposing a new approach that improves the precision of pneumoconiosis diagnosis and staging through enhanced fine-grained learning and better utilization of domain knowledge. Methods The proposed Multimodal Similarity-aware and Knowledge-driven Pre-Training (MSK-PT) approach involves two stages. In the first stage, we deeply analyze the similar features of pneumoconiosis images and use a similarity-aware modality alignment strategy to explore the fine-grained representations and associated disturbances of pneumoconiosis lesions between images and texts, guiding the model to match more appropriate feature representations. In the second stage, we utilize data-associated features and pre-stored domain knowledge features as priors and constraints to guide the downstream model in the visual domain without annotations. To address potential erroneous labels generated by model predictions, we further introduce an uncertainty threshold strategy to mitigate the negative impact of imperfect prediction labels and enhance model interpretability. Results We collected and created the pneumoconiosis chest X-ray (PneumoCXR) dataset to evaluate our proposed MSK-PT method. The experimental results show that our method achieved a classification accuracy of 81.73%, outperforming the state-of-the-art algorithms by 2.53%. Conclusions MSK-PT showed diagnostic performance that matches or exceeds the average radiologist's level, even with limited labeled data, highlighting the method's effectiveness and robustness.

Wireless capsule endoscopy anomaly classification via dynamic multi-task learning

Wireless capsule endoscopy (WCE) provides a painless, non-invasive means for early gastrointestinal disease detection and cancer prevention. However, clinicians must diagnose only about 5% of lesion images from tens of thousands of frames, highlighting the need for computer-assisted diagnostic methods to enhance efficiency and reduce the elevated misdiagnosis rates attributed to visual fatigue. Previous research heavily relied on module design, an effective yet highly coupled method with the baseline and incurring additional computational costs. This paper proposes a dynamic multi-task learning method that combines triplet loss and weighted cross-entropy loss to respectively guide the model in learning compact fine-grained representations and establishing less biased decision boundaries, without incurring additional computational costs. Our method outperforms previous advanced methods on two publicly available datasets, achieving an F1 score of 96.47% on Kvasir-Capsule and an F1 score of 96.75% with an accuracy of 96.72% on CAD-CAP. Visualization of the representations and heatmaps confirms the model’s precision in focusing on the lesion area. The prediction model has been uploaded to https://github.com/xli122/WCE_MTL.

Inferential knowledge and epistemic dimensions

Abstract Knowledge representation is one way to exploit expertise in a given domain by logical means. But, what kind of knowledge does one acquire from an inference (or inference on a query result over a knowledge base)? Such a question may appear awkward since the answer seems so obvious: from an inference, one simply acquires knowledge. This is undoubtedly the case when only one type of knowledge (for instance, expert knowledge) is involved in an inference. What if several types of knowledge are involved? What type of knowledge can one deduce from a plurality of knowledge types? I claim that reasoning with different knowledge concepts requires a fine-grained representation of knowledge in which every knowledge type finds a singular expression in order to avoid some epistemic equivocity associated with a coarse-grained representation of knowledge. In the first part of the paper, I revisit the Muddy Children Puzzle, which usually serves to illustrate common knowledge in dynamic epistemic logic. I try to show that this problem also shows some sort of epistemic equivocity between concepts of knowledge and, consequently, that the problem calls for some epistemological refinements concerning the representation of the types of knowledge at play in an inference. In the second part, I address this issue from a semantic point of view, and I develop a fragment of epistemic logic capable of providing a solution to the problem of epistemic equivocity.

Higher Order Polynomial Transformer for Fine-Grained Freezing of Gait Detection.

Freezing of Gait (FoG) is a common symptom of Parkinson's disease (PD), manifesting as a brief, episodic absence, or marked reduction in walking, despite a patient's intention to move. Clinical assessment of FoG events from manual observations by experts is both time-consuming and highly subjective. Therefore, machine learning-based FoG identification methods would be desirable. In this article, we address this task as a fine-grained human action recognition problem based on vision inputs. A novel deep learning architecture, namely, higher order polynomial transformer (HP-Transformer), is proposed to incorporate pose and appearance feature sequences to formulate fine-grained FoG patterns. In particular, a higher order self-attention mechanism is proposed based on higher order polynomials. To this end, linear, bilinear, and trilinear transformers are formulated in pursuit of discriminative fine-grained representations. These representations are treated as multiple streams and further fused by a cross-order fusion strategy for FoG detection. Comprehensive experiments on a large in-house dataset collected during clinical assessments demonstrate the effectiveness of the proposed method, and an area under the receiver operating characteristic (ROC) curve (AUC) of 0.92 is achieved for detecting FoG.

RAAFNet: Reverse Attention Adaptive Fusion Network for Large-Scale Point Cloud Semantic Segmentation

Point cloud semantic segmentation is essential for comprehending and analyzing scenes. However, performing semantic segmentation on large-scale point clouds presents challenges, including demanding high memory requirements, a lack of structured data, and the absence of topological information. This paper presents a novel method based on the Reverse Attention Adaptive Fusion network (RAAFNet) for segmenting large-scale point clouds. RAAFNet consists of a reverse attention encoder–decoder module, an adaptive fusion module, and a local feature aggregation module. The reverse attention encoder–decoder module is applied to extract point cloud features at different scales. The adaptive fusion module enhances fine-grained representation within multi-resolution feature maps. Furthermore, a local aggregation classifier is introduced, which aggregates the features of neighboring points to the center point in order to leverage contextual information and enhance the classifier’s perceptual capability. Finally, the predicted labels are generated. Notably, our method excels at extracting point cloud features across different dimensions and produces highly accurate segmentation results. Experimental results on the Semantic3D dataset achieved an overall accuracy of 89.9% and a mIoU of 74.4%.

Euclidean-Distance-Preserved Feature Reduction for efficient person re-identification

Person Re-identification (Re-ID) aims to match person images across non-overlapping cameras. The existing approaches formulate this task as fine-grained representation learning with deep neural networks, which involves extracting image features using a deep convolutional network, followed by mapping the features into a discriminative space through another smaller network, in order to make full use of all possible cues. However, recent Re-ID methods that strive to capture every cue and make the space more discriminative have resulted in longer features, ranging from 1024 to 14336, leading to higher time (distance computation) and space (feature storage) complexities. There are two potential solutions: reduction-after-training methods (such as Principal Component Analysis and Linear Discriminant Analysis) and reduction-during-training methods (such as 1 × 1 Convolution). The former utilizes a statistical approach aiming for a global optimum but lacking end-to-end optimization of large data and deep neural networks. The latter lacks theoretical guarantees and may be vulnerable to training noise such as dataset noise or initialization seed.To address these limitations, we propose a method called Euclidean-Distance-Preserving Feature Reduction (EDPFR) that combines the strengths of both reduction-after-training and reduction-during-training methods. EDPFR first formulates the feature reduction process as a matrix decomposition and derives a condition to preserve the Euclidean distance between features, thus ensuring accuracy in theory. Furthermore, the method integrates the matrix decomposition process into a deep neural network to enable end-to-end optimization and batch training, while maintaining the theoretical guarantee. The result of the EDPFR is a reduction of the feature dimensions from fa and fb to fa′ and fb′, while preserving their Euclidean distance, i.e.L2(fa,fb)=L2(fa′,fb′). In addition to its Euclidean-Distance-Preserving capability, EDPFR also features a novel feature-level distillation loss. One of the main challenges in knowledge distillation is dimension mismatch. While previous distillation losses, usually project the mismatched features to matched class-level, spatial-level, or similarity-level spaces, this can result in a loss of information and decrease the flexibility and efficiency of distillation. Our proposed feature-level distillation leverages the benefits of the Euclidean-Distance-Preserving property and performs distillation directly in the feature space, resulting in a more flexible and efficient approach. Extensive on three Re-ID datasets, Market-1501, DukeMTMC-reID and MSMT demonstrate the effectiveness of our proposed Euclidean-Distance-Preserving Feature Reduction.

Individual differences in spatial working memory strategies differentially reflected in the engagement of control and default brain networks.

Spatial locations can be encoded and maintained in working memory using different representations and strategies. Fine-grained representations provide detailed stimulus information, but are cognitively demanding and prone to inexactness. The uncertainty in fine-grained representations can be compensated by the use of coarse, but robust categorical representations. In this study, we employed an individual differences approach to identify brain activity correlates of the use of fine-grained and categorical representations in spatial working memory. We combined data from six functional magnetic resonance imaging studies, resulting in a sample of $155$ ($77$ women, $25 \pm 5$ years) healthy participants performing a spatial working memory task. Our results showed that individual differences in the use of spatial representations in working memory were associated with distinct patterns of brain activity. Higher precision of fine-grained representations was related to greater engagement of attentional and control brain systems throughout the task trial, and the stronger deactivation of the default network at the time of stimulus encoding. In contrast, the use of categorical representations was associated with lower default network activity during encoding and higher frontoparietal network activation during maintenance. These results may indicate a greater need for attentional resources and protection against interference for fine-grained compared with categorical representations.

Task-Related Saliency for Few-Shot Image Classification.

A weakness of the existing metric-based few-shot classification method is that task-unrelated objects or backgrounds may mislead the model since the small number of samples in the support set is insufficient to reveal the task-related targets. An essential cue of human wisdom in the few-shot classification task is that they can recognize the task-related targets by a glimpse of support images without being distracted by task-unrelated things. Thus, we propose to explicitly learn task-related saliency features and make use of them in the metric-based few-shot learning schema. We divide the tackling of the task into three phases, namely, the modeling, the analyzing, and the matching. In the modeling phase, we introduce a saliency sensitive module (SSM), which is an inexact supervision task jointly trained with a standard multiclass classification task. SSM not only enhances the fine-grained representation of feature embedding but also can locate the task-related saliency features. Meanwhile, we propose a self-training-based task-related saliency network (TRSN) which is a lightweight network to distill task-related salience produced by SSM. In the analyzing phase, we freeze TRSN and use it to handle novel tasks. TRSN extracts task-relevant features while suppressing the disturbing task-unrelated features. We, therefore, can discriminate samples accurately in the matching phase by strengthening the task-related features. We conduct extensive experiments on five-way 1-shot and 5-shot settings to evaluate the proposed method. Results show that our method achieves a consistent performance gain on benchmarks and achieves the state-of-the-art.

Individual differences in spatial working memory strategies differentially reflected in the engagement of control and default brain networks.

Spatial locations can be encoded and maintained in working memory using different representations and strategies. Fine-grained representations provide detailed stimulus information, but are cognitively demanding and prone to inexactness. The uncertainty in fine-grained representations can be compensated by the use of coarse, but robust categorical representations. In this study, we employed an individual differences approach to identify brain activity correlates of the use of fine-grained and categorical representations in spatial working memory. We combined data from six fMRI studies, resulting in a sample of 155 (77 women, 25 ± 5 years) healthy participants performing a spatial working memory task. Our results showed that individual differences in the use of spatial representations in working memory were associated with distinct patterns of brain activity. Higher precision of fine-grained representations was related to greater engagement of attentional and control brain systems throughout the task trial, and the stronger deactivation of the default network at the time of stimulus encoding. In contrast, the use of categorical representations was associated with lower default network activity during encoding and higher frontoparietal network activation during maintenance. These results may indicate a greater need for attentional resources and protection against interference for fine-grained compared to categorical representations.

SFPL: Sample-specific fine-grained prototype learning for imbalanced medical image classification

Imbalanced classification is a common and difficult task in many medical image analysis applications. However, most existing approaches focus on balancing feature distribution and classifier weights between classes, while ignoring the inner-class heterogeneity and the individuality of each sample. In this paper, we proposed a sample-specific fine-grained prototype learning (SFPL) method to learn the fine-grained representation of the majority class and learn a cosine classifier specifically for each sample such that the classification model is highly tuned to the individual’s characteristic. SFPL first builds multiple prototypes to represent the majority class, and then updates the prototypes through a mixture weighting strategy. Moreover, we proposed a uniform loss based on set representations to make the fine-grained prototypes distribute uniformly. To establish associations between fine-grained prototypes and cosine classifier, we propose a selective attention aggregation module to select the effective fine-grained prototypes for final classification. Extensive experiments on three different tasks demonstrate that SFPL outperforms the state-of-the-art (SOTA) methods. Importantly, as the imbalance ratio increases from 10 to 100, the improvement of SFPL over SOTA methods increases from 2.2% to 2.4%; as the training data decreases from 800 to 100, the improvement of SFPL over SOTA methods increases from 2.2% to 3.8%.

Blind image quality index with high-level Semantic Guidance and low-level fine-grained Representation

Image Quality Assessment (IQA) has received unprecedented attention due to the extensive applications in benchmarking image processing algorithms and systems. Despite great progress in IQA, most previous frameworks either utilized only high-level semantic features or simply stacked multi-level features to account for the distortions, resulting in limited performance. The initial visual perception is formed after that the information is processed by the primary visual cortex and the advanced visual cortex. However, the information transmission of the cerebral cortex is not unidirectional, that is, the higher brain area can affect the primary brain area in turn, regulate its sensitivity and preference, so as to help the brain to understand the external world more finely. Inspired by this, we propose a novel blind image quality index with high-level Semantic Guidance and low-level fine-grained Representation (SGRNet). First, the versatile backbone, called pyramid vision Transformer, is used to simulate the multilevel information processing in the brain, generating multilevel feature representation. Second, we propose a novel high-level semantic guidance module to simulate the feedback mechanism between levels of the visual cortex. Third, a simple but effective fine-grained feature extraction module is proposed for high-level information compensation and lower-level content perception. After this, an attention mechanism-based enhancement module is proposed to further learn the above two features respectively. Finally, a bilinear pooling-based regression module is proposed to integrate the enhanced features of the two parts and map them to the quality score. Extensive experiments on six challenging public datasets show that the proposed SGRNet can deal well with both the simulated and authentic distortions and achieves state-of-the-art performance.

Clustering for Clarity: Improving Word Sense Disambiguation through Multilevel Analysis

In natural language processing, a critical activity known as word sense disambiguation (WSD) seeks to ascertain the precise meaning of an ambiguous wordin context. Traditional methods for WSD frequently involve supervised learning methods and lexical databases like WordNet. However, these methods fallshort in managing word meaning complexity and capturing fine-grained differences. In this paper, for increasing the precision and granularity of word sensedisambiguation we proposed multilevel clustering method that goes deeper in the nested levels as locate groups of linked context words and categorize themaccording to their word meanings. With this method, we can more effectively manage polysemy and homonymy as well as detect minute differences in meaning. An actual investigation of the SemCor corpus demonstrates the performance score of multilevel clustering in WSD. This proposed method successfullyseparated clusters and groups context terms according to how semantically related they are, producing improved disambiguation outcomes. A more detailedknowledge of word senses and their relationships may be obtained thanks to the clustering process, which makes it possible to identify smaller clusters inside larger clusters. The outcomes demonstrate how multilevel clustering may enhance the granularity and accuracy of WSD. Our solution overcomes the drawbacks of conventional approaches and provides a more fine-grained representation of word senses by combining clustering algorithms.

MIST: Multi-instance selective transformer for histopathological subtype prediction

Accurate histopathological subtype prediction is clinically significant for cancer diagnosis and tumor microenvironment analysis. However, achieving accurate histopathological subtype prediction is a challenging task due to (1) instance-level discrimination of histopathological images, (2) low inter-class and large intra-class variances among histopathological images in their shape and chromatin texture, and (3) heterogeneous feature distribution over different images. In this paper, we formulate subtype prediction as fine-grained representation learning and propose a novel multi-instance selective transformer (MIST) framework, effectively achieving accurate histopathological subtype prediction. The proposed MIST designs an effective selective self-attention mechanism with multi-instance learning (MIL) and vision transformer (ViT) to adaptive identify informative instances for fine-grained representation. Innovatively, the MIST entrusts each instance with different contributions to the bag representation based on its interactions with instances and bags. Specifically, a SiT module with selective multi-head self-attention (S-MSA) is well-designed to identify the representative instances by modeling the instance-to-instance interactions. On the contrary, a MIFD module with the information bottleneck is proposed to learn the discriminative fine-grained representation for histopathological images by modeling instance-to-bag interactions with the selected instances. Substantial experiments on five clinical benchmarks demonstrate that the MIST achieves accurate histopathological subtype prediction and obtains state-of-the-art performance with an accuracy of 0.936. The MIST shows great potential to handle fine-grained medical image analysis, such as histopathological subtype prediction in clinical applications.

Accurate learning of graph representation with the consideration of fuzzy overlapping community

Graph classification task plays a crucial role in many practical applications, for which the model is required to be capable of learning an accurate representation with discriminative characteristics, but existing methods typically fail to exploit the most authentic substructures for better representation. Aiming at this limitation, a fuzzy overlapping community guided subgraph neural network is proposed in this paper to make the best use of graph latent topologies for fine-grained representation learning and discriminative feature extraction, namely FS-GRAL. Taking multi-functional elements and their preferences fully into consideration, FS-GRAL allows the nodes to appear in more than one subgraph with different contributions for message passing, so that the model is powerful enough in capturing those natural aggregations inherent in complex networks to achieve accurate representation learning. Meanwhile, on the basis of learned accurate representations, a two-level pooling strategy dominated by intra-subgraph node discarding is presented for feature extraction, which enables graph latent topology can be integrated into extracted discriminative features, and thus the coarsened graph is more representative for graph classification. Extensive experiments on real-world benchmarks demonstrate that our fuzzy overlapping community guided subgraph neural network is highly competitive in learning the accurate graph representation and its intra-subgraph dominated two-level pooling strategy promotes a more promising classification performance.

MedicalCLIP: Anomaly-Detection Domain Generalization with Asymmetric Constraints.

Medical data have unique specificity and professionalism, requiring substantial domain expertise for their annotation. Precise data annotation is essential for anomaly-detection tasks, making the training process complex. Domain generalization (DG) is an important approach to enhancing medical image anomaly detection (AD). This paper introduces a novel multimodal anomaly-detection framework called MedicalCLIP. MedicalCLIP utilizes multimodal data in anomaly-detection tasks and establishes irregular constraints within modalities for images and text. The key to MedicalCLIP lies in learning intramodal detailed representations, which are combined with text semantic-guided cross-modal contrastive learning, allowing the model to focus on semantic information while capturing more detailed information, thus achieving more fine-grained anomaly detection. MedicalCLIP relies on GPT prompts to generate text, reducing the demand for professional descriptions of medical data. Text construction for medical data helps to improve the generalization ability of multimodal models for anomaly-detection tasks. Additionally, during the text-image contrast-enhancement process, the model's ability to select and extract information from image data is improved. Through hierarchical contrastive loss, fine-grained representations are achieved in the image-representation process. MedicalCLIP has been validated on various medical datasets, showing commendable domain generalization performance in medical-data anomaly detection. Improvements were observed in both anomaly classification and segmentation metrics. In the anomaly classification (AC) task involving brain data, the method demonstrated a 2.81 enhancement in performance over the best existing approach.

Fine-Grained Cross-Modal Semantic Consistency in Natural Conservation Image Data from a Multi-Task Perspective.

Fine-grained representation is fundamental to species classification based on deep learning, and in this context, cross-modal contrastive learning is an effective method. The diversity of species coupled with the inherent contextual ambiguity of natural language poses a primary challenge in the cross-modal representation alignment of conservation area image data. Integrating cross-modal retrieval tasks with generation tasks contributes to cross-modal representation alignment based on contextual understanding. However, during the contrastive learning process, apart from learning the differences in the data itself, a pair of encoders inevitably learns the differences caused by encoder fluctuations. The latter leads to convergence shortcuts, resulting in poor representation quality and an inaccurate reflection of the similarity relationships between samples in the original dataset within the shared space of features. To achieve fine-grained cross-modal representation alignment, we first propose a residual attention network to enhance consistency during momentum updates in cross-modal encoders. Building upon this, we propose momentum encoding from a multi-task perspective as a bridge for cross-modal information, effectively improving cross-modal mutual information, representation quality, and optimizing the distribution of feature points within the cross-modal shared semantic space. By acquiring momentum encoding queues for cross-modal semantic understanding through multi-tasking, we align ambiguous natural language representations around the invariant image features of factual information, alleviating contextual ambiguity and enhancing model robustness. Experimental validation shows that our proposed multi-task perspective of cross-modal momentum encoders outperforms similar models on standardized image classification tasks and image-text cross-modal retrieval tasks on public datasets by up to 8% on the leaderboard, demonstrating the effectiveness of the proposed method. Qualitative experiments on our self-built conservation area image-text paired dataset show that our proposed method accurately performs cross-modal retrieval and generation tasks among 8142 species, proving its effectiveness on fine-grained cross-modal image-text conservation area image datasets.

MAFormer: A transformer network with multi-scale attention fusion for visual recognition

Vision Transformer and its variants have demonstrated great potential in various computer vision tasks. However conventional vision transformers often focus on global dependency at a coarse level, which results in a learning challenge on global relationships and fine-grained representation at a token level. In this paper, we introduce Multi-scale Attention Fusion into transformer (MAFormer), which explores local aggregation and global feature extraction in a dual-stream framework for visual recognition. We develop a simple but effective module to explore the full potential of transformers for visual representation by learning fine-grained and coarse-grained features at a token level and dynamically fusing them. Our Multi-scale Attention Fusion (MAF) block consists of: i) a local window attention branch that learns short-range interactions within windows, aggregating fine-grained local features; ii) global feature extraction through a novel Global Learning with Down-sampling (GLD) operation to efficiently capture long-range context information within the whole image; iii) a fusion module that self-explores the integration of both features via attention. Our MAFormer achieves state-of-the-art results on several common vision tasks. In particular, MAFormer-L achieves 85.9% Top-1 accuracy on ImageNet, surpassing CSWin-B and LV-ViT-L by 1.7% and 0.6% respectively. On MSCOCO, MAFormer outperforms the prior art CSWin by 1.7% mAPs on object detection and 1.4% on instance segmentation with similar-sized parameters. With the performance, MAFormer demonstrates the ability to generalize across various visual benchmarks and prospects as a general backbone for different self-supervised pre-training tasks in the future.

Explanations for combinatorial optimization problems

We introduce a representation for generating explanations for the outcomes of combinatorial optimization algorithms. The two key ideas are (A) to maintain fine-grained representations of the values manipulated by these algorithms and (B) to derive explanations from these representations through merge, filter, and aggregation operations. An explanation in our model presents essentially a high-level comparison of the solution to a problem with a hypothesized alternative, illuminating why the solution is better than the alternative. Our value representation results in explanations smaller than other dynamic program representations, such as traces. Based on a measure for the conciseness of explanations we demonstrate through a number of experiments that the explanations produced by our approach are small and scale well with problem size across a number of different applications.

An Analysis on Matching Mechanisms and Token Pruning for Late-interaction Models

With the development of pre-trained language models, the dense retrieval models have become promising alternatives to the traditional retrieval models that rely on exact match and sparse bag-of-words representations. Different from most dense retrieval models using a bi-encoder to encode each query or document into a dense vector, the recently proposed late-interaction multi-vector models (i.e., ColBERT and COIL) achieve state-of-the-art retrieval effectiveness by using all token embeddings to represent documents and queries and modeling their relevance with a sum-of-max operation. However, these fine-grained representations may cause unacceptable storage overhead for practical search systems. In this study, we systematically analyze the matching mechanism of these late-interaction models and show that the sum-of-max operation heavily relies on the co-occurrence signals and some important words in the document. Based on these findings, we then propose several simple document pruning methods to reduce the storage overhead and compare the effectiveness of different pruning methods on different late-interaction models. We also leverage query pruning methods to further reduce the retrieval latency. We conduct extensive experiments on both in-domain and out-domain datasets and show that some of the used pruning methods can significantly improve the efficiency of these late-interaction models without substantially hurting their retrieval effectiveness.