Yuchen Li

CL
h-index27
23papers
1,529citations
Novelty49%
AI Score45

23 Papers

0.8CLOct 21, 2022Code
EDUKG: a Heterogeneous Sustainable K-12 Educational Knowledge Graph

Bowen Zhao, Jiuding Sun, Bin Xu et al.

Web and artificial intelligence technologies, especially semantic web and knowledge graph (KG), have recently raised significant attention in educational scenarios. Nevertheless, subject-specific KGs for K-12 education still lack sufficiency and sustainability from knowledge and data perspectives. To tackle these issues, we propose EDUKG, a heterogeneous sustainable K-12 Educational Knowledge Graph. We first design an interdisciplinary and fine-grained ontology for uniformly modeling knowledge and resource in K-12 education, where we define 635 classes, 445 object properties, and 1314 datatype properties in total. Guided by this ontology, we propose a flexible methodology for interactively extracting factual knowledge from textbooks. Furthermore, we establish a general mechanism based on our proposed generalized entity linking system for EDUKG's sustainable maintenance, which can dynamically index numerous heterogeneous resources and data with knowledge topics in EDUKG. We further evaluate EDUKG to illustrate its sufficiency, richness, and variability. We publish EDUKG with more than 252 million entities and 3.86 billion triplets. Our code and data repository is now available at https://github.com/THU-KEG/EDUKG.

33.9ROMar 17, 2023
Motion Planning for Autonomous Driving: The State of the Art and Future Perspectives

Siyu Teng, Xuemin Hu, Peng Deng et al.

Intelligent vehicles (IVs) have gained worldwide attention due to their increased convenience, safety advantages, and potential commercial value. Despite predictions of commercial deployment by 2025, implementation remains limited to small-scale validation, with precise tracking controllers and motion planners being essential prerequisites for IVs. This paper reviews state-of-the-art motion planning methods for IVs, including pipeline planning and end-to-end planning methods. The study examines the selection, expansion, and optimization operations in a pipeline method, while it investigates training approaches and validation scenarios for driving tasks in end-to-end methods. Experimental platforms are reviewed to assist readers in choosing suitable training and validation strategies. A side-by-side comparison of the methods is provided to highlight their strengths and limitations, aiding system-level design choices. Current challenges and future perspectives are also discussed in this survey.

4.2CLJul 22, 2024Code
Promises and Pitfalls of Generative Masked Language Modeling: Theoretical Framework and Practical Guidelines

Yuchen Li, Alexandre Kirchmeyer, Aashay Mehta et al.

Autoregressive language models are the currently dominant paradigm for text generation, but they have some fundamental limitations that cannot be remedied by scale-for example inherently sequential and unidirectional generation. While alternate classes of models have been explored, we have limited mathematical understanding of their fundamental power and limitations. In this paper we focus on Generative Masked Language Models (GMLMs), a non-autoregressive paradigm in which we train a model to fit conditional probabilities of the data distribution via masking, which are subsequently used as inputs to a Markov Chain to draw samples from the model, These models empirically strike a promising speed-quality trade-off as each step can be typically parallelized by decoding the entire sequence in parallel. We develop a mathematical framework for analyzing and improving such models which sheds light on questions of sample complexity and inference speed and quality. Empirically, we adapt the T5 model for iteratively-refined parallel decoding, achieving 2-3x speedup in machine translation with minimal sacrifice in quality compared with autoregressive models. We run careful ablation experiments to give recommendations on key design choices, and make fine-grained observations on the common error modes in connection with our theory. Our mathematical analyses and empirical observations characterize both potentials and limitations of this approach, and can be applied to future works on improving understanding and performance of GMLMs. Our codes are released at https://github.com/google-research/google-research/tree/master/padir

31.6LGMar 7, 2023Code
How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding

Yuchen Li, Yuanzhi Li, Andrej Risteski

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and reasoning tasks -- but mathematical understanding is lagging substantially behind. Recent lines of work have begun studying representational aspects of this question: that is, the size/depth/complexity of attention-based networks to perform certain tasks. However, there is no guarantee the learning dynamics will converge to the constructions proposed. In our paper, we provide fine-grained mechanistic understanding of how transformers learn "semantic structure", understood as capturing co-occurrence structure of words. Precisely, we show, through a combination of mathematical analysis and experiments on Wikipedia data and synthetic data modeled by Latent Dirichlet Allocation (LDA), that the embedding layer and the self-attention layer encode the topical structure. In the former case, this manifests as higher average inner product of embeddings between same-topic words. In the latter, it manifests as higher average pairwise attention between same-topic words. The mathematical results involve several assumptions to make the analysis tractable, which we verify on data, and might be of independent interest as well.

4.3DSNov 2, 2022Code
Balancing Utility and Fairness in Submodular Maximization (Technical Report)

Yanhao Wang, Yuchen Li, Francesco Bonchi et al.

Submodular function maximization is a fundamental combinatorial optimization problem with plenty of applications -- including data summarization, influence maximization, and recommendation. In many of these problems, the goal is to find a solution that maximizes the average utility over all users, for each of whom the utility is defined by a monotone submodular function. However, when the population of users is composed of several demographic groups, another critical problem is whether the utility is fairly distributed across different groups. Although the \emph{utility} and \emph{fairness} objectives are both desirable, they might contradict each other, and, to the best of our knowledge, little attention has been paid to optimizing them jointly. To fill this gap, we propose a new problem called \emph{Bicriteria Submodular Maximization} (BSM) to balance utility and fairness. Specifically, it requires finding a fixed-size solution to maximize the utility function, subject to the value of the fairness function not being below a threshold. Since BSM is inapproximable within any constant factor, we focus on designing efficient instance-dependent approximation schemes. Our algorithmic proposal comprises two methods, with different approximation factors, obtained by converting a BSM instance into other submodular optimization problem instances. Using real-world and synthetic datasets, we showcase applications of our proposed methods in three submodular maximization problems: maximum coverage, influence maximization, and facility location.

20.5LGMar 29, 2022Code
Contrasting the landscape of contrastive and non-contrastive learning

Ashwini Pokle, Jinjin Tian, Yuchen Li et al.

A lot of recent advances in unsupervised feature learning are based on designing features which are invariant under semantic data augmentations. A common way to do this is contrastive learning, which uses positive and negative samples. Some recent works however have shown promising results for non-contrastive learning, which does not require negative samples. However, the non-contrastive losses have obvious "collapsed" minima, in which the encoders output a constant feature embedding, independent of the input. A folk conjecture is that so long as these collapsed solutions are avoided, the produced feature representations should be good. In our paper, we cast doubt on this story: we show through theoretical results and controlled experiments that even on simple data models, non-contrastive losses have a preponderance of non-collapsed bad minima. Moreover, we show that the training process does not avoid these minima.

2.6CVAug 12, 2022
SFF-DA: Sptialtemporal Feature Fusion for Detecting Anxiety Nonintrusively

Haimiao Mo, Yuchen Li, Shanlin Yang et al.

Early detection of anxiety is crucial for reducing the suffering of individuals with mental disorders and improving treatment outcomes. Utilizing an mHealth platform for anxiety screening can be particularly practical in improving screening efficiency and reducing costs. However, the effectiveness of existing methods has been hindered by differences in mobile devices used to capture subjects' physical and mental evaluations, as well as by the variability in data quality and small sample size problems encountered in real-world settings. To address these issues, we propose a framework with spatiotemporal feature fusion for detecting anxiety nonintrusively. We use a feature extraction network based on a 3D convolutional network and long short-term memory ("3DCNN+LSTM") to fuse the spatiotemporal features of facial behavior and noncontact physiology, which reduces the impact of uneven data quality. Additionally, we design a similarity assessment strategy to address the issue of deteriorating model accuracy due to small sample sizes. Our framework is validated with a crew dataset from the real world and two public datasets: the University of Burgundy Franche-Comté Psychophysiological (UBFC-Phys) dataset and the Smart Reasoning for Well-being at Home and at Work for Knowledge Work (SWELL-KW) dataset. The experimental results indicate that our framework outperforms the comparison methods.

3.9AINov 20, 2023
Web News Timeline Generation with Extended Task Prompting

Sha Wang, Yuchen Li, Hanhua Xiao et al.

The creation of news timeline is essential for a comprehensive and contextual understanding of events as they unfold over time. This approach aids in discerning patterns and trends that might be obscured when news is viewed in isolation. By organizing news in a chronological sequence, it becomes easier to track the development of stories, understand the interrelation of events, and grasp the broader implications of news items. This is particularly helpful in sectors like finance and insurance, where timely understanding of the event development-ranging from extreme weather to political upheavals and health crises-is indispensable for effective risk management. While traditional natural language processing (NLP) techniques have had some success, they often fail to capture the news with nuanced relevance that are readily apparent to domain experts, hindering broader industry integration. The advance of Large Language Models (LLMs) offers a renewed opportunity to tackle this challenge. However, direct prompting LLMs for this task is often ineffective. Our study investigates the application of an extended task prompting technique to assess past news relevance. We demonstrate that enhancing conventional prompts with additional tasks boosts their effectiveness on various news dataset, rendering news timeline generation practical for professional use. This work has been deployed as a publicly accessible browser extension which is adopted within our network.

2.7CLOct 31, 2025
Cognitive Alignment in Personality Reasoning: Leveraging Prototype Theory for MBTI Inference

Haoyuan Li, Yuanbo Tong, Yuchen Li et al.

Personality recognition from text is typically cast as hard-label classification, which obscures the graded, prototype-like nature of human personality judgments. We present ProtoMBTI, a cognitively aligned framework for MBTI inference that operationalizes prototype theory within an LLM-based pipeline. First, we construct a balanced, quality-controlled corpus via LLM-guided multi-dimensional augmentation (semantic, linguistic, sentiment). Next, we LoRA-fine-tune a lightweight (<=2B) encoder to learn discriminative embeddings and to standardize a bank of personality prototypes. At inference, we retrieve top-k prototypes for a query post and perform a retrieve--reuse--revise--retain cycle: the model aggregates prototype evidence via prompt-based voting, revises when inconsistencies arise, and, upon correct prediction, retains the sample to continually enrich the prototype library. Across Kaggle and Pandora benchmarks, ProtoMBTI improves over baselines on both the four MBTI dichotomies and the full 16-type task, and exhibits robust cross-dataset generalization. Our results indicate that aligning the inference process with psychological prototype reasoning yields gains in accuracy, interpretability, and transfer for text-based personality modeling.

5.8AIFeb 20, 2025
HPS: Hard Preference Sampling for Human Preference Alignment

Xiandong Zou, Wanyu Lin, Yuchen Li et al.

Aligning Large Language Model (LLM) responses with human preferences is vital for building safe and controllable AI systems. While preference optimization methods based on Plackett-Luce (PL) and Bradley-Terry (BT) models have shown promise, they face challenges such as poor handling of harmful content, inefficient use of dispreferred responses, and, specifically for PL, high computational costs. To address these issues, we propose Hard Preference Sampling (HPS), a novel framework for robust and efficient human preference alignment. HPS introduces a training loss that prioritizes the most preferred response while rejecting all dispreferred and harmful ones. It emphasizes "hard" dispreferred responses -- those closely resembling preferred ones -- to enhance the model's rejection capabilities. By leveraging a single-sample Monte Carlo sampling strategy, HPS reduces computational overhead while maintaining alignment quality. Theoretically, HPS improves sample efficiency over existing PL methods and maximizes the reward margin between preferred and dispreferred responses, ensuring clearer distinctions. Experiments on HH-RLHF and PKU-Safety datasets validate HPS's effectiveness, achieving comparable BLEU and reward scores while greatly improving reward margins and thus reducing harmful content generation.

11.8CVMay 21, 2025
GS2E: Gaussian Splatting is an Effective Data Generator for Event Stream Generation

Yuchen Li, Chaoran Feng, Zhenyu Tang et al.

We introduce GS2E (Gaussian Splatting to Event), a large-scale synthetic event dataset for high-fidelity event vision tasks, captured from real-world sparse multi-view RGB images. Existing event datasets are often synthesized from dense RGB videos, which typically lack viewpoint diversity and geometric consistency, or depend on expensive, difficult-to-scale hardware setups. GS2E overcomes these limitations by first reconstructing photorealistic static scenes using 3D Gaussian Splatting, and subsequently employing a novel, physically-informed event simulation pipeline. This pipeline generally integrates adaptive trajectory interpolation with physically-consistent event contrast threshold modeling. Such an approach yields temporally dense and geometrically consistent event streams under diverse motion and lighting conditions, while ensuring strong alignment with underlying scene structures. Experimental results on event-based 3D reconstruction demonstrate GS2E's superior generalization capabilities and its practical value as a benchmark for advancing event vision research.

1.8LGFeb 9, 2022
Improving greedy core-set configurations for active learning with uncertainty-scaled distances

Yuchen Li, Frank Rudzicz

We scale perceived distances of the core-set algorithm by a factor of uncertainty and search for low-confidence configurations, finding significant improvements in sample efficiency across CIFAR10/100 and SVHN image classification, especially in larger acquisition sizes. We show the necessity of our modifications and explain how the improvement is due to a probabilistic quadratic speed-up in the convergence of core-set loss, under assumptions about the relationship of model uncertainty and misclassification.

6.5LGJun 24, 2021
Privacy Threats Analysis to Secure Federated Learning

Yuchen Li, Yifan Bao, Liyao Xiang et al.

Federated learning is emerging as a machine learning technique that trains a model across multiple decentralized parties. It is renowned for preserving privacy as the data never leaves the computational devices, and recent approaches further enhance its privacy by hiding messages transferred in encryption. However, we found that despite the efforts, federated learning remains privacy-threatening, due to its interactive nature across different parties. In this paper, we analyze the privacy threats in industrial-level federated learning frameworks with secure computation, and reveal such threats widely exist in typical machine learning models such as linear regression, logistic regression and decision tree. For the linear and logistic regression, we show through theoretical analysis that it is possible for the attacker to invert the entire private input of the victim, given very few information. For the decision tree model, we launch an attack to infer the range of victim's private inputs. All attacks are evaluated on popular federated learning frameworks and real-world datasets.

31.5CLJun 3, 2021
The Limitations of Limited Context for Constituency Parsing

Yuchen Li, Andrej Risteski

Incorporating syntax into neural approaches in NLP has a multitude of practical and scientific benefits. For instance, a language model that is syntax-aware is likely to be able to produce better samples; even a discriminative model like BERT with a syntax module could be used for core NLP tasks like unsupervised syntactic parsing. Rapid progress in recent years was arguably spurred on by the empirical success of the Parsing-Reading-Predict architecture of (Shen et al., 2018a), later simplified by the Order Neuron LSTM of (Shen et al., 2019). Most notably, this is the first time neural approaches were able to successfully perform unsupervised syntactic parsing (evaluated by various metrics like F-1 score). However, even heuristic (much less fully mathematical) understanding of why and when these architectures work is lagging severely behind. In this work, we answer representational questions raised by the architectures in (Shen et al., 2018a, 2019), as well as some transition-based syntax-aware language models (Dyer et al., 2016): what kind of syntactic structure can current neural approaches to syntax represent? Concretely, we ground this question in the sandbox of probabilistic context-free-grammars (PCFGs), and identify a key aspect of the representational power of these approaches: the amount and directionality of context that the predictor has access to when forced to make parsing decision. We show that with limited context (either bounded, or unidirectional), there are PCFGs, for which these approaches cannot represent the max-likelihood parse; conversely, if the context is unlimited, they can represent the max-likelihood parse of any PCFG.

11.9OCDec 7, 2020Code
Block majorization-minimization with diminishing radius for constrained nonsmooth nonconvex optimization

Hanbaek Lyu, Yuchen Li

Block majorization-minimization (BMM) is a simple iterative algorithm for constrained nonconvex optimization that sequentially minimizes majorizing surrogates of the objective function in each block while the others are held fixed. BMM entails a large class of optimization algorithms such as block coordinate descent and its proximal-point variant, expectation-minimization, and block projected gradient descent. We first establish that for general constrained nonsmooth nonconvex optimization, BMM with $ρ$-strongly convex and $L_g$-smooth surrogates can produce an $ε$-approximate first-order optimal point within $\widetilde{O}((1+L_g+ρ^{-1})ε^{-2})$ iterations and asymptotically converges to the set of first-order optimal points. Next, we show that BMM combined with trust-region methods with diminishing radius has an improved complexity of $\widetilde{O}((1+L_g) ε^{-2})$, independent of the inverse strong convexity parameter $ρ^{-1}$, allowing improved theoretical and practical performance with `flat' surrogates. Our results hold robustly even when the convex sub-problems are solved as long as the optimality gaps are summable. Central to our analysis is a novel continuous first-order optimality measure, by which we bound the worst-case sub-optimality in each iteration by the first-order improvement the algorithm makes. We apply our general framework to obtain new results on various algorithms such as the celebrated multiplicative update algorithm for nonnegative matrix factorization by Lee and Seung, regularized nonnegative tensor decomposition, and the classical block projected gradient descent algorithm. Lastly, we numerically demonstrate that the additional use of diminishing radius can improve the convergence rate of BMM in many instances.

5.1SIJul 28, 2020Code
Efficient Sampling Algorithms for Approximate Temporal Motif Counting (Extended Version)

Jingjing Wang, Yanhao Wang, Wenjun Jiang et al.

A great variety of complex systems ranging from user interactions in communication networks to transactions in financial markets can be modeled as temporal graphs, which consist of a set of vertices and a series of timestamped and directed edges. Temporal motifs in temporal graphs are generalized from subgraph patterns in static graphs which take into account edge orderings and durations in addition to structures. Counting the number of occurrences of temporal motifs is a fundamental problem for temporal network analysis. However, existing methods either cannot support temporal motifs or suffer from performance issues. In this paper, we focus on approximate temporal motif counting via random sampling. We first propose a generic edge sampling (ES) algorithm for estimating the number of instances of any temporal motif. Furthermore, we devise an improved EWS algorithm that hybridizes edge sampling with wedge sampling for counting temporal motifs with 3 vertices and 3 edges. We provide comprehensive analyses of the theoretical bounds and complexities of our proposed algorithms. Finally, we conduct extensive experiments on several real-world datasets, and the results show that our ES and EWS algorithms have higher efficiency, better accuracy, and greater scalability than the state-of-the-art sampling method for temporal motif counting.

1.0CLSep 4, 2019Code
Discovering Hypernymy in Text-Rich Heterogeneous Information Network by Exploiting Context Granularity

Yu Shi, Jiaming Shen, Yuchen Li et al.

Text-rich heterogeneous information networks (text-rich HINs) are ubiquitous in real-world applications. Hypernymy, also known as is-a relation or subclass-of relation, lays in the core of many knowledge graphs and benefits many downstream applications. Existing methods of hypernymy discovery either leverage textual patterns to extract explicitly mentioned hypernym-hyponym pairs, or learn a distributional representation for each term of interest based its context. These approaches rely on statistical signals from the textual corpus, and their effectiveness would therefore be hindered when the signals from the corpus are not sufficient for all terms of interest. In this work, we propose to discover hypernymy in text-rich HINs, which can introduce additional high-quality signals. We develop a new framework, named HyperMine, that exploits multi-granular contexts and combines signals from both text and network without human labeled data. HyperMine extends the definition of context to the scenario of text-rich HIN. For example, we can define typed nodes and communities as contexts. These contexts encode signals of different granularities and we feed them into a hypernymy inference model. HyperMine learns this model using weak supervision acquired based on high-precision textual patterns. Extensive experiments on two large real-world datasets demonstrate the effectiveness of HyperMine and the utility of modeling context granularity. We further show a case study that a high-quality taxonomy can be generated solely based on the hypernymy discovered by HyperMine.

1.0LGJun 24, 2019
Variations on the Chebyshev-Lagrange Activation Function

Yuchen Li, Frank Rudzicz, Jekaterina Novikova

We seek to improve the data efficiency of neural networks and present novel implementations of parameterized piece-wise polynomial activation functions. The parameters are the y-coordinates of n+1 Chebyshev nodes per hidden unit and Lagrangian interpolation between the nodes produces the polynomial on [-1, 1]. We show results for different methods of handling inputs outside [-1, 1] on synthetic datasets, finding significant improvements in capacity of expression and accuracy of interpolation in models that compute some form of linear extrapolation from either ends. We demonstrate competitive or state-of-the-art performance on the classification of images (MNIST and CIFAR-10) and minimally-correlated vectors (DementiaBank) when we replace ReLU or tanh with linearly extrapolated Chebyshev-Lagrange activations in deep residual architectures.

2.3DSMay 9, 2019Code
Coresets for Minimum Enclosing Balls over Sliding Windows

Yanhao Wang, Yuchen Li, Kian-Lee Tan

\emph{Coresets} are important tools to generate concise summaries of massive datasets for approximate analysis. A coreset is a small subset of points extracted from the original point set such that certain geometric properties are preserved with provable guarantees. This paper investigates the problem of maintaining a coreset to preserve the minimum enclosing ball (MEB) for a sliding window of points that are continuously updated in a data stream. Although the problem has been extensively studied in batch and append-only streaming settings, no efficient sliding-window solution is available yet. In this work, we first introduce an algorithm, called AOMEB, to build a coreset for MEB in an append-only stream. AOMEB improves the practical performance of the state-of-the-art algorithm while having the same approximation ratio. Furthermore, using AOMEB as a building block, we propose two novel algorithms, namely SWMEB and SWMEB+, to maintain coresets for MEB over the sliding window with constant approximation ratios. The proposed algorithms also support coresets for MEB in a reproducing kernel Hilbert space (RKHS). Finally, extensive experiments on real-world and synthetic datasets demonstrate that SWMEB and SWMEB+ achieve speedups of up to four orders of magnitude over the state-of-the-art batch algorithm while providing coresets for MEB with rather small errors compared to the optimal ones.

1.5CLJan 23, 2019
Context-Sensitive Malicious Spelling Error Correction

Hongyu Gong, Yuchen Li, Suma Bhat et al.

Misspelled words of the malicious kind work by changing specific keywords and are intended to thwart existing automated applications for cyber-environment control such as harassing content detection on the Internet and email spam detection. In this paper, we focus on malicious spelling correction, which requires an approach that relies on the context and the surface forms of targeted keywords. In the context of two applications--profanity detection and email spam detection--we show that malicious misspellings seriously degrade their performance. We then propose a context-sensitive approach for malicious spelling correction using word embeddings and demonstrate its superior performance compared to state-of-the-art spell checkers.

2.2LGNov 20, 2018Code
ChainGAN: A sequential approach to GANs

Safwan Hossain, Kiarash Jamali, Yuchen Li et al.

We propose a new architecture and training methodology for generative adversarial networks. Current approaches attempt to learn the transformation from a noise sample to a generated data sample in one shot. Our proposed generator architecture, called $\textit{ChainGAN}$, uses a two-step process. It first attempts to transform a noise vector into a crude sample, similar to a traditional generator. Next, a chain of networks, called $\textit{editors}$, attempt to sequentially enhance this sample. We train each of these units independently, instead of with end-to-end backpropagation on the entire chain. Our model is robust, efficient, and flexible as we can apply it to various network architectures. We provide rationale for our choices and experimentally evaluate our model, achieving competitive results on several datasets.

1.7CVNov 18, 2018Code
DeepConsensus: using the consensus of features from multiple layers to attain robust image classification

Yuchen Li, Safwan Hossain, Kiarash Jamali et al.

We consider a classifier whose test set is exposed to various perturbations that are not present in the training set. These test samples still contain enough features to map them to the same class as their unperturbed counterpart. Current architectures exhibit rapid degradation of accuracy when trained on standard datasets but then used to classify perturbed samples of that data. To address this, we present a novel architecture named DeepConsensus that significantly improves generalization to these test-time perturbations. Our key insight is that deep neural networks should directly consider summaries of low and high level features when making classifications. Existing convolutional neural networks can be augmented with DeepConsensus, leading to improved resistance against large and small perturbations on MNIST, EMNIST, FashionMNIST, CIFAR10 and SVHN datasets.

6.6DSJun 15, 2017Code
Efficient Representative Subset Selection over Sliding Windows

Yanhao Wang, Yuchen Li, Kian-Lee Tan

Representative subset selection (RSS) is an important tool for users to draw insights from massive datasets. Existing literature models RSS as the submodular maximization problem to capture the "diminishing returns" property of the representativeness of selected subsets, but often only has a single constraint (e.g., cardinality), which limits its applications in many real-world problems. To capture the data recency issue and support different types of constraints, we formulate dynamic RSS in data streams as maximizing submodular functions subject to general $d$-knapsack constraints (SMDK) over sliding windows. We propose a \textsc{KnapWindow} framework (KW) for SMDK. KW utilizes the \textsc{KnapStream} algorithm (KS) for SMDK in append-only streams as a subroutine. It maintains a sequence of checkpoints and KS instances over the sliding window. Theoretically, KW is $\frac{1-\varepsilon}{1+d}$-approximate for SMDK. Furthermore, we propose a \textsc{KnapWindowPlus} framework (KW$^{+}$) to improve upon KW. KW$^{+}$ builds an index \textsc{SubKnapChk} to manage the checkpoints and KS instances. \textsc{SubKnapChk} deletes a checkpoint whenever it can be approximated by its successors. By keeping much fewer checkpoints, KW$^{+}$ achieves higher efficiency than KW while still guaranteeing a $\frac{1-\varepsilon'}{2+2d}$-approximate solution for SMDK. Finally, we evaluate the efficiency and solution quality of KW and KW$^{+}$ in real-world datasets. The experimental results demonstrate that KW achieves more than two orders of magnitude speedups over the batch baseline and preserves high-quality solutions for SMDK over sliding windows. KW$^{+}$ further runs 5-10 times faster than KW while providing solutions with equivalent or even better utilities.