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Ruiwen Li

Publications and source records attributed to Ruiwen Li.

17 recordsLinked to original sources
arXiv2026

On the denseness of distal points

We give an answer to a question of Xu and Ye (Disjointness with all minimal systems under group actions, to appear in Israel J. Math., arxiv:2212.07830) on the denseness of distal points in the Bernoulli shift $2^G$ for a countable discrete group $G$. For a related but stronger notion of almost automorphic points, we answer the similar question by showing that the corresponding collection of the groups coincides with maximal almost periodic ones. These characterizations allow us to construct 2-step nilpotent groups for which the answers to the Xu-Ye question differ. In search for an intrinsic answer to the Xu-Ye question, we introduce a notion of point-distal radical for a countable discrete group and show that a necessary condition is for the point-distal radical to be trivial. Finally, we consider some related questions, and show that the collection of all countable groups $G$ for which the set of distal points is dense in $2^G$ is closed under finite-index extension, and that the collection of countable groups $G$ for which the constant sequences are the only distal (almost automorphic) points coincides with the minimally almost periodic ones.

math.DS↗
arXiv2026

Orbit equivalence of Cantor minimal systems

In this paper we study the descriptive complexity of the topological orbit equvalence relation for some Borel classes of Cantor minimal systems. Specifically, we study the Borel class of all Cantor minimal systems with only finitely many ergodic measures, and show that the orbit equivalence for this class is Borel bireducible with the equivalence relation $=^+$. We prove the same for the subclass of regular $\{0, 1\}$-Toeplitz subshifts or that of the uniquely ergodic minimal subshifts. We also study the orbit equivalence for the Borel class of minimal subshifts of finite topological rank. Denote by $R_n$ the orbit equivalence for minimal subshifts of topological rank $n\geq 2$. We prove that for any $n\geq 2$, $R_n$ is virtually countable, i.e., Borel reducible to a countable Borel equivalence relation. Moreover, $R_2$ is virtually amenable. On the other hand, $R_n$ is not smooth when $n\geq 2$, is not virtually hyperfinite when $n\geq 4$, and is not virtually treeable when $n\geq 5$. For any $n\geq 2$, our contructions yield uniquely ergodic minimal subshifts of topological rank exactly $n$.

math.DS↗
arXiv2025

Toeplitz subshifts of finite rank

In this paper we study some basic problems about Toeplitz subshifts of finite topological rank. We define the notion of a strong Toeplitz subshift of finite rank $K$ by combining the characterizations of Toeplitz-ness and of finite topological rank $K$ from the point of view of the Bratteli--Vershik representation or from the $\mathcal{S}$-adic point of view. The characterization problem asks if for every $K\geq 2$, every Toeplitz subshift of topological rank $K$ is a strong Toeplitz subshift of rank $K$. We give a negative answer to the characterization problem by constructing a Toeplitz subshift of topological rank $2$ which fails to be a strong Toeplitz subshift of rank $2$. However, we show that the set of all strong Toeplitz subshifts of finite rank is generic in the space of all infinite minimal subshifts. In the second part we consider several classification problems for Toeplitz subshifts of topological rank $2$ from the point of view of descriptive set theory. We completely determine the complexity of the conjugacy problem, the flip conjugacy problem, and the bi-factor problem by showing that, as equivalence relations, they are hyperfinite and not smooth. We also consider the inverse problem for all Toeplitz subshifts. We give a criterion for when a Toeplitz subshift is conjugate to its own inverse, and use it to show that the set of all such Toeplitz subshifts is a meager set in the space of all infinite minimal subshifts. Finally, we show that the automorphism group of any Toeplitz subshift of finite rank is isomorphic to $\mathbb{Z}\oplus C$ for some finite cyclic group $C$, and for every nontrivial finite cyclic group $C$, $\mathbb{Z}\oplus C$ can be realized as the isomorphism type of an automorphism group of a strong Toeplitz subshift of finite rank greater than $2$.

math.DS↗
arXiv2024

Extremely amenable automorphism groups of countable structures

In this paper we address the question: How many pairwise non-isomorphic extremely amenable groups are there which are separable metrizable or even Polish? We show that there are continuum many such groups. In fact we construct continuum many pairwise non-isomorphic extremely amenable groups as automorphism groups of countable structures. We also consider this classification problem from the point of view of descriptive set theory by showing that the class of all extremely amenable closed subgroups of $S_\infty$ is Borel and their isomorphism relation is more complex than any isomorphism relation of countable structures in the Borel reducibility hierarchy.

math.LO↗
arXiv2024

Performance analysis of satellite-terrestrial integrated radio access networks based on stochastic geometry

To enhance coverage and improve service continuity, satellite-terrestrial integrated radio access network (STIRAN) has been seen as an essential trend in the development of 6G. However, there is still a lack of theoretical analysis on its coverage performance. To fill this gap, we first establish a system model to characterize a typical scenario where low-earth-orbit (LEO) satellites and terrestrial base stations are both deployed. Then, stochastic geometry is utilized to analyze the downlink coverage probability under the setting of shared frequency and distinct frequencies. Specifically, we derive mathematical expressions for the distances distribution from the serving station to the typical user and the associated probability based on the maximum bias power selection strategy (Max-BPR). Taking into account real-world satellite antenna beamforming patterns in two system scenarios, we derive the downlink coverage probabilities in terms of parameters such as base station density and orbital inclination. Finally, the correctness of the theoretical derivations is verified through experimental simulations, and the influence of network design parameters on the downlink coverage probability is analyzed.

cs.IT↗
arXiv2023

Segment Anything Model (SAM) Enhanced Pseudo Labels for Weakly Supervised Semantic Segmentation

Weakly supervised semantic segmentation (WSSS) aims to bypass the need for laborious pixel-level annotation by using only image-level annotation. Most existing methods rely on Class Activation Maps (CAM) to derive pixel-level pseudo-labels and use them to train a fully supervised semantic segmentation model. Although these pseudo-labels are class-aware, indicating the coarse regions for particular classes, they are not object-aware and fail to delineate accurate object boundaries. To address this, we introduce a simple yet effective method harnessing the Segment Anything Model (SAM), a class-agnostic foundation model capable of producing fine-grained instance masks of objects, parts, and subparts. We use CAM pseudo-labels as cues to select and combine SAM masks, resulting in high-quality pseudo-labels that are both class-aware and object-aware. Our approach is highly versatile and can be easily integrated into existing WSSS methods without any modification. Despite its simplicity, our approach shows consistent gain over the state-of-the-art WSSS methods on both PASCAL VOC and MS-COCO datasets.

cs.CV↗
arXiv2023

Subshifts of finite symbolic rank

The definition of subshifts of finite symbolic rank is motivated by the finite rank measure-preserving transformations which have been extensively studied in ergodic theory. In this paper we study subshifts of finite symbolic rank as essentially minimal Cantor systems. We show that minimal subshifts of finite symbolic rank have finite topological rank, and conversely, every minimal Cantor system of finite topological rank is either an odometer or conjugate to a minimal subshift of finite symbolic rank. We characterize the class of all minimal Cantor systems conjugate to a rank-$1$ subshift and show that it is dense but not generic in the Polish space of all minimal Cantor systems. Within some different Polish coding spaces of subshifts we also show that the rank-1 subshifts are dense but not generic. Finally we study topological factors of minimal subshifts of finite symbolic rank. We show that every infinite odometer and every irrational rotation is the maximal equicontinuous factor of a minimal subshift of symbolic rank $2$, and that a subshift factor of a minimal subshift of finite symbolic rank has finite symbolic rank.

math.DS↗
arXiv2022

ExCon: Explanation-driven Supervised Contrastive Learning for Image Classification

Contrastive learning has led to substantial improvements in the quality of learned embedding representations for tasks such as image classification. However, a key drawback of existing contrastive augmentation methods is that they may lead to the modification of the image content which can yield undesired alterations of its semantics. This can affect the performance of the model on downstream tasks. Hence, in this paper, we ask whether we can augment image data in contrastive learning such that the task-relevant semantic content of an image is preserved. For this purpose, we propose to leverage saliency-based explanation methods to create content-preserving masked augmentations for contrastive learning. Our novel explanation-driven supervised contrastive learning (ExCon) methodology critically serves the dual goals of encouraging nearby image embeddings to have similar content and explanation. To quantify the impact of ExCon, we conduct experiments on the CIFAR-100 and the Tiny ImageNet datasets. We demonstrate that ExCon outperforms vanilla supervised contrastive learning in terms of classification, explanation quality, adversarial robustness as well as probabilistic calibration in the context of distributional shift.

cs.CV↗
arXiv2022

Defending against Co-residence Attack in Energy-Efficient Cloud: An Optimization based Real-time Secure VM Allocation Strategy

Resource sharing among users serves as the foundation of cloud computing, which, however, may also cause vulnerabilities to diverse co-residence attacks launched by malicious virtual machines (VM) residing in the same physical server with the victim VMs. In this paper, we aim to defend against such co-residence attacks through a secure, workload-balanced, and energy-efficient VM allocation strategy. Specifically, we model the problem as an optimization problem by quantifying and minimizing three key factors: (1) the security risks, (2) the power consumption and (3) the unbalanced workloads among different physical servers. Furthermore, this work considers a realistic environmental setting by assuming a random number of VMs from different users arriving at random timings, which requires the optimization solution to be continuously evolving. As the optimization problem is NP-hard, we propose to first cluster VMs in time windows, and further adopt the Ant Colony Optimization (ACO) algorithm to identify the optimal allocation strategy for each time window. Comprehensive experimental results based on real world cloud traces validates the effectiveness of the proposed scheme.

cs.DC↗
arXiv2022

TransCAM: Transformer Attention-based CAM Refinement for Weakly Supervised Semantic Segmentation

Weakly supervised semantic segmentation (WSSS) with only image-level supervision is a challenging task. Most existing methods exploit Class Activation Maps (CAM) to generate pixel-level pseudo labels for supervised training. However, due to the local receptive field of Convolution Neural Networks (CNN), CAM applied to CNNs often suffers from partial activation -- highlighting the most discriminative part instead of the entire object area. In order to capture both local features and global representations, the Conformer has been proposed to combine a visual transformer branch with a CNN branch. In this paper, we propose TransCAM, a Conformer-based solution to WSSS that explicitly leverages the attention weights from the transformer branch of the Conformer to refine the CAM generated from the CNN branch. TransCAM is motivated by our observation that attention weights from shallow transformer blocks are able to capture low-level spatial feature similarities while attention weights from deep transformer blocks capture high-level semantic context. Despite its simplicity, TransCAM achieves a new state-of-the-art performance of 69.3% and 69.6% on the respective PASCAL VOC 2012 validation and test sets, showing the effectiveness of transformer attention-based refinement of CAM for WSSS.

cs.CV↗
arXiv2021

Online Continual Learning in Image Classification: An Empirical Survey

Online continual learning for image classification studies the problem of learning to classify images from an online stream of data and tasks, where tasks may include new classes (class incremental) or data nonstationarity (domain incremental). One of the key challenges of continual learning is to avoid catastrophic forgetting (CF), i.e., forgetting old tasks in the presence of more recent tasks. Over the past few years, many methods and tricks have been introduced to address this problem, but many have not been fairly and systematically compared under a variety of realistic and practical settings. To better understand the relative advantages of various approaches and the settings where they work best, this survey aims to (1) compare state-of-the-art methods such as MIR, iCARL, and GDumb and determine which works best at different experimental settings; (2) determine if the best class incremental methods are also competitive in domain incremental setting; (3) evaluate the performance of 7 simple but effective trick such as "review" trick and nearest class mean (NCM) classifier to assess their relative impact. Regarding (1), we observe iCaRL remains competitive when the memory buffer is small; GDumb outperforms many recently proposed methods in medium-size datasets and MIR performs the best in larger-scale datasets. For (2), we note that GDumb performs quite poorly while MIR -- already competitive for (1) -- is also strongly competitive in this very different but important setting. Overall, this allows us to conclude that MIR is overall a strong and versatile method across a wide variety of settings. For (3), we find that all 7 tricks are beneficial, and when augmented with the "review" trick and NCM classifier, MIR produces performance levels that bring online continual learning much closer to its ultimate goal of matching offline training.

cs.LG↗
arXiv2021

EDDA: Explanation-driven Data Augmentation to Improve Explanation Faithfulness

Recent years have seen the introduction of a range of methods for post-hoc explainability of image classifier predictions. However, these post-hoc explanations may not always be faithful to classifier predictions, which poses a significant challenge when attempting to debug models based on such explanations. To this end, we seek a methodology that can improve the faithfulness of an explanation method with respect to model predictions which does not require ground truth explanations. We achieve this through a novel explanation-driven data augmentation (EDDA) technique that augments the training data with occlusions inferred from model explanations; this is based on the simple motivating principle that \emph{if} the explainer is faithful to the model \emph{then} occluding salient regions for the model prediction should decrease the model confidence in the prediction, while occluding non-salient regions should not change the prediction. To verify that the proposed augmentation method has the potential to improve faithfulness, we evaluate EDDA using a variety of datasets and classification models. We demonstrate empirically that our approach leads to a significant increase of faithfulness, which can facilitate better debugging and successful deployment of image classification models in real-world applications.

cs.LG↗
arXiv2021

Supervised Contrastive Replay: Revisiting the Nearest Class Mean Classifier in Online Class-Incremental Continual Learning

Online class-incremental continual learning (CL) studies the problem of learning new classes continually from an online non-stationary data stream, intending to adapt to new data while mitigating catastrophic forgetting. While memory replay has shown promising results, the recency bias in online learning caused by the commonly used Softmax classifier remains an unsolved challenge. Although the Nearest-Class-Mean (NCM) classifier is significantly undervalued in the CL community, we demonstrate that it is a simple yet effective substitute for the Softmax classifier. It addresses the recency bias and avoids structural changes in the fully-connected layer for new classes. Moreover, we observe considerable and consistent performance gains when replacing the Softmax classifier with the NCM classifier for several state-of-the-art replay methods. To leverage the NCM classifier more effectively, data embeddings belonging to the same class should be clustered and well-separated from those with a different class label. To this end, we contribute Supervised Contrastive Replay (SCR), which explicitly encourages samples from the same class to cluster tightly in embedding space while pushing those of different classes further apart during replay-based training. Overall, we observe that our proposed SCR substantially reduces catastrophic forgetting and outperforms state-of-the-art CL methods by a significant margin on a variety of datasets.

cs.LG↗
arXiv2020

On finite spacer rank for words and subshifts

We define a notion of rank for words and subshifts that we call spacer rank, extending the notion of rank-one symbolic shifts of Gao and Hill. We construct infinite words of each finite spacer rank, of unbounded spacer rank, and show there exist words that do not have a spacer rank construction. We consider words that are fixed points of substitutions and give explicit conditions for the word to have an at most spacer rank two construction, and not to be rank one. We prove that finite spacer rank subshifts have topological entropy zero, and that there are zero entropy subshifts not defined by a word with a finite spacer rank construction. We also study shift systems associated with infinite words, including those associated to Sturmian sequences, which we show are spacer rank-two systems.

math.DS↗