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Shicheng Wang

Publications and source records attributed to Shicheng Wang.

At least 19 recordsLinked to original sources
arXiv2026

Denoising Implicit Feedback for Cold-start Recommendation

Implicit feedback is widely used in recommender systems due to its accessibility and generality, yet it usually presents noisy samples (e.g., clickbait, position bias). Meanwhile, recommenders inevitably face the item cold-start problem due to the continuous influx of new items. We identify that cold items are more prone to noisy samples due to the aforementioned factors, and researchers often overlook the significance of denoising implicit feedback for cold items. Previous denoising studies usually identify noisy samples based on heuristic patterns, such as higher loss values, and mitigate noise through sample selection or re-weighting. However, these methods have limited adaptability and are ineffective in cold-start scenarios. To achieve denoising implicit feedback for cold-start recommendation, we propose a model-agnostic denoising method called DIF. First, user preferences for content remain stable, which allows us to infer pseudo-labels indicating whether a user is interested in a cold item through content-similar warm items. Furthermore, to improve pseudo-label accuracy, we model the confidence of pseudo-labels based on the content similarity between the cold item and warm items, and then aggregate multiple pseudo-labels for each sample. Finally, we explicitly estimate the uncertainty of the noisy sample label by considering its relative entropy and the cold-start status of the item, which adaptively guides the role of pseudo-labels to correct the noisy labels at the sample level. DIF's superiority is supported by both theoretical justification and extensive experiments on real-world datasets. The method has been deployed on a billion-user scale short video application Kuaishou and has significantly improved various commercial metrics within cold-start scenarios.

cs.AI↗
arXiv2026

Flexible exponent of geometric 3-manifolds and Legendrian maps of Seifert spaces

A classical question in quantitative topology is to bound the mapping degree $\operatorname{deg}(f)$ in terms of its Lipchitz constant $\operatorname{Lip}(f)$. For a closed, oriented manifold $M$, the flexible exponent $α(M)$ is the infimum of $α\geq 0$ such that $|\operatorname{deg} f|\leq C(\operatorname{Lip} f)^α$ holds for all differentiable map $f:M\to M$. The flexible exponent measures how effectively a manifold can wrap itself through self-maps. For geometric 3-manifolds $M$ in the sense of Thurston, we give the complete result for $α(M)$: \[ α(M)= \begin{cases} 3 & M \text{ modeled on } \mathbb S^3,\mathbb E^3,\mathbb S^2\times\mathbb E^1,\\ \frac83 & M \text{ modeled on Nil},\\ 2 & M \text{ modeled on Sol},\\ 1 & M \text{ modeled on }\mathbb H^2\times\mathbb E^1,\\ 0 & M \text{ modeled on } \mathbb H^3,\widetilde{\rm SL_2}. \end{cases} \] To prove $α(M)=8/3$ for Nil 3-manifold $M$, we construct the so-called Legendrian map: a smooth self-map $f: M\to M$ such that $f$ is homotopic to the identity and $f$ maps all $S^1$-fibers into the orthogonal contact plane field simultaneously. Moreover, we prove that any Legendrian map must not be a diffeomorphism.

math.GT↗
arXiv2025

Representation Quantization for Collaborative Filtering Augmentation

As the core algorithm in recommendation systems, collaborative filtering (CF) algorithms inevitably face the problem of data sparsity. Since CF captures similar users and items for recommendations, it is effective to augment the lacking user-user and item-item homogeneous linkages. However, existing methods are typically limited to connecting through overlapping interacted neighbors or through similar attributes and contents. These approaches are constrained by coarse-grained, sparse attributes and fail to effectively extract behavioral characteristics jointly from interaction sequences and attributes. To address these challenges, we propose a novel two-stage collaborative recommendation algorithm, DQRec: Decomposition-based Quantized Variational AutoEncoder (DQ-VAE) for Recommendation. DQRec augments features and homogeneous linkages by extracting the behavior characteristics jointly from interaction sequences and attributes, namely patterns, such as user multi-aspect interests. Inspired by vector quantization (VQ) technology, we propose a new VQ algorithm, DQ-VAE, which decomposes the pre-trained representation embeddings into distinct dimensions, and quantize them to generates semantic IDs. We utilize the generated semantic IDs as the extracted patterns mentioned above. By integrating these semantic ID patterns into the recommendation process through feature and linkage augmentation, the system enriches both latent and explicit user and item features, identifies pattern-similar neighbors, and thereby improves the efficiency of information diffusion. Experimental comparisons with baselines across multiple datasets demonstrate the superior performance of the proposed DQRec method.

cs.IR↗
arXiv2025

Maps between circle bundles: Fiber-preserving, Finiteness and Realization of mapping degree sets

Let $E_i$ be an oriented circle bundle over a closed oriented aspherical $n$-manifold $M_i$ with Euler class $e_i\in H^2(M_i;\mathbb{Z})$, $i=1,2$. We prove the following: (i) If every finite-index subgroup of $π_1(M_2)$ has trivial center, then any non-zero degree map from $E_1$ to $E_2$ is homotopic to a fiber-preserving map. (ii) The mapping degree set of fiber-preserving maps from $E_1$ to $E_2$ is given by $$\{0\} \cup\{k\cdot \mathrm{deg}(f) \ | \, k\ne 0, \ f\colon M_1\to M_2 \, \text{with} \, \mathrm{deg}(f)\ne 0 \ \text{such that}\, f^\#(e_2)=ke_1\},$$ where $f^\# \colon H^2(M_2;\mathbb{Z})\to H^2(M_1;\mathbb{Z})$ is the induced homomorphism. As applications of (i) and (ii), we obtain the following results with respect to the finiteness and the realization problems for mapping degree sets: ($\mathcal F$) The mapping degree set $D(E_1, E_2)$ is finite if $M_2$ is hyperbolic and $e_2$ is not torsion. ($\mathcal R$) For any finite set $A$ of integers containing $0$ and each $n>2$, $A$ is the mapping degree set $D(M,N)$ for some closed oriented $n$-manifolds $M$ and $N$. Items (i) and ($\mathcal F$) extend in all dimensions $\geq 3$ the previously known $3$-dimensional case (i.e., for maps between circle bundles over hyperbolic surfaces). Item ($\mathcal R$) gives a complete answer to the realization problem for finite sets (containing $0$) in any dimension, establishing in particular the previously unknown cases in dimensions $n= 4, 5$.

math.GT↗
arXiv2024

Embedding periodic maps of surfaces into those of spheres with minimal dimensions

It is known that any periodic map of order $n$ on a closed oriented surface of genus $g$ can be equivariantly embedded into $S^m$ for some $m$. In the orientable and smooth category, we determine the smallest possible $m$ when $n\geq 3g$. We show that for each integer $k>1$ there exist infinitely many periodic maps such that the smallest possible $m$ is equal to $k$.

math.GT↗
arXiv2024

IBMEA: Exploring Variational Information Bottleneck for Multi-modal Entity Alignment

Multi-modal entity alignment (MMEA) aims to identify equivalent entities between multi-modal knowledge graphs (MMKGs), where the entities can be associated with related images. Most existing studies integrate multi-modal information heavily relying on the automatically-learned fusion module, rarely suppressing the redundant information for MMEA explicitly. To this end, we explore variational information bottleneck for multi-modal entity alignment (IBMEA), which emphasizes the alignment-relevant information and suppresses the alignment-irrelevant information in generating entity representations. Specifically, we devise multi-modal variational encoders to generate modal-specific entity representations as probability distributions. Then, we propose four modal-specific information bottleneck regularizers, limiting the misleading clues in refining modal-specific entity representations. Finally, we propose a modal-hybrid information contrastive regularizer to integrate all the refined modal-specific representations, enhancing the entity similarity between MMKGs to achieve MMEA. We conduct extensive experiments on two cross-KG and three bilingual MMEA datasets. Experimental results demonstrate that our model consistently outperforms previous state-of-the-art methods, and also shows promising and robust performance in low-resource and high-noise data scenarios.

cs.CL↗
arXiv2024

Achirality of Sol 3-Manifolds, Stevenhagen Conjecture and Shimizu's L-series

A closed orientable manifold is {\em achiral} if it admits an orientation reversing homeomorphism. A commensurable class of closed manifolds is achiral if it contains an achiral element, or equivalently, each manifold in $\CM$ has an achiral finite cover. Each commensurable class containing non-orientable elements must be achiral. It is natural to wonder how many commensurable classes are achiral and how many achiral classes have non-orientable elements. We study this problem for Sol 3-manifolds. Each commensurable class $\CM$ of Sol 3-manifold has a complete topological invariant $D_{\CM}$, the discriminant of $\CM$. Our main result is: (1) Among all commensurable classes of Sol 3-manifolds, there are infinitely many achiral classes; however ordered by discriminants, the density of achiral commensurable classes is 0. (2) Among all achiral commensurable classes of Sol 3-manifolds, ordered by discriminants, the density of classes containing non-orientable elements is $1-ρ$, where $$ρ:=\prod_{j=1}^\infty \left(1+2^{-j}\right)^{-1} = 0.41942\cdots.$$

math.GT↗
arXiv2023

On the realisation problem for mapping degree sets

The set of degrees of maps $D(M,N)$, where $M,N$ are closed oriented $n$-manifolds, always contains $0$ and the set of degrees of self-maps $D(M)$ always contains $0$ and $1$. Also, if $a,b\in D(M)$, then $ab\in D(M)$; a set $A\subseteq\mathbb Z$ so that $ab\in A$ for each $a,b\in A$ is called multiplicative. On the one hand, not every infinite set of integers (containing $0$) is a mapping degree set [NWW] and, on the other hand, every finite set of integers (containing $0$) is the mapping degree set of some $3$-manifolds [CMV]. We show the following: (i) Not every multiplicative set $A$ containing $0,1$ is a self-mapping degree set. (ii) For each $n\in\mathbb N$ and $k\geq3$, every $D(M,N)$ for $n$-manifolds $M$ and $N$ is $D(P,Q)$ for some $(n+k)$-manifolds $P$ and $Q$. As a consequence of (ii) and [CMV], every finite set of integers (containing $0$) is the mapping degree set of some $n$-manifolds for all $n\neq 1,2,4,5$.

math.GT↗
arXiv2022

Extending periodic maps on surfaces over the 4-sphere

Let $F_g$ be the closed orientable surface of genus $g$. We address the problem to extend torsion elements of the mapping class group ${\mathcal{M}}(F_g)$ over the 4-sphere $S^4$. Let $w_g$ be a torsion element of maximum order in ${\mathcal{M}}(F_g)$. Results including: (1) For each $g$, $w_g$ is periodically extendable over $S^4$ for some non-smooth embedding $e: F_g\to S^4$, and not periodically extendable over $S^4$ for any smooth embedding $e: F_g\to S^4$. (2) For each $g$, $w_g$ is extendable over $S^4$ for some smooth embedding $e: F_g\to S^4$ if and only if $g=4k, 4k+3$. (3) Each torsion element of order $p$ in ${\mathcal{M}}(F_g)$ is extendable over $S^4$ for some smooth embedding $e: F_g\to S^4$ if either (i) $p=3^m$ and $g$ is even; or (ii) $p=5^m$ and $g\ne 4k+2$; or (iii) $p=7^m$. Moreover the conditions on $g$ in (i) and (ii) can not be removed .

math.GT↗
arXiv2022

Realising sets of integers as mapping degree sets

Given two closed oriented manifolds $M,N$ of the same dimension, we denote the set of degrees of maps from $M$ to $N$ by $D(M,N)$. The set $D(M,N)$ always contains zero. We show the following (non-)realisability results: (i) There exists an infinite subset $A$ of $\mathbb Z$ containing $0$ which cannot be realised as $D(M,N)$, for any closed oriented $n$-manifolds $M,N$. (ii) Every finite arithmetic progression of integers containing $0$ can be realised as $D(M,N)$, for some closed oriented $3$-manifolds $M,N$. (iii) Together with $0$, every finite geometric progression of positive integers starting from $1$ can be realised as $D(M,N)$, for some closed oriented manifolds $M,N$.

math.GT↗
arXiv2020

Volume of Seifert representations for graph manifolds and their finite covers

For any closed orientable 3-manifold, there is a volume function defined on the space of all Seifert representations of the fundamental group. The maximum absolute value of this function agrees with the Seifert volume of the manifold due to Brooks and Goldman. For any Seifert representation of a graph manifold, the authors establish an effective formula for computing its volume, and obtain restrictions to the representation as analogous to the Milnor--Wood inequality (about transversely projective foliations on Seifert fiber spaces). It is shown that the Seifert volume of any graph manifold is a rational multiple of $π^2$. Among all finite covers of a given non-geometric graph manifold, the supremum ratio of the Seifert volume over the covering degree can be a positive number, and can be infinite. Examples of both possibilities are discovered, and confirmed, with the explicit values determined for the finite ones.

math.GT↗
arXiv2020

Extending periodic automorphisms of surfaces to 3-manifolds

Let $G$ be a finite group acting on a connected compact surface $Σ$, and $M$ be an integer homology 3-sphere. We show that if each element of $G$ is extendable over $M$ with respect to a fixed embedding $Σ\rightarrow M$, then $G$ is extendable over some $M'$ which is 1-dominated by $M$. From this result, in the orientable category we classify all periodic automorphisms of closed surfaces that are extendable over the 3-sphere. The corresponding embedded surface of such an automorphism can always be a Heegaard surface.

math.GT↗
arXiv2020

Systoles of hyperbolic surfaces with big cyclic symmetry

We obtain the exact values of the systoles of these hyperbolic surfaces of genus $g$ with cyclic symmetries of the maximum order and the next maximum order. Precisely: for genus $g$ hyperbolic surface with order $4g+2$ cyclic symmetry, the systole is $2\mathrm{arccosh} (1+\cos \fracπ{2g+1}+\cos \frac{2π}{2g+1})$ when $g\ge 7$, and for genus $g$ hyperbolic surface with order $4g$ cyclic symmetry, the systole is $2\mathrm{arccosh} (1+2\cos \fracπ{2g})$ when $g\ge4$.

math.GT↗
arXiv2019

Road-network-based Rapid Geolocalization

It has always been a research hotspot to use geographic information to assist the navigation of unmanned aerial vehicles. In this paper, a road-network-based localization method is proposed. We match roads in the measurement images to the reference road vector map, and realize successful localization on areas as large as a whole city. The road network matching problem is treated as a point cloud registration problem under two-dimensional projective transformation, and solved under a hypothesise-and-test framework. To deal with the projective point cloud registration problem, a global projective invariant feature is proposed, which consists of two road intersections augmented with the information of their tangents. We call it two road intersections tuple. We deduce the closed-form solution for determining the alignment transformation from a pair of matching two road intersections tuples. In addition, we propose the necessary conditions for the tuples to match. This can reduce the candidate matching tuples, thus accelerating the search to a great extent. We test all the candidate matching tuples under a hypothesise-and-test framework to search for the best match. The experiments show that our method can localize the target area over an area of 400 within 1 second on a single cpu.

cs.CV↗
arXiv2018

The spectral radius of graphs without trees of diameter at most four

Nikiforov (LAA, 2010) conjectured that for given integer $k$, any graph $G$ of sufficiently large order $n$ with spectral radius $μ(G)\geq μ(S_{n,k})$ contains all trees of order $2k+2$, unless $G=S_{n,k}$, where $S_{n,k}=K_k\vee \overline{K_{n-k}}$, the join of a complete graph of order $k$ and an empty graph of order $n-k$. In this paper, we show that the conjecture is true for trees of diameter at most four.

math.CO↗
arXiv2018

Minimal surfaces in the three dimensional sphere with high symmetry

Using the Lawson's existence theorem of minimal surfaces and the symmetries of the Hopf fibration, we will construct symmetric embedded closed minimal surfaces in the three dimensional sphere. These surfaces contain the Clifford torus, the Lawson's minimal surfaces, and seven new minimal surfaces with genera 9, 25, 49, 121, 121, 361 and 841. We will also discuss the relation between such surfaces and the maximal extendable group actions on subsurfaces of the three dimensional sphere.

math.GT↗
arXiv2017

Graphs in the 3--sphere with maximum symmetry

We consider the orientation-preserving actions of finite groups $G$ on pairs $(S^3, Γ)$, where $Γ$ is a connected graph of genus $g>1$, embedded in $S^3$. For each $g$ we give the maximum order $m_g$ of such $G$ acting on $(S^3, Γ)$ for all such $Γ\subset S^3$. Indeed we will classify all graphs $Γ\subset S^3$ which realize these $m_g$ in different levels: as abstract graphs and as spatial graphs, as well as their group actions. Such maximum orders without the condition "orientation-preserving" are also addressed.

math.GT↗