arXiv subjects

Guangfu Wang

Publications and source records attributed to Guangfu Wang.

11 recordsLinked to original sources

arXiv2026

On the Lei--Bai conjecture on $5$-regular Lin--Lu--Yau Ricci-flat graphs

We study the Ricci curvature introduced by Lin, Lu, and Yau. A graph is called Ricci-flat if every edge has curvature zero. Lei and Bai classified $5$-regular symmetric Ricci-flat graphs by proving that every such graph is isomorphic to a particular $72$-vertex graph $\RF$, and conjectured that every $5$-regular Ricci-flat graph is either isomorphic to $\RF$ or admits a nontrivial Cartesian product decomposition. In this paper, we disprove this conjecture by constructing an infinite family of connected $5$-regular Ricci-flat graphs, none of which is isomorphic to $\RF$ or admits a nontrivial Cartesian product decomposition. This shows that the conjectured extension of the classification from the symmetric setting to general $5$-regular Ricci-flat graphs fails and that the class of such graphs is substantially richer than previously conjectured. To establish these results, we use an optimal-assignment formulation of Lin--Lu--Yau curvature to verify the Ricci-flatness of the constructed graphs.

math.CO↗

arXiv2026

Almost complete graphs determined by Laplacian hook immanantal polynomials

Let $\mathscr{G}_n$ be the family of simple graphs obtained from $K_n$ by deleting at most five edges. For a fixed integer $1\leq k\leq n$, let $\Phi_k(L(G),x)$ denote the immanantal polynomial of the Laplacian matrix associated with the hook partition $(k,1^{n-k})$. We prove that, for $n>7$ and $n\neq 2k-1$, every graph in $\mathscr{G}_n$ is determined by $\Phi_k(L(G),x)$ among all simple graphs. We prove that, for $n>7$ and $n\neq 2k-1$, every graph in $\mathscr{G}_n$ is determined by $\Phi_k(L(G),x)$ among all simple graphs. The proof recovers the order, size, and degree-square sum from the first coefficients, and then separates the remaining candidates by explicit third- and fourth-coefficient comparisons based on the finite classification of complements with at most five edges. The case $n=2k-1$ is left open because the binomial differences used in these comparisons vanish.

math.CO↗

arXiv2026

Root cubes and two-vertex deletions from daisy grids

Daisy cubes are finite partial cubes that admit an isometric hypercube embedding whose labels form a Boolean down-set. Call a vertex a root if it can receive the all-zero label in such an embedding. Using the peripheral $\Theta$-class characterization implicit in earlier work of Taranenko and of Xie--Xu, and Vesel's description of possible zero vertices, we prove the following intrinsic refinement. If exactly $b$ classes are peripheral on both sides, then $G\cong G_0\square Q_b$, where $G_0$ has a unique root and the roots of $G$ induce the displayed convex $b$-cube. Our main results concern the daisy grids $B_{r,s}=P_3^{\square r}\square Q_s$. We classify every nonempty graph $B_{r,s}-\{x,y\}$ that is a partial cube, a daisy cube, or a minimal forbidden partial-cube minor for daisy cubes. The ambient-isometric cases admit a uniform coordinate description. A local four-cycle argument reduces every non-isometric noncorner partial-cube deletion to $r+s\leq3$, and an exact orbit analysis leaves precisely eleven sporadic orbits. None is daisy or pc-minor-minimal. Consequently, a deletion is pc-minor-minimal non-daisy exactly when the deleted vertices are opposite corners with $s\geq1$ and $2r+s\geq3$, or when a boundary $P_3$-edge is deleted from $B_{1,1}$. This recovers the known hypercube and one-$P_3$ examples and produces a new infinite family with at least two $P_3$-factors. A dependency-free program provides exact certificates for the finite orbit analysis.

math.CO↗

arXiv2026

Principal minors of effective-resistance matrices and local resistance radii

Let $G$ be a finite connected weighted graph and let $R$ be its effective-resistance matrix. For every nonempty vertex set $S$, we factor the cofactor sum and determinant of the principal resistance submatrix $R[S]$ into an enumerative term and a boundary potential-theoretic term. If $\tau(G)$ is the weighted spanning tree enumerator and $\kappa_G(S)$ is the weighted enumerator of $S$-rooted spanning forests, then \[ \cof R[S]=(-2)^{|S|-1}\kappa_G(S)/\tau(G). \] After Kron reduction to $S$, with reduced Laplacian $K=L^S$, $Q=K^+$, and $q=\diag(Q)$, the remaining normalized factor is \[ \det R[S]/\cof R[S] =\frac{2}{|S|}\tr Q+\frac12 q^{\mathsf T}Kq. \] The cofactor factor is a principal specialization of known resistance-minor identities; the contribution here is the boundary/Kron-reduction factorization and local radius calculus. Equivalently, the normalized factor is the maximum of $u^{\mathsf T}R[S]u$ over all $u\in\R^S$ satisfying $\one^{\mathsf T}u=1$. This optimization viewpoint yields monotonicity under enlargement of $S$, an exact one-point update formula, and a support criterion for equality. Small star examples show that the resulting set function is neither submodular nor supermodular in general.

math.CO↗

arXiv2026

A complete classification of metrizable and strictly metrizable theta graphs

Cizma and Linial asked for a classification of the metrizable theta graphs. We solve both their problem and its strict analogue. For $a\le b\le c$, the theta graph $\Theta_{a,b,c}$ is metrizable if and only if $a\le 2$ or $(a,b,c)=(3,3,3)$, and it is strictly metrizable if and only if $a\le2$. Thus $\Theta_{3,3,3}$ is precisely the exceptional theta graph that is metrizable but not strictly metrizable. The negative directions follow from the known obstructions $\Theta_{3,3,4}$ and $\Theta_{3,3,3}$ together with topological-minor closure. The positive direction is constructive. Consistency turns the possible detours through a length-two arm into compatible Ferrers relations, which are represented by one-dimensional potentials; all resulting shortest-path comparisons have positive slack. The exceptional ordinary-metrizable graph $\Theta_{3,3,3}$ is handled by a two-threshold weak Ferrers representation. The proof is structural, yields rational edge lengths algorithmically, and uses no enumeration of path systems.

math.CO↗

arXiv2025

OpenS2S: Advancing Fully Open-Source End-to-End Empathetic Large Speech Language Model

Empathetic interaction is a cornerstone of human-machine communication, due to the need for understanding speech enriched with paralinguistic cues and generating emotional and expressive responses. However, the most powerful empathetic LSLMs are increasingly closed off, leaving the crucial details about the architecture, data and development opaque to researchers. Given the critical need for transparent research into the LSLMs and empathetic behavior, we present OpenS2S, a fully open-source, transparent and end-to-end LSLM designed to enable empathetic speech interactions. Based on our empathetic speech-to-text model BLSP-Emo, OpenS2S further employs a streaming interleaved decoding architecture to achieve low-latency speech generation. To facilitate end-to-end training, OpenS2S incorporates an automated data construction pipeline that synthesizes diverse, high-quality empathetic speech dialogues at low cost. By leveraging large language models to generate empathetic content and controllable text-to-speech systems to introduce speaker and emotional variation, we construct a scalable training corpus with rich paralinguistic diversity and minimal human supervision. We release the fully open-source OpenS2S model, including the dataset, model weights, pre-training and fine-tuning codes, to empower the broader research community and accelerate innovation in empathetic speech systems. The project webpage can be accessed at https://casia-lm.github.io/OpenS2S

cs.CL↗

arXiv2022

JigsawGAN: Auxiliary Learning for Solving Jigsaw Puzzles with Generative Adversarial Networks

The paper proposes a solution based on Generative Adversarial Network (GAN) for solving jigsaw puzzles. The problem assumes that an image is divided into equal square pieces, and asks to recover the image according to information provided by the pieces. Conventional jigsaw puzzle solvers often determine the relationships based on the boundaries of pieces, which ignore the important semantic information. In this paper, we propose JigsawGAN, a GAN-based auxiliary learning method for solving jigsaw puzzles with unpaired images (with no prior knowledge of the initial images). We design a multi-task pipeline that includes, (1) a classification branch to classify jigsaw permutations, and (2) a GAN branch to recover features to images in correct orders. The classification branch is constrained by the pseudo-labels generated according to the shuffled pieces. The GAN branch concentrates on the image semantic information, where the generator produces the natural images to fool the discriminator, while the discriminator distinguishes whether a given image belongs to the synthesized or the real target domain. These two branches are connected by a flow-based warp module that is applied to warp features to correct the order according to the classification results. The proposed method can solve jigsaw puzzles more efficiently by utilizing both semantic information and boundary information simultaneously. Qualitative and quantitative comparisons against several representative jigsaw puzzle solvers demonstrate the superiority of our method.

cs.CV↗

arXiv2021

OMNet: Learning Overlapping Mask for Partial-to-Partial Point Cloud Registration

Point cloud registration is a key task in many computational fields. Previous correspondence matching based methods require the inputs to have distinctive geometric structures to fit a 3D rigid transformation according to point-wise sparse feature matches. However, the accuracy of transformation heavily relies on the quality of extracted features, which are prone to errors with respect to partiality and noise. In addition, they can not utilize the geometric knowledge of all the overlapping regions. On the other hand, previous global feature based approaches can utilize the entire point cloud for the registration, however they ignore the negative effect of non-overlapping points when aggregating global features. In this paper, we present OMNet, a global feature based iterative network for partial-to-partial point cloud registration. We learn overlapping masks to reject non-overlapping regions, which converts the partial-to-partial registration to the registration of the same shape. Moreover, the previously used data is sampled only once from the CAD models for each object, resulting in the same point clouds for the source and reference. We propose a more practical manner of data generation where a CAD model is sampled twice for the source and reference, avoiding the previously prevalent over-fitting issue. Experimental results show that our method achieves state-of-the-art performance compared to traditional and deep learning based methods. Code is available at https://github.com/megvii-research/OMNet.

cs.CV↗

arXiv2021

RIN: Textured Human Model Recovery and Imitation with a Single Image

Human imitation has become topical recently, driven by GAN's ability to disentangle human pose and body content. However, the latest methods hardly focus on 3D information, and to avoid self-occlusion, a massive amount of input images are needed. In this paper, we propose RIN, a novel volume-based framework for reconstructing a textured 3D model from a single picture and imitating a subject with the generated model. Specifically, to estimate most of the human texture, we propose a U-Net-like front-to-back translation network. With both front and back images input, the textured volume recovery module allows us to color a volumetric human. A sequence of 3D poses then guides the colored volume via Flowable Disentangle Networks as a volume-to-volume translation task. To project volumes to a 2D plane during training, we design a differentiable depth-aware renderer. Our experiments demonstrate that our volume-based model is adequate for human imitation, and the back view can be estimated reliably using our network. While prior works based on either 2D pose or semantic map often fail for the unstable appearance of a human, our framework can still produce concrete results, which are competitive to those imagined from multi-view input.

cs.CV↗

arXiv2020

On the Fibonacci $(p,r)$-cubes

In this paper, first it is shown that the "FSibonacci $(p,r)$-cube"(denoted as $IΓ_{n}^{(p,r)}$) studied in many papers, such as \cite{OZY}, \cite{K1}, \cite{OZ}, \cite{KR} and \cite{JZ}, is a new topological structure different from the original one (denoted as $OΓ_{n}^{(p,r)}$) presented by Egiazarian and Astola $\cite{EA}$. Then some topological properties of $IΓ_{n}^{(p,r)}$ and $OΓ_{n}^{(p,r)}$ are studied, including the recursive structure of them, the cubes $OΓ_{n}^{(p,r)}$ which are partial cubes and median graphs, some distance invariants of $IΓ_{n}^{(p,r)}$ and $OΓ_{n}^{(p,r)}$, and the maximum and minimum degree of these two types of cubes. Finally, several problems and conjectures on $IΓ_{n}^{(p,r)}$ and $OΓ_{n}^{(p,r)}$ are listed

math.CO↗

arXiv2019

O-Fibonacci $(p,r)$-cube as Cartesian products

Let $p ,r $ and $n $ be positive integers. Then the O-Fibonacci $(p,r)$-cube $OΓ^{(p,r)}_{n}$ is the subgraph of $Q_{n}$ induced on the binary words in which there is at least $p-1$ zeros between any two $1$s and there is at most $r$ consecutive $10^{p-1}$. These cubes include a wide range of cubes as their special cases, such as hypercubes, Fibonacci cubes, and postal networks. In this note it is proved that $OΓ^{(p,r)}_{n}$ is a non-trivial Cartesian product if and only if $p=1$ and $r\geq n\geq2$.

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