arXiv subjects

Yucheng Liu

Publications and source records attributed to Yucheng Liu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Computation and Communication Efficient Lightweighting Vertical Federated Learning for Smart Building IoT

With the increasing number and enhanced capabilities of IoT devices in smart buildings, these devices are evolving beyond basic data collection and control to actively participate in deep learning tasks. Federated Learning (FL), as a decentralized learning paradigm, is well-suited for such scenarios. However, the limited computational and communication resources of IoT devices present significant challenges. While existing research has extensively explored efficiency improvements in Horizontal FL, these techniques cannot be directly applied to Vertical FL due to fundamental differences in data partitioning and model structure. To address this gap, we propose a Lightweight Vertical Federated Learning (LVFL) framework that jointly optimizes computational and communication efficiency. Our approach introduces two distinct lightweighting strategies: one for reducing the complexity of the feature model to improve local computation, and another for compressing feature embeddings to reduce communication overhead. Furthermore, we derive a convergence bound for the proposed LVFL algorithm that explicitly incorporates both computation and communication lightweighting ratios. Experimental results on an image classification task demonstrate that LVFL effectively mitigates resource demands while maintaining competitive learning performance.

cs.LG↗

arXiv2025

Passive Underwater Acoustic Signal Separation based on Feature Decoupling Dual-path Network

Signal separation in the passive underwater acoustic domain has heavily relied on deep learning techniques to isolate ship radiated noise. However, the separation networks commonly used in this domain stem from speech separation applications and may not fully consider the unique aspects of underwater acoustics beforehand, such as the influence of different propagation media, signal frequencies and modulation characteristics. This oversight highlights the need for tailored approaches that account for the specific characteristics of underwater sound propagation. This study introduces a novel temporal network designed to separate ship radiated noise by employing a dual-path model and a feature decoupling approach. The mixed signals' features are transformed into a space where they exhibit greater independence, with each dimension's significance decoupled. Subsequently, a fusion of local and global attention mechanisms is employed in the separation layer. Extensive comparisons showcase the effectiveness of this method when compared to other prevalent network models, as evidenced by its performance in the ShipsEar and DeepShip datasets.

cs.SD↗

arXiv2025

The torus plateau for the high-dimensional Ising model

We consider the Ising model on a $d$-dimensional discrete torus of volume $r^d$, in dimensions $d>4$ and for large $r$, in the vicinity of the infinite-volume critical point $β_c$. We prove that for $β=β_c- {\rm const}\, r^{-d/2}$ (with a suitable constant) the susceptibility is bounded above and below by multiples of $r^{d/2}$. Additionally, again for $β=β_c- {\rm const}\, r^{-d/2}$, the two-point function has a ``plateau'': it decays like $|x|^{-(d-2)}$ when $|x|$ is small relative to the volume, but for larger $|x|$, it levels off to a constant value of order $r^{-d/2}$. We also prove that at $β=β_c- {\rm const}\, r^{-d/2}$ the renormalised coupling constant is nonzero, which implies a non-Gaussian limit for the average spin. The proof relies on near-critical estimates for the infinite-volume two-point function obtained recently by Duminil-Copin and Panis, and builds upon a strategy proposed by Papathanakos. The random current representation of the Ising model plays a central role in our analysis.

math-ph↗

arXiv2025

Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models

We investigate how to select the number of communities for weighted networks without a full likelihood modeling. First, we propose a novel weighted degree-corrected stochastic block model (DCSBM), where the mean adjacency matrix is modeled in the same way as in the standard DCSBM, while the variance profile matrix is assumed to be related to the mean adjacency matrix through a given variance function. Our method of selecting the number of communities is based on a sequential testing framework. In each step, the weighted DCSBM is fitted via some spectral clustering method. A key component of our method is matrix scaling on the estimated variance profile matrix. The resulting scaling factors can be used to normalize the adjacency matrix, from which the test statistic is then obtained. Under mild conditions on the weighted DCSBM, our proposed procedure is shown to be consistent in estimating the true number of communities. Numerical experiments on both simulated and real-world network data demonstrate the desirable empirical properties of our method.

stat.ME↗

arXiv2025

Near-critical and finite-size scaling for high-dimensional lattice trees and animals

We consider spread-out models of lattice trees and lattice animals on $\mathbb Z^d$, for $d$ above the upper critical dimension $d_{\mathrm c}=8$. We define a correlation length and prove that it diverges as $(p_c-p)^{-1/4}$ at the critical point $p_c$. Using this, we prove that the near-critical two-point function is bounded above by $C|x|^{-(d-2)}\exp[-c(p_c-p)^{1/4}|x|]$. We apply the near-critical bound to study lattice trees and lattice animals on a discrete $d$-dimensional torus (with $d > d_{\mathrm c}$) of volume $V$. For $p_c-p$ of order $V^{-1/2}$, we prove that the torus susceptibility is of order $V^{1/4}$, and that the torus two-point function behaves as $|x|^{-(d-2)} + V^{-3/4}$ and thus has a plateau of size $V^{-3/4}$. The proofs require significant extensions of previous results obtained using the lace expansion.

math.PR↗

arXiv2025

Learning a generalized multiscale prolongation operator

In this research, we address Darcy flow problems with random permeability using iterative solvers, enhanced by a two-grid preconditioner based on a generalized multiscale prolongation operator, which has been demonstrated to be stable for high contrast profiles. To circumvent the need for repeatedly solving spectral problems with varying coefficients, we harness deep learning techniques to expedite the construction of the generalized multiscale prolongation operator. Considering linear transformations on multiscale basis have no impact on the performance of the preconditioner, we devise a loss function by the coefficient-based distance between subspaces instead of the plain $l^2$-norm of the difference of the corresponding multiscale bases. We discover that leveraging the inherent symmetry in the local spectral problem can effectively accelerate the neural network training process. In scenarios where training data are limited, we utilize the Karhunen-Loève expansion to augment the dataset. Extensive numerical experiments with various types of random coefficient models are exhibited, showing that the proposed method can significantly reduce the time required to generate the prolongation operator while maintaining the original efficiency of the two-grid preconditioner. Notably, the neural network demonstrates strong generalization capabilities, as evidenced by its satisfactory performance on unseen random permeability fields.

math.NA↗

arXiv2025

A robust solver for large-scale heat transfer topology optimization

This paper presents a large-scale parallel solver, specifically designed to tackle the challenges of solving high-dimensional and high-contrast linear systems in heat transfer topology optimization. The solver incorporates an interpolation technique to accelerate convergence in high-resolution domains, along with a multiscale multigrid preconditioner to handle complex coefficient fields with significant contrast. All modules of the optimization solver are implemented on a high performance computing cluster by the PETSc numerical library. Through a series of numerical investigations, we demonstrate the effectiveness of our approach in enhancing convergence and robustness during the optimization process, particularly in high-contrast scenarios with resolutions up to $1024^3$. Our performance results indicate that the proposed preconditioner achieves over $2\times$ speedup against the default algebraic multigrid in PETSc for high-contrast cases.

math.NA↗

arXiv2024

Gaussian deconvolution on $\mathbb R^d$ with application to self-repellent Brownian motion

We consider the convolution equation $(δ- J) * G = g$ on $\mathbb R^d$, $d>2$, where $δ$ is the Dirac delta function and $J,g$ are given functions. We provide conditions on $J, g$ that ensure the deconvolution $G(x)$ to decay as $( x \cdot Σ^{-1} x)^{-(d-2)/2}$ for large $|x|$, where $Σ$ is a positive-definite diagonal matrix. This extends a recent deconvolution theorem on $\mathbb Z^d$ proved by the author and Slade to the possibly anisotropic, continuum setting while maintaining its simplicity. Our motivation comes from studies of statistical mechanical models on $\mathbb R^d$ based on the lace expansion. As an example, we apply our theorem to a self-repellent Brownian motion in dimensions $d>4$, proving its critical two-point function to decay as $|x|^{-(d-2)}$, like the Green function of the Laplace operator $Δ$.

math.PR↗

arXiv2024

Gaussian deconvolution and the lace expansion

We give conditions on a real-valued function $F$ on $\mathbb{Z}^d$, for $d>2$, which ensure that the solution $G$ to the convolution equation $(F*G)(x) = δ_{0,x}$ has Gaussian decay $|x|^{-(d-2)}$ for large $|x|$. Precursors of our results were obtained in the 2000s, using intricate Fourier analysis. In 2022, a very simple deconvolution theorem was proved, but its applicability was limited. We extend the 2022 theorem to remove its limitations while maintaining its simplicity -- our main tools are Hölder's inequality, weak derivatives, and basic Fourier theory in $L^p$ space. Our motivation comes from critical phenomena in equilibrium statistical mechanics, where the convolution equation is provided by the lace expansion and $G$ is a critical two-point function. Our results significantly simplify existing proofs of critical $|x|^{-(d-2)}$ decay in high dimensions for self-avoiding walk, Ising and $φ^4$ models, percolation, and lattice trees and lattice animals. We also improve previous error estimates.

math.PR↗

arXiv2024

SilverCycling: Exploring the Impact of Bike-Based Locomotion on Spatial Orientation for Older Adults in VR

Spatial orientation is essential for people to effectively navigate and interact with the environment in everyday life. With age-related cognitive decline, providing VR locomotion techniques with better spatial orientation performance for older adults becomes important. Such advancements not only make VR more accessible to older adults but also enable them to reap the potential health benefits of VR technology. Natural motion-based locomotion has been shown to be effective in enhancing younger users' performance in VR navigation tasks that require spatial orientation. However, there is a lack of understanding regarding the impact of natural motion-based locomotion on spatial orientation for older adults in VR. To address this gap, we selected the SilverCycling system, a VR bike-based locomotion technique that we developed, as a representative of natural motion-based locomotion, guided by findings from our pilot study. We conducted a user study with 16 older adults to compare SilverCycling with the joystick-based controller. The findings suggest SilverCycling's potential to significantly enhance spatial orientation in the open-road urban environment for older adults, offering a better user experience. Based on our findings, we identify key factors influencing spatial orientation and propose design recommendations to make VR locomotion more accessible and user-friendly for older adults.

cs.HC↗

arXiv2024

Continuous-time weakly self-avoiding walk on $\mathbb{Z}$ has strictly monotone escape speed

Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On $\mathbb{Z}$, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing. The proof uses a transfer matrix method implemented via a supersymmetric version of the BFS--Dynkin isomorphism theorem, spectral theory, Tauberian theory, and stochastic dominance.

math.PR↗

arXiv2024

Gaussian deconvolution and the lace expansion for spread-out models

We present a new proof of $|x|^{-(d-2)}$ decay of critical two-point functions for spread-out statistical mechanical models on $\mathbb{Z}^d$ above the upper critical dimension, based on the lace expansion and assuming appropriate diagrammatic estimates. Applications include spread-out models of the Ising model and self-avoiding walk in dimensions $d>4$, and spread-out percolation for $d>6$. The proof is based on an extension of the new Gaussian deconvolution theorem we obtained in a recent paper. It provides a technically simpler and conceptually more transparent approach than the method of Hara, van der Hofstad and Slade (2003).

math.PR↗

arXiv2024

Filtrations and torsion pairs in Abramovich Polishchuk's heart

We study some abelian subcategories and torsion pairs in Abramovich Polishchuk's heart. And we construct stability conditions on a full triangulated subcategory $\mathcal{D}^{\leq 1}_S$ in $D(X\times S)$, for an arbitrary smooth projective variety S. We also define a notion of $l$-th level stability, which is a generalization of the slope stability and the Gieseker stability. We show that for any object E in Abramovich Polishchuk's heart, there is a unique filtration whose factors are $l$-th level semistable, and the phase vectors are decreasing in a lexicographic order.

math.AG↗

arXiv2023

Stability conditions on cyclic categories I: basic definitions and examples

A triangulated category $\mathcal{C}$ with a canonical Bott's isomorphism $[2]\xrightarrow{\sim}id$ is called a cyclic category in this paper. We give a new notion of stability conditions on a $k$-linear Krull-Schmidt cyclic category. Given such a stability condition $σ$, we can assign a Maslov index to each basic loop in such a category. If all Maslov indexes vanish, we get $\mathcal{C}',σ'$ as the $\mathbb{Z}$-lifts of $\mathcal{C},σ$ respectively such that $\mathcal{C}'$ is a $\mathbb{Z}$-graded triangulated category and $σ'$ is a Bridgeland stability condition on $\mathcal{C}'$. Moreover, we showed that there is an isomorphism $$Stab^{0,e}(\mathcal{C})\xrightarrow{\simeq} BStab(\mathcal{C}')$$ where $Stab^{0,e}(\mathcal{C})$ denotes the equivalence classes of stability conditions which are deformation equivalent to $σ$, and $BStab(\mathcal{C}')$ denotes the space of Bridgeland stability conditions on $\mathcal{C}'$. We provide examples of stability conditions on a simple cyclic category. We also discuss some interesting phenomena in these examples, such as the chirality symmetry breaking phenomenon and nontrivial monodromy. The chirality symmetry breaking phenomenon involves stability conditions which can not be lifted to Bridgeland stability conditions.

math.AG↗

arXiv2022

Some quadratic inequalities on product varieties

We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for semi-stable objects on product varieties. The leading quadratic inequality can be viewed as a weak version of Bogomolov's inequality holding in arbitrary characteristics.

math.AG↗

arXiv2022

Information Leakage in Index Coding

We study the information leakage to a guessing adversary in index coding with a general message distribution. Under both vanishing-error and zero-error decoding assumptions, we develop lower and upper bounds on the optimal leakage rate, which are based on the broadcast rate of the subproblem induced by the set of messages the adversary tries to guess. When the messages are independent and uniformly distributed, the lower and upper bounds match, establishing an equivalence between the two rates.

cs.IT↗

arXiv2022

Information Leakage in Index Coding With Sensitive and Non-Sensitive Messages

Information leakage to a guessing adversary in index coding is studied, where some messages in the system are sensitive and others are not. The non-sensitive messages can be used by the server like secret keys to mitigate leakage of the sensitive messages to the adversary. We construct a deterministic linear coding scheme, developed from the rank minimization method based on fitting matrices (Bar-Yossef et al. 2011). The linear scheme leads to a novel upper bound on the optimal information leakage rate, which is proved to be tight over all deterministic scalar linear codes. We also derive a converse result from a graph-theoretic perspective, which holds in general over all deterministic and stochastic coding schemes.

cs.IT↗

arXiv2021

Opinion Extraction as A Structured Sentiment Analysis using Transformers

Relationship extraction and named entity recognition have always been considered as two distinct tasks that require different input data, labels, and models. However, both are essential for structured sentiment analysis. We believe that both tasks can be combined into a single stacked model with the same input data. We performed different experiments to find the best model to extract multiple opinion tuples from a single sentence. The opinion tuples will consist of holders, targets, and expressions. With the opinion tuples, we will be able to extract the relationship we need.

cs.CL↗