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Hongjia Chen

Publications and source records attributed to Hongjia Chen.

At least 19 recordsLinked to original sources
arXiv2026

Presenting mirabolic quantum Schur algebras $\mathcal{MS}_v(2,d)$

Let $v$ be an indeterminate. We give a presentation of the mirabolic quantum Schur algebra $\mathcal{MS}_v(2,d)$ in terms of generators and defining relations. More precisely, we determine the kernel of the natural epimorphism from Rosso's mirabolic quantum $\mathfrak{sl}_2$, $\mathbf U^{\mathrm{mir}}_v(2)=\langle e,f,k^{\pm 1},\ell\rangle$, onto $\mathcal{MS}_v(2,d)$. Setting $P_d(k)=\prod_{r=0}^{d}(k-v^{2r-d})$ and $Q_d(k)=\prod_{r=1}^{d}(k-v^{2r-d})$, we prove $\mathcal{MS}_v(2,d)\cong \mathbf U^{\mathrm{mir}}_v(2)/ \left\langle P_d(k),(\ell-1)Q_d(k)\right\rangle$. We further determine the split Wedderburn decomposition of this quotient and provide an equivalent presentation in terms of weight idempotents.

math.RT↗
arXiv2026

vToken: Token-Level Virtualization for Reclaimable KV Caches

Large language model serving faces a critical memory bottleneck: the KV cache grows with sequence length and batch size. PagedAttention uses fixed-size memory blocks to reduce allocator-level fragmentation, but recent KV eviction algorithms operate at a token granularity finer than block-level management. This mismatch causes intra-block fragmentation, leaving a large fraction of allocated KV memory unreclaimable. We present vToken, a lightweight token-level virtualization layer that decouples logical token liveness from physical block placement. vToken maintains a stable logical token view through token-table indirection and realizes physical reclamation by repacking live tokens asynchronously. The design preserves PagedAttention kernels and CUDA Graph compatibility. We implement vToken in vLLM and evaluate it with H2O, Random, and Scissorhands across models. Compared with a paired Naive-Evict baseline, vToken reduces retained KV blocks per request by 27.2\%--72.3\% and improves SLA-constrained throughput by up to 1.37$\times$. Under a constrained active-KV budget, it extends the maximum feasible concurrency by up to 2$\times$, while reducing the per-policy integration footprint from 500+ lines to under 50.

cs.AI↗
arXiv2026

Optimal Quantum Eigenvalue Transformation via Linear Combinations of Hermitian Matrices

We discover two complementary linear-combination-of-Hermitian-matrices (LCHM) formulations to achieve a general non-normal matrix eigenvalue transformation $g(A)$. Firstly, for $A=L+\mathrm{i} H$ with Hermitian $L$ and $H$, the vanilla LCHM formula represents $g(A)$ as a kernel integral of $g(\mathrm{i}(H+kL))$, and it contains linear-combination-of-Hamiltonian-simulation (LCHS) [An, Liu, Lin, Phys. Rev. Lett. 2023] as the special case for matrix exponentials. Secondly, for the angular Hermitian $X_\theta = \cos\theta L+\sin\theta H$, the Weyl LCHM formula expresses $g(A)$ via integrating $g(\mathrm{e}^{\mathrm{i}\theta} (X_\theta\pm\mathrm{i}(I-X_\theta^2)^{1/2}))$. For the matrix power $g(A)=A^m$, the Fourier projection of Weyl LCHM gives \[ A^m=\frac{2}{\pi}\int_0^\pi \text{e}^{\text{i} m\theta}T_m(X_\theta) \text{d}\theta = \frac{2}{N}\sum_{j=0}^{N-1} \text{e}^{\text{i} m\theta_j}T_m(X_{\theta_j}),\quad\theta_j=\frac{\pi j}{N},\quad \text{for every } N>m \] with Chebyshev polynomial of Hermitian $T_m(X_\theta)$ and $N$ samples. The discrete formula is exact, introduces no truncation and angular quadrature error, and offers $\mathcal{O}(1)$ post-selection weights. LCHM formulas lead to new quantum eigenvalue transformation (QET) algorithms. For a degree-$d$ polynomial $p_d(A)$ on $|\psi\rangle$, our QET algorithm can achieve optimal $\Theta(d)$ circuit depth and optimal $\mathcal{O}(||p_d||_{\infty}/||p_d(A)|\psi\rangle||)$ post-selection repetitions. LCHM-based QETs unify various quantum linear algebraic problems with near-optimal $\mathcal{\widetilde O}(d\log(d/\epsilon))$ Clifford$+T$ gates, including driven ODEs (reduced to standard LCHS), iterative methods, resolvents, $\log(I+A)$, $(\lambda I+A)^\nu$, Sign and ReLU transforms, and Faber approximation on noncircular domains.

quant-ph↗
arXiv2026

Compensated Splitting For Generalized Lyapunov Equations

The generalized Lyapunov equation has a natural splitting that leads to the standard fixed-point iteration (sFPI) for its numerical solution. sFPI is convergent, for an arbitrarily given initial guess, if and only if the spectral radius of the associated linear operator is smaller than $1$. This means that sFPI may diverge if the spectral radius is $1$ or bigger. In this paper, we propose a compensated splitting scheme that aims to reduce the spectral radius so that the resulting compensated fixed-point iteration (cFPI) has a better convergence property, namely, cFPI may still converge even if sFPI does not or cFPI converges faster than sFPI does when the latter is also convergent. Numerical results are presented to demonstrate the superiority of cFPI to sFPI.

math.NA↗
arXiv2026

Efficient Solution of Generalized Sylvester Equations via Preconditioned Alternating Anderson Acceleration

This paper considers the numerical solution of generalized Sylvester matrix equations, which arise in many scientific and engineering applications but remain challenging to solve efficiently, particularly when the coefficient matrices are general and the spectral radius of the associated operator is large but not greater than $1$. We propose a new iterative method, termed preconditioned-alternating Anderson acceleration (P-aAA), which combines a matrix-oriented variant of Anderson acceleration (AA) with a novel preconditioning strategy. The method alternates between preconditioned fixed-point iterations and Anderson acceleration updates, thereby reducing both computational cost and iteration count. A key contribution is the development of an efficient preconditioning operator based on a first-order Neumann series approximation, which avoids expensive operator inversions while enhancing convergence. We theoretically prove that the proposed preconditioning operator accelerates the convergence rate without increasing the overall computational complexity. Extensive numerical experiments further demonstrate that the proposed approach consistently outperforms existing state-of-the-art methods for both medium- and large-scale problems, achieving substantial reductions in computation time and iteration number.

math.NA↗
arXiv2025

New simple modules for the $W$-algebra $W(2,2)$

In this paper, we construct a novel class of simple modules for the $W$-algebra $W(2,2)$. Our approach involves taking tensor products of finitely many non-weight simple modules $\Omega(\lambda,\alpha,h)$ with an arbitrary simple restricted module. We provide a necessary and sufficient condition for these modules to be simple, and subsequently determine their isomorphism classes. Through a comparative analysis with other known simple modules in the literature, we establish that these constructed modules are generically new.

math.RT↗
arXiv2025

DAM-Net: Domain Adaptation Network with Micro-Labeled Fine-Tuning for Change Detection

Change detection (CD) in remote sensing imagery plays a crucial role in various applications such as urban planning, damage assessment, and resource management. While deep learning approaches have significantly advanced CD performance, current methods suffer from poor domain adaptability, requiring extensive labeled data for retraining when applied to new scenarios. This limitation severely restricts their practical applications across different datasets. In this work, we propose DAM-Net: a Domain Adaptation Network with Micro-Labeled Fine-Tuning for CD. Our network introduces adversarial domain adaptation to CD for, utilizing a specially designed segmentation-discriminator and alternating training strategy to enable effective transfer between domains. Additionally, we propose a novel Micro-Labeled Fine-Tuning approach that strategically selects and labels a minimal amount of samples (less than 1%) to enhance domain adaptation. The network incorporates a Multi-Temporal Transformer for feature fusion and optimized backbone structure based on previous research. Experiments conducted on the LEVIR-CD and WHU-CD datasets demonstrate that DAM-Net significantly outperforms existing domain adaptation methods, achieving comparable performance to semi-supervised approaches that require 10% labeled data while using only 0.3% labeled samples. Our approach significantly advances cross-dataset CD applications and provides a new paradigm for efficient domain adaptation in remote sensing. The source code of DAM-Net will be made publicly available upon publication.

cs.CV↗
arXiv2024

SRC-Net: Bi-Temporal Spatial Relationship Concerned Network for Change Detection

Change detection (CD) in remote sensing imagery is a crucial task with applications in environmental monitoring, urban development, and disaster management. CD involves utilizing bi-temporal images to identify changes over time. The bi-temporal spatial relationships between features at the same location at different times play a key role in this process. However, existing change detection networks often do not fully leverage these spatial relationships during bi-temporal feature extraction and fusion. In this work, we propose SRC-Net: a bi-temporal spatial relationship concerned network for CD. The proposed SRC-Net includes a Perception and Interaction Module that incorporates spatial relationships and establishes a cross-branch perception mechanism to enhance the precision and robustness of feature extraction. Additionally, a Patch-Mode joint Feature Fusion Module is introduced to address information loss in current methods. It considers different change modes and concerns about spatial relationships, resulting in more expressive fusion features. Furthermore, we construct a novel network using these two relationship concerned modules and conducted experiments on the LEVIR-CD and WHU Building datasets. The experimental results demonstrate that our network outperforms state-of-the-art (SOTA) methods while maintaining a modest parameter count. We believe our approach sets a new paradigm for change detection and will inspire further advancements in the field. The code and models are publicly available at https://github.com/Chnja/SRCNet.

cs.CV↗
arXiv2023

Algorithms for square root of semi-infinite quasi-Toeplitz $M$-matrices

A quasi-Toeplitz $M$-matrix $A$ is an infinite $M$-matrix that can be written as the sum of a semi-infinite Toeplitz matrix and a correction matrix. This paper is concerned with computing the square root of invertible quasi-Toeplitz $M$-matrices which preserves the quasi-Toeplitz structure. We show that the Toeplitz part of the square root can be easily computed through evaluation/interpolation at the $m$ roots of unity. This advantage allows to propose algorithms solely for the computation of correction part, whence we propose a fixed-point iteration and a structure-preserving doubling algorithm. Additionally, we show that the correction part can be approximated by solving a nonlinear matrix equation with coefficients of finite size followed by extending the solution to infinity. Numerical experiments showing the efficiency of the proposed algorithms are performed.

math.NA↗
arXiv2022

RDP-Net: Region Detail Preserving Network for Change Detection

Change detection (CD) is an essential earth observation technique. It captures the dynamic information of land objects. With the rise of deep learning, convolutional neural networks (CNN) have shown great potential in CD. However, current CNN models introduce backbone architectures that lose detailed information during learning. Moreover, current CNN models are heavy in parameters, which prevents their deployment on edge devices such as UAVs. In this work, we tackle this issue by proposing RDP-Net: a region detail preserving network for CD. We propose an efficient training strategy that constructs the training tasks during the warmup period of CNN training and lets the CNN learn from easy to hard. The training strategy enables CNN to learn more powerful features with fewer FLOPs and achieve better performance. Next, we propose an effective edge loss that increases the penalty for errors on details and improves the network's attention to details such as boundary regions and small areas. Furthermore, we provide a CNN model with a brand new backbone that achieves the state-of-the-art empirical performance in CD with only 1.70M parameters. We hope our RDP-Net would benefit the practical CD applications on compact devices and could inspire more people to bring change detection to a new level with the efficient training strategy. The code and models are publicly available at https://github.com/Chnja/RDPNet.

eess.IV↗
arXiv2014

A family of representations of the affine Lie superalgebra $\widehat{\mathfrak{gl}_{m|n}}(\mathbb{C})$

In this paper, we used the free fields of Wakimoto to construct a class of irreducible representations for the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb{C})$. The structures of the representations over the general linear Lie superalgebra and the special linear Lie superalgebra are studied in this paper. Then we extend the construction to the affine Kac-Moody Lie superalgebra $\widehat{\mathfrak{gl}_{m|n}}(\mathbb{C})$ on the tensor product of a polynomial algebra and an exterior algebra with infinitely many variables involving one parameter $μ$, and we also obtain the necessary and sufficient condition for the representations to be irreducible. In fact, the representation is irreducible if and only if the parameter $μ$ is nonzero.

math.RT↗
arXiv2014

Universal central extensions of $sl_{m|n}$ over $Z/2Z$-graded algebras

We study central extensions of the Lie superalgebra $sl_{m|n}(A)$, where $A$ is a $Z/2Z$-graded superalgebra over a commutative ring $K$. The Steinberg Lie superalgebra $st_{m|n}(A)$ plays a crucial role. We show that $st_{m|n}(A)$ is a central extension of $sl_{m|n}(A)$ for $m+n\geq 3$. We use a $Z/2Z$-graded version of cyclic homology to show that the center of the extension is isomorphic to $HC_1(A)$ as $K$-modules. For $m+n\geq 5$, we prove that $st_{m|n}(A)$ is the universal central extension of $sl_{m|n}(A)$. For $m+n=3,4$, we prove that $st_{2|1}(A)$ and $st_{3|1}(A)$ are both centrally closed. The universal central extension of $st_{2|2}(A)$ is constructed explicitly.

math.RA↗
arXiv2014

Modules over the Heisenberg-Virasoro and $W(2,2)$ algebras

In this paper, we consider the modules for the Heisenberg-Virasoro algebra and the W algebra $W(2,2)$. We determine the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank $1$ for the two algebras. We also determine the simplicity of these modules. These modules provide new simple modules for the W algebra $W(2,2)$.

math.RT↗
arXiv2013

Tensor product weight modules over the Virasoro algebra

The tensor product of highest weight modules with intermediate series modules over the Virasoro algebra was discussed by Zhang [Z] in 1997. Since then the irreducibility problem for the tensor products has been open. In this paper, we determine the necessary and sufficient conditions for these tensor products to be simple. From non-simple tensor products, we can get other interesting simple Virasoro modules. We also obtain that any two such tensor products are isomorphic if and only if the corresponding highest weight modules and intermediate series modules are isomorphic respectively. Our method is to develop a "shifting technique" and to widely use Feigin-Fuchs' Theorem on singular vectors of Verma modules over the Virasoro algebra.

math.RT↗
arXiv2007

Classification of Graded Left-symmetric Algebra Structures on Witt and Virasoro Algebras

We find that a compatible graded left-symmetric algebra structure on the Witt algebra induces an indecomposable module of the Witt algebra with 1-dimensional weight spaces by its left multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebra structures on the Witt algebra are classified. All of them are simple and they include the examples given by Chapoton and Kupershmidt. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebra structures on the Virasoro algebra. They coincide with the examples given by Kupershmidt.

math.QA↗