arXiv subjects

Yixiao Qian

Publications and source records attributed to Yixiao Qian.

7 recordsLinked to original sources

arXiv2026

DART: Decoded Attention over Recurrent States for Efficient Long-Context Sequence Modeling

Modern language models are built primarily from Transformers, recurrent models, and their hybrid architectures. Transformers rely on token-level attention memories, while recurrent models such as state space models (SSMs) and linear attention maintain compact recurrent states. These architectures are typically instantiated separately or interleaved at the layer level, leaving open whether a shared memory representation can support both recurrent compression and attention-style retrieval. We study this question through the state space duality (SSD) view of Mamba-2, where the SSM state can be interpreted as a compressed associative key--value (KV) cache. We observe that Mamba-2 decodes token-conditioned values from this state but does not decode token-conditioned keys. Based on this observation, we propose DART (Decoded Attention over Recurrent sTates), which retains the chunk state contributions produced by the Mamba-2 chunked scan as chunk state memories, decodes token-conditioned keys and values from these memories, and performs state-memory attention (SMA) over the resulting KV pairs. The retrieved output is then combined with the native Mamba-2 output through a gated residual connection. DART supports practical training by reusing the Mamba-2 chunked scan and implementing SMA as a FlashAttention-style computation. Our analysis and experiments show that DART substantially reduces the length-dependent inference cache compared with a matched attention baseline (e.g., $75\%$ savings when the chunk size is $S=256$ and the state size is $N=128$). Compared with Mamba-2, DART substantially improves associative recall and retrieval while preserving general language-modeling quality.

cs.LG↗

arXiv2026

DSSMs: State Space Models with Explicit Memory via Delay Differential Equations

State Space Models (SSMs) have emerged as a powerful paradigm for efficient long-sequence modeling, offering parallel training and fast linear-time recurrent inference. However, like other recurrent architectures, SSMs must compress an unbounded history into a fixed-size state, which limits context retention and makes precise retrieval over long-range context inherently difficult. To overcome this limitation, we propose Delay State Space Models (DSSMs), a delay differential equation (DDE)-inspired extension of diagonal SSMs that augments discrete SSM recurrences with explicit delayed-state feedback. Making explicit delayed feedback practical requires new stability parameterization, history management, and FFT-training tools. We address these challenges with a practical discretization and parameterization grounded in a simple delay-independent stability condition. To bypass direct time-domain kernel construction, we derive the DSSM transfer function and compute kernels in the frequency domain, using a kernel contour shift to suppress aliasing and recover accurate FFT training. Empirically, DSSMs substantially improve targeted delayed-retrieval tasks while outperforming S4D on most standard sequence metrics and remaining close on the others.

cs.LG↗

arXiv2026

A multiphase cubic MARS method for fourth- and higher-order interface tracking of two or more materials with arbitrary topology and geometry

For interface tracking of an arbitrary number of materials in two dimensions, we propose a multiphase cubic MARS method that (a) represents the topology and geometry of the interface via graphs, cycles, and cubic splines, (b) applies to any number of materials with arbitrarily complex topology and geometry, (c) maintains an $(r,h)$-regularity of the interface so that the distance between any pair of adjacent markers is within a user-specified range, (d) distributes the markers adaptively along the interface so that arcs with high curvature are resolved by densely populated markers, and (e) achieves fourth-, sixth-, and eighth-order accuracy both in time and in space.} In particular, all possible types of junctions, which pose challenges to VOF methods and level-set methods, are handled with ease. Results of a variety of benchmark tests confirm the analysis and demonstrate the superior accuracy, efficiency, and versatility of the proposed method.

math.NA↗

arXiv2026

Distributed physics-informed neural networks via domain decomposition for fast flow reconstruction

Physics-Informed Neural Networks (PINNs) offer a powerful paradigm for flow reconstruction, seamlessly integrating sparse velocity measurements with the governing Navier-Stokes equations to recover complete velocity and latent pressure fields. However, scaling such models to large spatiotemporal domains is hindered by computational bottlenecks and optimization instabilities. In this work, we propose a robust distributed PINNs framework designed for efficient flow reconstruction via spatiotemporal domain decomposition. A critical challenge in such distributed solvers is pressure indeterminacy, where independent sub-networks drift into inconsistent local pressure baselines. We address this issue through a reference anchor normalization strategy coupled with decoupled asymmetric weighting. By enforcing a unidirectional information flow from designated master ranks where the anchor point lies to neighboring ranks, our approach eliminates gauge freedom and guarantees global pressure uniqueness while preserving temporal continuity. Furthermore, to mitigate the Python interpreter overhead associated with computing high-order physics residuals, we implement a high-performance training pipeline accelerated by CUDA graphs and JIT compilation. Extensive validation on complex flow benchmarks demonstrates that our method achieves near-linear strong scaling and high-fidelity reconstruction, establishing a scalable and physically rigorous pathway for flow reconstruction and understanding of complex hydrodynamics.

cs.LG↗

arXiv2024

A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains

We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order discretization, (c) optimal complexity. Feature (a) is achieved by Yin space, which is a mathematical model for three-dimensional continua. Feature (b) is accomplished by poised lattice generation (PLG) algorithm, which finds stencils near the irregular boundary for polynomial fitting. Besides, for feature (c), we design a modified multigrid solver whose complexity is theoretically optimal by applying nested dissection (ND) ordering method.

math.NA↗

arXiv2021

Improving the doping efficiency of Al in 4H-SiC by co-doping group-IVB elements

The p-type doping efficiency of 4H silicon carbide (4H-SiC) is rather low due to the large ionization energies of p-type dopants. Such an issue impedes the exploration of the full advantage of 4H-SiC for semiconductor devices. In this letter, we show that co-doping group-IVB elements effectively decreases the ionization energy of the most widely used p-type dopant, i. e., aluminum (Al), through the Coulomb repulsion between the energy levels of group-IVB elements and that of Al in 4H-SiC. Among group-IVB elements Ti has the most prominent effectiveness. Ti decreases the ionization energy of Al by nearly 50%, leading to a value as low as ~ 0.13 eV. As a result, the ionization rate of Al with Ti co-doping is up to ~ 5 times larger than that without co-doping at room temperature when the doping concentration is up to 1018 cm-3. This work may encourage the experimental co-doping of group-IB elements such as Ti and Al to significantly improve the p-type doping efficiency of 4H-SiC.

cond-mat.mtrl-sci↗

arXiv2019

Computing characteristic functions of quantum work in phase space

In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys. Rev. E, 77, 021128 (2008)], and coupled harmonic oscillators under driving forces in a simple and unified way. For general quantum systems, a numerical method that approximates the CFs to $\hbar^2$ order is proposed. We exemplify the method with a time-dependent frequency harmonic oscillator and a family of quantum systems with time-dependent even power-law potentials.

cond-mat.stat-mech↗