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Jianwei Zhou

Publications and source records attributed to Jianwei Zhou.

11 recordsLinked to original sources
arXiv2026

Adaptive Matrix Multiplication for Dynamic Shapes on Ascend NPUs

Matrix Multiplication (MatMul) faces a "generalization crisis" driven by highly dynamic tensor shapes. This crisis is particularly acute on Ascend NPUs, where explicitly controlled architectures and strict physical constraints render existing GPU-centric optimizations ineffective. To resolve this, we propose AdaptCore, an adaptive framework for universally high-performance MatMul on Ascend NPUs. AdaptCore systematically decouples operator optimization into spatial tiling and instruction orchestration. It first maps dynamic shapes into a hardware-aware 2D tiling taxonomy to balance on-chip capacity limits and multi-core parallelism. Furthermore, it integrates a composable optimization library with a deterministic analytical performance model. By mathematically evaluating hardware state mutations, AdaptCore proactively selects and caches optimal implementations, enabling O(1) overhead runtime dispatching. Evaluations demonstrate that AdaptCore delivers a remarkable 1.85x mean speedup across 80,000 input shapes, and achieves up to a 1.48x acceleration in representative end-to-end models over the highly-tuned native vendor library (ACLNN).

cs.AR↗
arXiv2026

A novel Chebyshev collocation method for elliptic -type differential equations with degenerate coefficient

A novel collocation scheme is presented for elliptic-type differential equations with degenerate coefficients and homogeneous Dirichlet boundary conditions. The use of weighted orthogonal Chebyshev polynomials for the basis functions leads to stiffness matrices with sparse structure, enabling efficient direct calculations. By an orthogonal projection, rigorous analyses are devoted to deriving a-priori error estimates of spectral accuracy in two norms. Furthermore, ample numerical experiments are conducted and compared with error data, convergence rates, condition numbers and $N$-$\log$ curves to confirm the theoretical analyses results. Our proposed method achieves spectral accuracy and handles boundary singularities efficiently, as demonstrated by theoretical analyses and numerical experiments.

math.NA↗
arXiv2026

A novel mixed spectral method with ball polynomials for the Biharmonic equation on a unit ball

A novel mixed spectral-Galerkin method based on generalized ball polynomials is proposed for solving the biharmonic equation on a unit ball. By introducing an auxiliary variable to decouple the biharmonic equation into a system of second-order equations, the corresponding discrete scheme yields a strictly diagonal stiffness matrix, which significantly enhances the computational efficiency. Rigorous a-priori error estimates are established to demonstrate the exponential convergence rates in both the $L^2$- and $H^1$-norms. Extensive numerical experiments are conducted to verify the theoretical analysis and confirm the high efficiency and accuracy of the proposed scheme.

math.NA↗
arXiv2018

Attention-based sequence-to-sequence model for speech recognition: development of state-of-the-art system on LibriSpeech and its application to non-native English

Recent research has shown that attention-based sequence-to-sequence models such as Listen, Attend, and Spell (LAS) yield comparable results to state-of-the-art ASR systems on various tasks. In this paper, we describe the development of such a system and demonstrate its performance on two tasks: first we achieve a new state-of-the-art word error rate of 3.43% on the test clean subset of LibriSpeech English data; second on non-native English speech, including both read speech and spontaneous speech, we obtain very competitive results compared to a conventional system built with the most updated Kaldi recipe.

cs.CL↗
arXiv2017

The Complex Structures on $S^{2n}$

Let $\widetilde{\cal J}(S^{2n})$ be the set of orthogonal complex structures on $TS^{2n}$. We show that the twistor space $\widetilde{\cal J}(S^{2n})$ is a Kaehler manifold. Then we show that an orthogonal almost complex structure $J_f$ on $S^{2n}$ is integrable if and only if the corresponding section $f\colon\; S^{2n}\to \widetilde{\cal J}(S^{2n}) $ is holomorphic. These shows there is no integrable orthogonal complex structure on the sphere $S^{2n}$ for $n>1$. We also show that there is no complex structure in a neighborhood of the space $\widetilde{\cal J}(S^{2n})$. The method is to study the first Chern class of $T^{(1,0)}S^{2n}$.

math.DG↗
arXiv2011

Almost Complex Structure on $S^{2n}$

We show that there is no complex structure in a neighborhood of the space of orthogonal almost complex structures on the sphere $S^{2n}, \ n>1$. The method is to study the first Chern class of vetcor bundle $T^{(1,0)}S^{2n}$.

math.DG↗
arXiv2008

Characteristic Classes on Grassmann Manifolds

In this paper, we use characteristic classes of the canonical vector bundles and the Poincar\' {e} dualality to study the structure of the real homology and cohomology groups of oriented Grassmann manifold $G(k, n)$. Show that for $k=2$ or $n\leq 8$, the cohomology groups $H^*(G(k,n),{\bf R})$ are generated by the first Pontrjagin class, the Euler classes of the canonical vector bundles. In these cases, the Poincar\' {e} dualality: $H^q(G(k,n),{\bf R}) \to H_{k(n-k)-q}(G(k,n),{\bf R})$ can be given explicitly.

math.FA↗
arXiv2006

Grassmann Manifold G(2,8) and Complex Structure on $S^6$

In this paper, we use Clifford algebra and the spinor calculus to study the complex structures on Euclidean space $R^8$ and the spheres $S^4,S^6$. By the spin representation of $G(2,8)\subset Spin(8)$ we show that the Grassmann manifold G(2,8) can be looked as the set of orthogonal complex structures on $R^8$. In this way, we show that G(2,8) and $CP^{3}$ can be looked as twistor spaces of $S^6$ and $S^4$ respectively. Then we show that there is no almost complex structure on sphere $S^4$ and there is no orthogonal complex structure on the sphere $S^6$.

math.DG↗
arXiv2006

A Note on Characteristic Classes

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

math.DG↗
arXiv2006

The Geometry and Topology on Grassmann Manifolds

This paper shows that the Grassmann Manifolds $G_{\bf F}(n,N)$ can all be imbedded in an Euclidean space $M_{\bf F}(N)$ naturally and the imbedding can be realized by the eigenfunctions of Laplacian $\triangle$ on $G_{\bf F}(n,N)$. They are all minimal submanifolds in some spheres of $M_{\bf F}(N)$ respectively. Using these imbeddings, we construct some degenerate Morse functions on Grassmann Manifolds, show that the homology of the complex and quaternion Grassmann Manifolds can be computed easily.

math.DG↗