Search arXiv⌕ Search

arXiv subjects

Jiayu Li

Publications and source records attributed to Jiayu Li.

At least 145 records · Page 8Linked to original sources
arXiv2018

On the Universal Approximation Property and Equivalence of Stochastic Computing-based Neural Networks and Binary Neural Networks

Large-scale deep neural networks are both memory intensive and computation-intensive, thereby posing stringent requirements on the computing platforms. Hardware accelerations of deep neural networks have been extensively investigated in both industry and academia. Specific forms of binary neural networks (BNNs) and stochastic computing based neural networks (SCNNs) are particularly appealing to hardware implementations since they can be implemented almost entirely with binary operations. Despite the obvious advantages in hardware implementation, these approximate computing techniques are questioned by researchers in terms of accuracy and universal applicability. Also it is important to understand the relative pros and cons of SCNNs and BNNs in theory and in actual hardware implementations. In order to address these concerns, in this paper we prove that the "ideal" SCNNs and BNNs satisfy the universal approximation property with probability 1 (due to the stochastic behavior). The proof is conducted by first proving the property for SCNNs from the strong law of large numbers, and then using SCNNs as a "bridge" to prove for BNNs. Based on the universal approximation property, we further prove that SCNNs and BNNs exhibit the same energy complexity. In other words, they have the same asymptotic energy consumption with the growing of network size. We also provide a detailed analysis of the pros and cons of SCNNs and BNNs for hardware implementations and conclude that SCNNs are more suitable for hardware.

cs.LG↗
arXiv2018

Structured Weight Matrices-Based Hardware Accelerators in Deep Neural Networks: FPGAs and ASICs

Both industry and academia have extensively investigated hardware accelerations. In this work, to address the increasing demands in computational capability and memory requirement, we propose structured weight matrices (SWM)-based compression techniques for both \emph{field programmable gate array} (FPGA) and \emph{application-specific integrated circuit} (ASIC) implementations. In algorithm part, SWM-based framework adopts block-circulant matrices to achieve a fine-grained tradeoff between accuracy and compression ratio. The SWM-based technique can reduce computational complexity from O($n^2$) to O($n\log n$) and storage complexity from O($n^2$) to O($n$) for each layer and both training and inference phases. For FPGA implementations on deep convolutional neural networks (DCNNs), we achieve at least 152X and 72X improvement in performance and energy efficiency, respectively using the SWM-based framework, compared with the baseline of IBM TrueNorth processor under same accuracy constraints using the data set of MNIST, SVHN, and CIFAR-10. For FPGA implementations on long short term memory (LSTM) networks, the proposed SWM-based LSTM can achieve up to 21X enhancement in performance and 33.5X gains in energy efficiency compared with the baseline accelerator. For ASIC implementations, the SWM-based ASIC design exhibits impressive advantages in terms of power, throughput, and energy efficiency. Experimental results indicate that this method is greatly suitable for applying DNNs onto both FPGAs and mobile/IoT devices.

cs.DC↗
arXiv2018

Charge transport and electron-hole asymmetry in low-mobility graphene/hexagonal boron nitride heterostructures

Graphene/hexagonal boron nitride (G/$h$-BN) heterostructures offer an excellent platform for developing nanoelectronic devices and for exploring correlated states in graphene under modulation by a periodic superlattice potential. Here, we report on transport measurements of nearly $0^{\circ}$-twisted G/$h$-BN heterostructures. The heterostructures investigated are prepared by dry transfer and thermally annealing processes and are in the low mobility regime (approximately $3000~\mathrm{cm}^{2}\mathrm{V}^{-1}\mathrm{s}^{-1}$ at 1.9 K). The replica Dirac spectra and Hofstadter butterfly spectra are observed on the hole transport side, but not on the electron transport side, of the heterostructures. We associate the observed electron-hole asymmetry to the presences of a large difference between the opened gaps in the conduction and valence bands and a strong enhancement in the interband contribution to the conductivity on the electron transport side in the low-mobility G/$h$-BN heterostructures. We also show that the gaps opened at the central Dirac point and the hole-branch secondary Dirac point are large, suggesting the presence of strong graphene-substrate interaction and electron-electron interaction in our G/$h$-BN heterostructures. Our results provide additional helpful insight into the transport mechanism in G/$h$-BN heterostructures.

cond-mat.mes-hall↗
arXiv2017

Electron-Hole Symmetry Breaking in Charge Transport in Nitrogen-Doped Graphene

Graphitic nitrogen-doped graphene is an excellent platform to study scattering processes of massless Dirac fermions by charged impurities, in which high mobility can be preserved due to the absence of lattice defects through direct substitution of carbon atoms in the graphene lattice by nitrogen atoms. In this work, we report on electrical and magnetotransport measurements of high-quality graphitic nitrogen-doped graphene. We show that the substitutional nitrogen dopants in graphene introduce atomically sharp scatters for electrons but long-range Coulomb scatters for holes and, thus, graphitic nitrogen-doped graphene exhibits clear electron-hole asymmetry in transport properties. Dominant scattering processes of charge carriers in graphitic nitrogen-doped graphene are analyzed. It is shown that the electron-hole asymmetry originates from a distinct difference in intervalley scattering of electrons and holes. We have also carried out the magnetotransport measurements of graphitic nitrogen-doped graphene at different temperatures and the temperature dependences of intervalley scattering, intravalley scattering and phase coherent scattering rates are extracted and discussed. Our results provide an evidence for the electron-hole asymmetry in the intervalley scattering induced by substitutional nitrogen dopants in graphene and shine a light on versatile and potential applications of graphitic nitrogen-doped graphene in electronic and valleytronic devices.

cond-mat.mes-hall↗
arXiv2017

Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold

In this paper, we will study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map $(u,v)$ from a smooth bounded open domain $Ω\subset\R^m$ to a Lorentzian manifold with Dirichlet boundary condition, we prove that it is smooth outside a closed set whose $(m-2)$-dimension Hausdorff measure is zero. Moreover, if the target manifold $N$ does not admit any harmonic sphere $S^l$, $l=2,...,m-1$, we will show $(u,v)$ is smooth.

math.AP↗
arXiv2017

The limit of the Hermitian-Yang-Mills flow on reflexive sheaves

In this paper, we study the asymptotic behavior of the Hermitian-Yang-Mills flow on a reflexive sheaf. We prove that the limiting reflexive sheaf is isomorphic to the double dual of the graded sheaf associated to the Harder-Narasimhan-Seshadri filtration, this answers a question by Bando and Siu.

math.DG↗
arXiv2016

Quasi-Normal Mode Theory for Thermal Radiation from Lossy and Dispersive Optical Resonators

Although optical resonators are widely used for controlling and engineering thermal radiation, what has been lacking is a general theoretical framework to elucidate the thermal emission of optical resonators, and guide the design and application of thermally driven optical resonators. We developed a general and self-consistent formalism to describe the thermal radiation from arbitrary optical resonators made by lossy and dispersive materials like metals, with the only assumption that the resonators have a single predominant resonance mode. Our formalism demonstrates that the thermal emission of an optical resonator is maximized when the mode losses to the emitter and the absorber (or far-field background) are matched, and meanwhile the predominant resonant modes are electrically quasi-static. By efficiently calculating the resonant modes using the finite element methods, our formalism serves as a general principle of designing the arbitrary optical resonator thermal emitters with perfect or maximized emission.

physics.optics↗
arXiv2016

A note on curvature estimate of the Hermitian-Yang-Mills flow

In this paper, we study the curvature estimate of the Hermitian-Yang-Mills flow on holomorphic vector bundles. In one simple case, we show that the curvature of the evolved Hermitian metric is uniformly bounded away from the analytic subvariety determined by the Harder-Narasimhan-Seshadri filtration of the holomorphic vector bundle.

math.DG↗
arXiv2016

The deformation of symplectic critical surfaces in a Kähler surface-II---Compactness

In this paper we consider the compactness of $β$-symplectic critical surfaces in a Kähler surface. Let $M$ be a compact Kähler surface and $Σ_i\subset M$ be a sequence of closed $β_i$-symplectic critical surfaces with $β_i\toβ_0\in (0,\infty)$. Suppose the quantity $\int_{Σ_i}\frac{1}{\cos^qα_i}dμ_i$ (for some $q>4$) and the genus of $Σ_{i}$ are bounded, then there exists a finite set of points ${\mathcal S}\subset M$ and a subsequence $Σ_{i'}$ that converges uniformly in the $C^l$ topology (for any $l<\infty$) on compact subsets of $M\backslash {\mathcal S}$ to a $β_0$-symplectic critical surface $Σ\subset M$, each connected component of $Σ\setminus {\mathcal S}$ can be extended smoothly across ${\mathcal S}$.

math.DG↗
arXiv2016

A note on the nonexistence of quasi-harmonic spheres

In this paper we study the properties of quasi-harmonic spheres from $\R^m, m>2$. We show that if the universal covering $\tilde N$ of $N$ admits a nonnegative strictly convex function $ρ$ with the exponential growth condition $ρ(y)\leq C\exp\left(\frac14\tilde d(y)^{2/m}\right)$ where $\tilde d(y)$ is the distance function on $\tilde N$, then $N$ does not admit a quasi-harmonic sphere, which generalize Li-Zhu's result \cite{Li2010non}. We also show that if $u$ is a quasi-harmonic sphere, then the property that $u$ is of finite energy ($\int_{\R^m}e(u)e^{-\abs{x}^2/4}\dif x<\infty$) is equivalent to the property that $u$ satisfies the large energy condition ($\lim_{R\to\infty}R^{m}e^{-R^2/4}\int_{B_R(0)}e(u)e^{-\abs{x}^2/4}\diff x=0$).

math.DG↗
arXiv2016

Semi-stable Higgs sheaves and Bogomolov type inequality

In this paper, we study semistable Higgs sheaves over compact Kähler manifolds, we prove that there is an approximate admissible Hermitian-Einstein structure on a semi-stable reflexive Higgs sheaf and consequently, the Bogomolove type inequality holds on a semi-stable reflexive Higgs sheaf.

math.DG↗
arXiv2015

The limit of the Yang-Mills-Higgs flow on Higgs bundles

In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a compact Kähler manifold $(M, ω)$. We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity, and show that the limiting Higgs sheaf is isomorphic to the double dual of the graded Higgs sheaves associated to the Harder-Narasimhan-Seshadri filtration of the initial Higgs bundle.

math.DG↗
arXiv2015

The deformation of symplectic critical surfaces in a Kähler surface-I

In this paper we derive the Euler-Lagrange equation of the functional $L_β=\int_Σ\frac{1}{\cos^βα}dμ, ~~β\neq -1$ in the class of symplectic surfaces. It is $\cos^3α{\bf{H}}=β(J(J\nabla\cosα)^\top)^\bot$, which is an elliptic equation when $β\geq 0$. We call such a surface a $β$-symplectic critical surface. We first study the properties for each fixed $β$-symplectic critical surface and then prove that the set of $β$ where there is a stable $β$-symplectic critical surface is open. We believe it should be also closed. As a precise example, we study rotationally symmetric $β$-symplectic critical surfaces in ${\mathbb C}^2$ carefully .

math.DG↗
arXiv2013

Lagrangian F-stability of closed Lagrangian self-shrinkers

In this paper, we study the Lagrangian F-stability of closed Lagrangian self-shrinkers immersed in complex Euclidean space. We show that any closed Lagrangian self-shrinker with first Betti number greater than one is Lagrangian F-unstable. In particular, any two-dimensional embedded closed Lagrangian self-shrinker is Lagrangian F-unstable. For a closed Lagrangian self-shrinker with first Betti number equal to one, we show that Lagrangian F-stability is equivalent to Hamiltonian F-stability. We also characterize Hamiltonian F-stability of a closed Lagrangian self-shrinker by its spectral property of the twisted Laplacian.

math.DG↗
arXiv2011

Long time existence of the symplectic mean curvature flow

Let $(M,\bar{g})$ be a Kähler surface with a constant holomorphic sectional curvature $k>0$, and $Σ$ an immersed symplectic surface in $M$. Suppose $Σ$ evolves along the mean curvature flow in $M$. In this paper, we show that the symplectic mean curvature flow exists for long time and converges to a holomorphic curve if the initial surface satisfies $|A|^2\leq 2/3|H|^2+1/2 k$ and $\cosα\geq \frac{\sqrt{30}}{6}$ or $|A|^2\leq 2/3 |H|^2+4/5 k\cosα$ and $\cosα\ge251/265$.

math.DG↗