arXiv subjects

Changqing Xu

Publications and source records attributed to Changqing Xu.

32 records · Page 2Linked to original sources

arXiv2022

Ultra-low Latency Spiking Neural Networks with Spatio-Temporal Compression and Synaptic Convolutional Block

Spiking neural networks (SNNs), as one of the brain-inspired models, has spatio-temporal information processing capability, low power feature, and high biological plausibility. The effective spatio-temporal feature makes it suitable for event streams classification. However, neuromorphic datasets, such as N-MNIST, CIFAR10-DVS, DVS128-gesture, need to aggregate individual events into frames with a new higher temporal resolution for event stream classification, which causes high training and inference latency. In this work, we proposed a spatio-temporal compression method to aggregate individual events into a few time steps of synaptic current to reduce the training and inference latency. To keep the accuracy of SNNs under high compression ratios, we also proposed a synaptic convolutional block to balance the dramatic change between adjacent time steps. And multi-threshold Leaky Integrate-and-Fire (LIF) with learnable membrane time constant is introduced to increase its information processing capability. We evaluate the proposed method for event streams classification tasks on neuromorphic N-MNIST, CIFAR10-DVS, DVS128 gesture datasets. The experiment results show that our proposed method outperforms the state-of-the-art accuracy on nearly all datasets, using fewer time steps.

cs.NE↗

arXiv2021

A Robust and Reliable Point Cloud Recognition Network Under Rigid Transformation

Point cloud recognition is an essential task in industrial robotics and autonomous driving. Recently, several point cloud processing models have achieved state-of-the-art performances. However, these methods lack rotation robustness, and their performances degrade severely under random rotations, failing to extend to real-world scenarios with varying orientations. To this end, we propose a method named Self Contour-based Transformation (SCT), which can be flexibly integrated into various existing point cloud recognition models against arbitrary rotations. SCT provides efficient rotation and translation invariance by introducing Contour-Aware Transformation (CAT), which linearly transforms Cartesian coordinates of points to translation and rotation-invariant representations. We prove that CAT is a rotation and translation-invariant transformation based on the theoretical analysis. Furthermore, the Frame Alignment module is proposed to enhance discriminative feature extraction by capturing contours and transforming self contour-based frames into intra-class frames. Extensive experimental results show that SCT outperforms the state-of-the-art approaches under arbitrary rotations in effectiveness and efficiency on synthetic and real-world benchmarks. Furthermore, the robustness and generality evaluations indicate that SCT is robust and is applicable to various point cloud processing models, which highlights the superiority of SCT in industrial applications.

cs.CV↗

arXiv2021

Direct Training via Backpropagation for Ultra-low Latency Spiking Neural Networks with Multi-threshold

Spiking neural networks (SNNs) can utilize spatio-temporal information and have a nature of energy efficiency which is a good alternative to deep neural networks(DNNs). The event-driven information processing makes SNNs can reduce the expensive computation of DNNs and save a lot of energy consumption. However, high training and inference latency is a limitation of the development of deeper SNNs. SNNs usually need tens or even hundreds of time steps during the training and inference process which causes not only the increase of latency but also the waste of energy consumption. To overcome this problem, we proposed a novel training method based on backpropagation (BP) for ultra-low latency(1-2 time steps) SNN with multi-threshold. In order to increase the information capacity of each spike, we introduce the multi-threshold Leaky Integrate and Fired (LIF) model. In our proposed training method, we proposed three approximated derivative for spike activity to solve the problem of the non-differentiable issue which cause difficulties for direct training SNNs based on BP. The experimental results show that our proposed method achieves an average accuracy of 99.56%, 93.08%, and 87.90% on MNIST, FashionMNIST, and CIFAR10, respectively with only 2 time steps. For the CIFAR10 dataset, our proposed method achieve 1.12% accuracy improvement over the previously reported direct trained SNNs with fewer time steps.

cs.NE↗

arXiv2021

Multi-dimensional wave steering with higher-order topological phononic crystal

The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at three different orders in a 3D phononic crystal with nontrivial bulk topology originated from the synergy of mirror symmetry of the unit cell and a non-symmorphic glide symmetry of the lattice. The multitude of topological states brings diverse possibility of wave manipulations. Through judicious engineering of the boundary modes, we experimentally demonstrate two functionalities at different dimensions: 2D negative refraction of sound wave enabled by a first-order topological surface state with negative dispersion, and a 3D acoustic interferometer leveraging on second-order topological hinge states. Our work showcases that topological modes at different orders promise diverse wave steering applications across different dimensions.

physics.app-ph↗

arXiv2020

Three-dimensional Electromagnetic Void Space

We report a realization of three-dimensional (3D) electromagnetic void space. Despite occupying a finite volume of space, such a medium is optically equivalent to an infinitesimal point where electromagnetic waves experience no phase accumulation. The 3D void space is realized by constructing all-dielectric 3D photonic crystals such that the effective permittivity and permeability vanish simultaneously, forming a six-fold Dirac-like point with Dirac-like linear dispersions at the center of the Brillouin Zone. We demonstrate, both theoretically and experimentally, that such a 3D void space exhibits unique properties and rich functionalities absent in any other electromagnetic media, such as boundary-control transmission switching and 3D perfect wave-steering mechanisms. Especially, contrary to the photonic "doping" effect in its two-dimensional counterpart, the 3D void space exhibits an amazing property of "impurity-immunity". Our work paves a road towards the realization of 3D void space where electromagnetic waves can be manipulated in unprecedented ways.

physics.optics↗

arXiv2020

High order tensor moments of random vectors

A random vector $\bx\in \R^n$ is a vector whose coordinates are all random variables. A random vector is called a Gaussian vector if it follows Gaussian distribution. These terminology can also be extended to a random (Gaussian) matrix and random (Gaussian) tensor. The classical form of an $k$-order moment (for any positive integer $k$) of a random vector $\bx\in \R^n$ is usually expressed in a matrix form of size $n\times n^{k-1}$ generated from the $k$th derivative of the characteristic function or the moment generating function of $\bx$ , and the expression of an $k$-order moment is very complicate even for a standard normal distributed vector. With the tensor form, we can simplify all the expressions related to high order moments. The main purpose of this paper is to introduce the high order moments of a random vector in tensor forms and the high order moments of a standard normal distributed vector. Finally we present an expression of high order moments of a random vector that follows a Gaussian distribution.

math.PR↗

arXiv2019

Boosting Throughput and Efficiency of Hardware Spiking Neural Accelerators using Time Compression Supporting Multiple Spike Codes

Spiking neural networks (SNNs) are the third generation of neural networks and can explore both rate and temporal coding for energy-efficient event-driven computation. However, the decision accuracy of existing SNN designs is contingent upon processing a large number of spikes over a long period. Nevertheless, the switching power of SNN hardware accelerators is proportional to the number of spikes processed while the length of spike trains limits throughput and static power efficiency. This paper presents the first study on developing temporal compression to significantly boost throughput and reduce energy dissipation of digital hardware SNN accelerators while being applicable to multiple spike codes. The proposed compression architectures consist of low-cost input spike compression units, novel input-and-output-weighted spiking neurons, and reconfigurable time constant scaling to support large and flexible time compression ratios. Our compression architectures can be transparently applied to any given pre-designed SNNs employing either rate or temporal codes while incurring minimal modification of the neural models, learning algorithms, and hardware design. Using spiking speech and image recognition datasets, we demonstrate the feasibility of supporting large time compression ratios of up to 16x, delivering up to 15.93x, 13.88x, and 86.21x improvements in throughput, energy dissipation, the tradeoffs between hardware area, runtime, energy, and classification accuracy, respectively based on different spike codes on a Xilinx Zynq-7000 FPGA. These results are achieved while incurring little extra hardware overhead.

cs.NE↗

arXiv2019

Three-dimensional acoustic double-zero-index medium with a Dirac-like point

We report a design and experimental realization of a three-dimensional (3D) acoustic double-zero-index medium (DZIM), whose effective mass density and compressibility are nearly zero simultaneously. The DZIM is constructed from a cubic lattice of three orthogonally-aligned metal rods in air. The combination of lattice symmetry and accidental degeneracy yields a four-fold degenerate point with conical dispersion at the Brillouin zone center, where the material becomes a 3D DZIM. Though occupying a finite volume, the 3D DZIM maintains the wave properties of a "void space," and enables rich applications. For demonstration, we fabricate an acoustic "periscope" by placing the designed 3D DZIM inside a 3D bending waveguide, and observe the unusual wave tunneling effect through this waveguide with undisturbed planar wavefront. Our findings establish a practical route to realize 3D DZIM as an effective acoustic "void space," which offers unprecedented opportunities for advanced sound manipulation.

physics.app-ph↗

arXiv2018

Commutation matrices and Commutation tensors

The commutation matrix was first introduced in statistics as a transposition matrix by Murnaghan in 1938. In this paper, we first investigate the commutation matrix which is employed to transform a matrix into its transpose. We then extend the concept of the commutation matrix to commutation tensor and use the commutation tensor to achieve the unification of the two formulae of the linear preserver of the matrix rank, a classical result of Marcus in 1971.

math.CO↗

arXiv2018

Topological transitions in continuously-deformed photonic crystals

We demonstrate that multiple topological transitions can occur, with high-sensitivity, by continuous change of the geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. By changing the radii of the holes and/or the distance between them, multiple transitions between normal and topological photonic band gaps (PBGs) can appear. The time-reversal symmetric topological PBGs resemble the quantum spin-Hall insulator of electrons and have two counter-propagating edge states. We search for optimal topological transitions, i.e., sharp transitions sensitive to the geometry, and optimal topological PBGs, i.e., large PBGs with clean spectrum of edge states. Such optimizations reveal that dielectric-frame photonic crystals are promising for optical sensors and unidirectional waveguides.

physics.optics↗

arXiv2016

On {0,1} CP Tensors and CP Multi-hypergraphs

A doubly nonnegative matrix can be written as a Gramian matrix, and a completely positive matrix can therefore be written as a Gramian matrix of some nonnegative vectors. In this paper, we introduce Gramian tensors and study 2-dimension completely positive tensors and {0,1} CP tensors. Also investigated are the complete positive multi-hypergraph, a generalized form of a cp graph. We also provide a necessary and sufficient condition for a 2-dimensional tensor to be completely positive.

math.CO↗

arXiv2015

Completely Positive Tensors and Multi-Hypergraphs

Completely positive graphs have been employed to associate with completely positive matrices for characterizing the intrinsic zero patterns. As tensors have been widely recognized as a higher-order extension of matrices, the multi-hypergraph, regarded as a generalization of graphs, is then introduced to associate with tensors for the study of complete positivity. To describe the dependence of the corresponding zero pattern for a special type of completely positive tensors--the $\{0,1\}$ completely positive tensors, the completely positive multi-hypergraph is defined. By characterizing properties of the associated multi-hypergraph, we provide necessary and sufficient conditions for any $(0,1)$ associated tensor to be $\{0,1\}$ completely positive. Furthermore, a necessary and sufficient condition for a uniform multi-hypergraph to be completely positive multi-hypergraph is proposed as well.

math.CO↗

arXiv2013

When does cp-rank equal rank?

The problem of finding completely positive matrices with equal cp-rank and rank is considered. We give some easy-to-check sufficient conditions on the entries of a doubly nonnegative matrix for it to be completely positive with equal cp-rank and rank. An algorithm is also presented to show its efficiency.

math.CO↗

arXiv2013

Nonnegative Tensor Factorization, Completely Positive Tensors and an Hierarchical Elimination Algorithm

Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has a symmetric nonnegative factorization, is called a completely positive (CP) tensor. The H-eigenvalues of a CP tensor are always nonnegative. When the order is even, the Z-eigenvalue of a CP tensor are all nonnegative. When the order is odd, a Z-eigenvector associated with a positive (negative) Z-eigenvalue of a CP tensor is always nonnegative (nonpositive). The entries of a CP tensor obey some dominance properties. The CP tensor cone and the copositive tensor cone of the same order are dual to each other. We introduce strongly symmetric tensors and show that a symmetric tensor has a symmetric binary decomposition if and only if it is strongly symmetric. Then we show that a strongly symmetric, hierarchically dominated nonnegative tensor is a CP tensor, and present a hierarchical elimination algorithm for checking this. Numerical examples are also given.

math.NA↗