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Yichao Zhang

Publications and source records attributed to Yichao Zhang.

At least 73 records · Page 4Linked to original sources
arXiv2024

Semi-supervised segmentation of land cover images using nonlinear canonical correlation analysis with multiple features and t-SNE

Image segmentation is a clustering task whereby each pixel is assigned a cluster label. Remote sensing data usually consists of multiple bands of spectral images in which there exist semantically meaningful land cover subregions, co-registered with other source data such as LIDAR (LIght Detection And Ranging) data, where available. This suggests that, in order to account for spatial correlation between pixels, a feature vector associated with each pixel may be a vectorized tensor representing the multiple bands and a local patch as appropriate. Similarly, multiple types of texture features based on a pixel's local patch would also be beneficial for encoding locally statistical information and spatial variations, without necessarily labelling pixel-wise a large amount of ground truth, then training a supervised model, which is sometimes impractical. In this work, by resorting to label only a small quantity of pixels, a new semi-supervised segmentation approach is proposed. Initially, over all pixels, an image data matrix is created in high dimensional feature space. Then, t-SNE projects the high dimensional data onto 3D embedding. By using radial basis functions as input features, which use the labelled data samples as centres, to pair with the output class labels, a modified canonical correlation analysis algorithm, referred to as RBF-CCA, is introduced which learns the associated projection matrix via the small labelled data set. The associated canonical variables, obtained for the full image, are applied by k-means clustering algorithm. The proposed semi-supervised RBF-CCA algorithm has been implemented on several remotely sensed multispectral images, demonstrating excellent segmentation results.

cs.CV↗
arXiv2024

MX: Enhancing RISC-V's Vector ISA for Ultra-Low Overhead, Energy-Efficient Matrix Multiplication

Dense Matrix Multiplication (MatMul) is arguably one of the most ubiquitous compute-intensive kernels, spanning linear algebra, DSP, graphics, and machine learning applications. Thus, MatMul optimization is crucial not only in high-performance processors but also in embedded low-power platforms. Several Instruction Set Architectures (ISAs) have recently included matrix extensions to improve MatMul performance and efficiency at the cost of added matrix register files and units. In this paper, we propose Matrix eXtension (MX), a lightweight approach that builds upon the open-source RISC-V Vector (RVV) ISA to boost MatMul energy efficiency. Instead of adding expensive dedicated hardware, MX uses the pre-existing vector register file and functional units to create a hybrid vector/matrix engine at a negligible area cost (< 3%), which comes from a compact near-FPU tile buffer for higher data reuse, and no clock frequency overhead. We implement MX on a compact and highly energy-optimized RVV processor and evaluate it in both a Dual- and 64-Core cluster in a 12-nm technology node. MX boosts the Dual-Core's energy efficiency by 10% for a double-precision 64x64x64 matrix multiplication with the same FPU utilization (~97%) and by 25% on the 64-Core cluster for the same benchmark on 32-bit data, with a 56% performance gain.

cs.AR↗
arXiv2024

DeepSeek LLM: Scaling Open-Source Language Models with Longtermism

The rapid development of open-source large language models (LLMs) has been truly remarkable. However, the scaling law described in previous literature presents varying conclusions, which casts a dark cloud over scaling LLMs. We delve into the study of scaling laws and present our distinctive findings that facilitate scaling of large scale models in two commonly used open-source configurations, 7B and 67B. Guided by the scaling laws, we introduce DeepSeek LLM, a project dedicated to advancing open-source language models with a long-term perspective. To support the pre-training phase, we have developed a dataset that currently consists of 2 trillion tokens and is continuously expanding. We further conduct supervised fine-tuning (SFT) and Direct Preference Optimization (DPO) on DeepSeek LLM Base models, resulting in the creation of DeepSeek Chat models. Our evaluation results demonstrate that DeepSeek LLM 67B surpasses LLaMA-2 70B on various benchmarks, particularly in the domains of code, mathematics, and reasoning. Furthermore, open-ended evaluations reveal that DeepSeek LLM 67B Chat exhibits superior performance compared to GPT-3.5.

cs.CL↗
arXiv2024

Hilbert Poincaré series and kernels for products of $L$-functions

We study Hilbert Poincaré series associated to general seed functions and construct Cohen's kernels and double Eisenstein series as series of Hilbert Poincaré series. Then we calculate the Rankin-Cohen brackets of Hilbert Poincaré series and Hilbert modular forms and extend Zagier's kernel formula to totally real number fields. Finally, we show that the Rankin-Cohen brackets of two different types of Eisenstein series are special values of double Eisenstein series up to a constant.

math.NT↗
arXiv2023

On the non-vanishing of Hilbert Poincaré series

We prove that if $ν$ has small norm with respect to the level and the weight, the $ν$-th Hilbert Poincaré series does not vanish identically. We also prove Selberg's identity on Kloosterman sums in the case of number fields, which implies certain vanishing and non-vanishing relations of Hilbert Poincaré series when the narrow class number is $1$. Finally, we pass to the adelic setting and interpret the problem via Hecke operators.

math.NT↗
arXiv2023

Fast Shared-Memory Barrier Synchronization for a 1024-Cores RISC-V Many-Core Cluster

Synchronization is likely the most critical performance killer in shared-memory parallel programs. With the rise of multi-core and many-core processors, the relative impact on performance and energy overhead of synchronization is bound to grow. This paper focuses on barrier synchronization for TeraPool, a cluster of 1024 RISC-V processors with non-uniform memory access to a tightly coupled 4MB shared L1 data memory. We compare the synchronization strategies available in other multi-core and many-core clusters to identify the optimal native barrier kernel for TeraPool. We benchmark a set of optimized barrier implementations and evaluate their performance in the framework of the widespread fork-join Open-MP style programming model. We test parallel kernels from the signal-processing and telecommunications domain, achieving less than 10% synchronization overhead over the total runtime for problems that fit TeraPool's L1 memory. By fine-tuning our tree barriers, we achieve 1.6x speed-up with respect to a naive central counter barrier and just 6.2% overhead on a typical 5G application, including a challenging multistage synchronization kernel. To our knowledge, this is the first work where shared-memory barriers are used for the synchronization of a thousand processing elements tightly coupled to shared data memory.

cs.DC↗
arXiv2023

In situ Imaging of an Anisotropic Layer-by-Layer Phase Transition in Few-Layer MoTe2

Understanding the phase transition mechanisms in two-dimensional (2D) materials is a key to precisely tailor their properties at the nanoscale. Molybdenum ditelluride (MoTe2) exhibits multiple phases at room temperature, making it a promising candidate for phase-change applications. Here, we fabricate lateral 2H-Td interfaces with laser irradiation and probe their phase transitions from micro- to atomic scales with in situ heating in the transmission electron microscope (TEM). By encapsulating the MoTe2 with graphene protection layers, we create an in situ reaction cell compatible with atomic resolution imaging. We find that the Td-to-2H phase transition initiates at phase boundaries at low temperatures (200-225 degree C) and propagates anisotropically along the b-axis in a layer-by-layer fashion. We also demonstrate a fully reversible 2H-Td-2H phase transition cycle, which generates a coherent 2H lattice containing inversion domain boundaries. Our results provide insights on fabricating 2D hetero-phase devices with atomically sharp and coherent interfaces.

cond-mat.mtrl-sci↗
arXiv2022

Efficient Parallelization of 5G-PUSCH on a Scalable RISC-V Many-core Processor

5G Radio access network disaggregation and softwarization pose challenges in terms of computational performance to the processing units. At the physical layer level, the baseband processing computational effort is typically offloaded to specialized hardware accelerators. However, the trend toward software-defined radio-access networks demands flexible, programmable architectures. In this paper, we explore the software design, parallelization and optimization of the key kernels of the lower physical layer (PHY) for physical uplink shared channel (PUSCH) reception on MemPool and TeraPool, two manycore systems having respectively 256 and 1024 small and efficient RISC-V cores with a large shared L1 data memory. PUSCH processing is demanding and strictly time-constrained, it represents a challenge for the baseband processors, and it is also common to most of the uplink channels. Our analysis thus generalizes to the entire lower PHY of the uplink receiver at gNodeB (gNB). Based on the evaluation of the computational effort (in multiply-accumulate operations) required by the PUSCH algorithmic stages, we focus on the parallel implementation of the dominant kernels, namely fast Fourier transform, matrix-matrix multiplication, and matrix decomposition kernels for the solution of linear systems. Our optimized parallel kernels achieve respectively on MemPool and TeraPool speedups of 211, 225, 158, and 762, 880, 722, at high utilization (0.81, 0.89, 0.71, and 0.74, 0.88, 0.71), comparable a single-core serial execution, moving a step closer toward a full-software PUSCH implementation.

cs.DC↗
arXiv2022

Soft Tiles: Capturing Physical Implementation Flexibility for Tightly-Coupled Parallel Processing Clusters

Modern high-performance computing architectures (Multicore, GPU, Manycore) are based on tightly-coupled clusters of processing elements, physically implemented as rectangular tiles. Their size and aspect ratio strongly impact the achievable operating frequency and energy efficiency, but they should be as flexible as possible to achieve a high utilization for the top-level die floorplan. In this paper, we explore the flexibility range for a high-performance cluster of RISC-V cores with shared L1 memory used to build scalable accelerators, with the goal of establishing a hierarchical implementation methodology where clusters can be modeled as soft tiles to achieve optimal die utilization.

cs.AR↗
arXiv2021

Rationality of the Petersson Inner Product of Cohen's Kernels

By explicitly calculating and then analytically continuing the Fourier expansion of the twisted double Eisenstein series $E_{s,k-s}^{*}(z,w; 1/2)$ of Diamantis and O'Sullivan, we prove a formula of the Petersson inner product of Cohen's kernel and one of its twists, and obtain a rationality result. This extends a result of Kohnen and Zagier.

math.NT↗
arXiv2021

Error estimate of a decoupled numerical scheme for the Cahn-Hilliard-Stokes-Darcy system

We analyze a fully discrete finite element numerical scheme for the Cahn-Hilliard-Stokes-Darcy system that models two-phase flows in coupled free flow and porous media. To avoid a well-known difficulty associated with the coupling between the Cahn-Hilliard equation and the fluid motion, we make use of the operator-splitting in the numerical scheme, so that these two solvers are decoupled, which in turn would greatly improve the computational efficiency. The unique solvability and the energy stability have been proved in~\cite{CHW2017}. In this work, we carry out a detailed convergence analysis and error estimate for the fully discrete finite element scheme, so that the optimal rate convergence order is established in the energy norm, i.e.,, in the $\ell^\infty (0, T; H^1) \cap \ell^2 (0, T; H^2)$ norm for the phase variables, as well as in the $\ell^\infty (0, T; H^1) \cap \ell^2 (0, T; H^2)$ norm for the velocity variable. Such an energy norm error estimate leads to a cancellation of a nonlinear error term associated with the convection part, which turns out to be a key step to pass through the analysis. In addition, a discrete $\ell^2 (0;T; H^3)$ bound of the numerical solution for the phase variables plays an important role in the error estimate, which is accomplished via a discrete version of Gagliardo-Nirenberg inequality in the finite element setting.

math.NA↗
arXiv2021

Multi-Task Variational Information Bottleneck

Multi-task learning (MTL) is an important subject in machine learning and artificial intelligence. Its applications to computer vision, signal processing, and speech recognition are ubiquitous. Although this subject has attracted considerable attention recently, the performance and robustness of the existing models to different tasks have not been well balanced. This article proposes an MTL model based on the architecture of the variational information bottleneck (VIB), which can provide a more effective latent representation of the input features for the downstream tasks. Extensive observations on three public data sets under adversarial attacks show that the proposed model is competitive to the state-of-the-art algorithms concerning the prediction accuracy. Experimental results suggest that combining the VIB and the task-dependent uncertainties is a very effective way to abstract valid information from the input features for accomplishing multiple tasks.

cs.LG↗
arXiv2020

Simultaneous nonvanishing of the Products of L-functions associated to elliptic cusp forms

A generalized Riemann hypothesis states that all zeros of the completed Hecke $L$-function $L^*(f,s)$ of a normalized Hecke eigenform $f$ on the full modular group should lie on the vertical line $Re(s)=\frac{k}{2}.$ It was shown by Kohnen that there exists a Hecke eigenform $f$ of weight $k$ such that $L^*(f,s) \neq 0$ for sufficiently large $k$ and any point on the line segments $Im(s)=t_0, \frac{k-1}{2} < Re(s) < \frac{k}{2}-ε, \frac{k }{2}+ε< Re(s) < \frac{k+1}{2},$ for any given real number $t_0$ and a positive real number $ε.$ This paper concerns the non-vanishing of the product $L^*(f,s)L^*(f,w)$ $(s,w\in \mathbb{C})$ on average.

math.NT↗
arXiv2019

Post-Disturbance Dynamic Frequency Features Prediction Based on Convolutional Neural Network

The significant imbalance between power generation and load caused by severe disturbance may make the power system unable to maintain a steady frequency. If the post-disturbance dynamic frequency features can be predicted and emergency controls are appropriately taken, the risk of frequency instability will be greatly reduced. In this paper, a predictive algorithm for post-disturbance dynamic frequency features is proposed based on convolutional neural network (CNN) . The operation data before and immediately after disturbance is used to construct the input tensor data of CNN, with the dynamic frequency features of the power system after the disturbance as the output. The operation data of the power system such as generators unbalanced power has spatial distribution characteristics. The electrical distance is presented to describe the spatial correlation of power system nodes, and the t-SNE dimensionality reduction algorithm is used to map the high-dimensional distance information of nodes to the 2-D plane, thereby constructing the CNN input tensor to reflect spatial distribution of nodes operation data on 2-D plane. The CNN with deep network structure and local connectivity characteristics is adopted and the network parameters are trained by utilizing the backpropagation-gradient descent algorithm. The case study results on an improved IEEE 39-node system and an actual power grid in USA shows that the proposed method can predict the lowest frequency of power system after the disturbance accurately and quickly.

eess.SP↗
arXiv2017

Half-Integral Weight Modular Forms and Modular forms for Weil representations

We establish an isomorphism between certain complex-valued and vector-valued modular form spaces of half-integral weight, generalizing the well-known isomorphism between modular forms for $Γ_0(4)$ with Kohnen's plus condition and modular forms for the Weil representation associated to the discriminant form for the lattice with Gram matrix $(2)$. With such an isomorphism, we prove the Zagier duality and write down the Borcherds lifts explicitly.

math.NT↗
arXiv2017

Video Acceleration Magnification

The ability to amplify or reduce subtle image changes over time is useful in contexts such as video editing, medical video analysis, product quality control and sports. In these contexts there is often large motion present which severely distorts current video amplification methods that magnify change linearly. In this work we propose a method to cope with large motions while still magnifying small changes. We make the following two observations: i) large motions are linear on the temporal scale of the small changes; ii) small changes deviate from this linearity. We ignore linear motion and propose to magnify acceleration. Our method is pure Eulerian and does not require any optical flow, temporal alignment or region annotations. We link temporal second-order derivative filtering to spatial acceleration magnification. We apply our method to moving objects where we show motion magnification and color magnification. We provide quantitative as well as qualitative evidence for our method while comparing to the state-of-the-art.

cs.CV↗