arXiv subjects

Weihong Xu

Publications and source records attributed to Weihong Xu.

At least 37 records · Page 2Linked to original sources

arXiv2025

On Vanishing of Gromov--Witten Invariants

We consider the decision problem of whether a particular Gromov--Witten invariant on a partial flag variety is zero. We prove that for the $3$-pointed, genus zero invariants, this problem is in the complexity class ${\sf AM}$ assuming the Generalized Riemann Hypothesis (GRH), and therefore lies in the second level of polynomial hierarchy ${\sf PH}$. For the proof, we construct an explicit system of polynomial equations through a translation of the defining equations. We also need to prove an extension of the Parametric Hilbert's Nullstellensatz to obtain our central reduction.

math.AG↗

arXiv2025

Clo-HDnn: A 4.66 TFLOPS/W and 3.78 TOPS/W Continual On-Device Learning Accelerator with Energy-efficient Hyperdimensional Computing via Progressive Search

Clo-HDnn is an on-device learning (ODL) accelerator designed for emerging continual learning (CL) tasks. Clo-HDnn integrates hyperdimensional computing (HDC) along with low-cost Kronecker HD Encoder and weight clustering feature extraction (WCFE) to optimize accuracy and efficiency. Clo-HDnn adopts gradient-free CL to efficiently update and store the learned knowledge in the form of class hypervectors. Its dual-mode operation enables bypassing costly feature extraction for simpler datasets, while progressive search reduces complexity by up to 61% by encoding and comparing only partial query hypervectors. Achieving 4.66 TFLOPS/W (FE) and 3.78 TOPS/W (classifier), Clo-HDnn delivers 7.77x and 4.85x higher energy efficiency compared to SOTA ODL accelerators.

cs.AR↗

arXiv2025

SLIM: A Heterogeneous Accelerator for Edge Inference of Sparse Large Language Model via Adaptive Thresholding

Large language models (LLMs) have demonstrated exceptional proficiency in understanding and generating human language, but efficient inference on resource-constrained embedded devices remains challenging due to large model sizes and memory-intensive operations in feedforward network (FFN) and multi-head attention (MHA) layers. While existing accelerators offload LLM inference to expensive heterogeneous computing systems, they fail to exploit the significant sparsity inherent in LLM operations, leaving hardware resources underutilized. We propose SLIM, an algorithm-hardware co-design optimized for sparse LLM serving on edge devices. SLIM exploits LLM sparsity through an adaptive thresholding algorithm that enables runtime-configurable sparsity with negligible accuracy loss, fetching only activated neurons to dramatically reduce data movement. Our heterogeneous hardware architecture strategically combines near-storage processing (NSP) and processing-in-memory (PIM): FFN weights are stored in high-density 3D NAND and computed using NSP units, while memory-intensive MHA operations are processed in PIM modules. This design significantly reduces memory footprint, data movement, and energy consumption. Our comprehensive evaluation demonstrates SLIM's effectiveness, achieving 13-18x throughput improvements over SSD-GPU systems and 9-10x better energy efficiency over DRAM-GPU systems while maintaining low latency, making cost-effective LLM deployment viable for edge computing environments.

cs.AR↗

arXiv2025

HPVM-HDC: A Heterogeneous Programming System for Accelerating Hyperdimensional Computing

Hyperdimensional Computing (HDC), a technique inspired by cognitive models of computation, has been proposed as an efficient and robust alternative basis for machine learning. HDC programs are often manually written in low-level and target specific languages targeting CPUs, GPUs, and FPGAs -- these codes cannot be easily retargeted onto HDC-specific accelerators. No previous programming system enables productive development of HDC programs and generates efficient code for several hardware targets. We propose a heterogeneous programming system for HDC: a novel programming language, HDC++, for writing applications using a unified programming model, including HDC-specific primitives to improve programmability, and a heterogeneous compiler, HPVM-HDC, that provides an intermediate representation for compiling HDC programs to many hardware targets. We implement two tuning optimizations, automatic binarization and reduction perforation, that exploit the error resilient nature of HDC. Our evaluation shows that HPVM-HDC generates performance-competitive code for CPUs and GPUs, achieving a geomean speed-up of 1.17x over optimized baseline CUDA implementations with a geomean reduction in total lines of code of 1.6x across CPUs and GPUs. Additionally, HPVM-HDC targets an HDC Digital ASIC and an HDC ReRAM accelerator simulator, enabling the first execution of HDC applications on these devices.

cs.PL↗

arXiv2025

DeePMD-kit v3: A Multiple-Backend Framework for Machine Learning Potentials

In recent years, machine learning potentials (MLPs) have become indispensable tools in physics, chemistry, and materials science, driving the development of software packages for molecular dynamics (MD) simulations and related applications. These packages, typically built on specific machine learning frameworks such as TensorFlow, PyTorch, or JAX, face integration challenges when advanced applications demand communication across different frameworks. The previous TensorFlow-based implementation of DeePMD-kit exemplified these limitations. In this work, we introduce DeePMD-kit version 3, a significant update featuring a multi-backend framework that supports TensorFlow, PyTorch, JAX, and PaddlePaddle backends, and demonstrate the versatility of this architecture through the integration of other MLPs packages and of Differentiable Molecular Force Field. This architecture allows seamless backend switching with minimal modifications, enabling users and developers to integrate DeePMD-kit with other packages using different machine learning frameworks. This innovation facilitates the development of more complex and interoperable workflows, paving the way for broader applications of MLPs in scientific research.

physics.chem-ph↗

arXiv2025

Stringy Chow rings and weighted blow ups

We compute the stringy chow ring of a general Deligne-Mumford stack of the form [X/G] for a smooth variety X and diagonalizable group scheme G, working over a base field that is not necessarily algebraically closed. We then specialize to the stringy chow ring of the weighted blow up of a smooth variety along a smooth center. We explore finite generation properties of this ring.

math.AG↗

arXiv2024

Quantum K Whitney relations for partial flag varieties

In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We start by proving a Nakayama type result for quantum K theory: if the conjectured set of relations deforms a complete set of relations of the classical K theory ring, then they must form a complete set of relations for the quantum K ring. We prove the conjectured presentation in the case of the incidence varieties, and we show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety. Finally, we briefly revisit the change of variables relating the mathematics and physics presentations.

math.AG↗

arXiv2024

RapidOMS: FPGA-based Open Modification Spectral Library Searching with HD Computing

Mass spectrometry (MS) is essential for protein analysis but faces significant challenges with large datasets and complex post-translational modifications, resulting in difficulties in spectral identification. Open Modification Search (OMS) improves the analysis of these modifications. We present RapidOMS, a solution leveraging the Samsung SmartSSD, which integrates SSD and FPGA in a near-storage configuration to minimize data movement and enhance the efficiency of large-scale database searching. RapidOMS employs hyperdimensional computing (HDC), a brain-inspired, high-dimensional data processing approach, exploiting the parallel processing and low-latency capabilities of FPGAs, making it well-suited for MS. Utilizing the parallelism and efficiency of bitwise operations in HDC, RapidOMS delivers up to a 60x speedup over the state-of-the-art (SOTA) CPU tool ANN-Solo and is 2.72x faster than the GPU tool HyperOMS. Furthermore, RapidOMS achieves an 11x improvement in energy efficiency compared to conventional systems, providing scalable, energy-efficient solutions for large-scale proteomics applications and advancing the efficient processing of proteomic data.

cs.DC↗

arXiv2024

FSL-HDnn: A 5.7 TOPS/W End-to-end Few-shot Learning Classifier Accelerator with Feature Extraction and Hyperdimensional Computing

This paper introduces FSL-HDnn, an energy-efficient accelerator that implements the end-to-end pipeline of feature extraction, classification, and on-chip few-shot learning (FSL) through gradient-free learning techniques in a 40 nm CMOS process. At its core, FSL-HDnn integrates two low-power modules: Weight clustering feature extractor and Hyperdimensional Computing (HDC). Feature extractor utilizes advanced weight clustering and pattern reuse strategies for optimized CNN-based feature extraction. Meanwhile, HDC emerges as a novel approach for lightweight FSL classifier, employing hyperdimensional vectors to improve training accuracy significantly compared to traditional distance-based approaches. This dual-module synergy not only simplifies the learning process by eliminating the need for complex gradients but also dramatically enhances energy efficiency and performance. Specifically, FSL-HDnn achieves an Intensity unprecedented energy efficiency of 5.7 TOPS/W for feature 1 extraction and 0.78 TOPS/W for classification and learning Training Intensity phases, achieving improvements of 2.6X and 6.6X, respectively, Storage over current state-of-the-art CNN and FSL processors.

cs.AR↗

arXiv2024

K-theoretic Gromov-Witten invariants of line degrees on flag varieties

A homology class $d \in H_2(X)$ of a complex flag variety $X = G/P$ is called a line degree if the moduli space $\overline{M}_{0,0}(X,d)$ of 0-pointed stable maps to $X$ of degree $d$ is also a flag variety $G/P'$. We prove a quantum equals classical formula stating that any $n$-pointed (equivariant, K-theoretic, genus zero) Gromov-Witten invariant of line degree on $X$ is equal to a classical intersection number computed on the flag variety $G/P'$. We also prove an $n$-pointed analogue of the Peterson comparison formula stating that these invariants coincide with Gromov-Witten invariants of the variety of complete flags $G/B$. Our formulas make it straightforward to compute the big quantum K-theory ring of $X$ modulo degrees larger than line degrees.

math.AG↗

arXiv2024

The Isomorphism Problem for cominuscule Schubert Varieties

Cominuscule flag varieties generalize Grassmannians to other Lie types. Schubert varieties in cominuscule flag varieties are indexed by posets of roots labeled long/short. These labeled posets generalize Young diagrams. We prove that Schubert varieties in potentially different cominuscule flag varieties are isomorphic as varieties if and only if their corresponding labeled posets are isomorphic, generalizing the classification of Grassmannian Schubert varieties using Young diagrams by the last two authors. Our proof is type-independent.

math.CO↗

arXiv2024

Quantum K-theory of Incidence Varieties

We prove a conjecture of Buch and Mihalcea in the case of the incidence variety X=Fl(1,n-1;n) and determine the structure of its (T-equivariant) quantum K-theory ring. Our results are an interplay between geometry and combinatorics. The geometric side concerns Gromov-Witten varieties of 3-pointed genus 0 stable maps to X with markings sent to Schubert varieties, while on the combinatorial side are formulas for the (equivariant) quantum K-theory ring of X. We prove that the Gromov-Witten variety is rationally connected when one of the defining Schubert varieties is a divisor and another is a point. This implies that the (equivariant) K-theoretic Gromov-Witten invariants defined by two Schubert classes and a Schubert divisor class can be computed in the ordinary (equivariant) K-theory ring of X. We derive a positive Chevalley formula for the equivariant quantum K-theory ring of X and a positive Littlewood-Richardson rule for the non-equivariant quantum K-theory ring of X. The Littlewood-Richardson rule in turn implies that non-empty Gromov-Witten varieties given by Schubert varieties in general position have arithmetic genus 0.

math.AG↗

arXiv2024

Quantum K-theory of IG(2, 2n)

We prove that the Schubert structure constants of the quantum K-theory rings of symplectic Grassmannians of lines have signs that alternate with codimension and vanish for degrees at least 3. We also give closed formulas that characterize the multiplicative structure of these rings, including the Seidel representation and a Chevalley formula.

math.AG↗

arXiv2023

FHEmem: A Processing In-Memory Accelerator for Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE) is a technique that allows arbitrary computations to be performed on encrypted data without the need for decryption, making it ideal for securing many emerging applications. However, FHE computation is significantly slower than computation on plain data due to the increase in data size after encryption. Processing In-Memory (PIM) is a promising technology that can accelerate data-intensive workloads with extensive parallelism. However, FHE is challenging for PIM acceleration due to the long-bitwidth multiplications and complex data movements involved. We propose a PIM-based FHE accelerator, FHEmem, which exploits a novel processing in-memory architecture to achieve high-throughput and efficient acceleration for FHE. We propose an optimized end-to-end processing flow, from low-level hardware processing to high-level application mapping, that fully exploits the high throughput of FHEmem hardware. Our evaluation shows FHEmem achieves significant speedup and efficiency improvement over state-of-the-art FHE accelerators.

cs.AR↗

arXiv2023

SpecHD: Hyperdimensional Computing Framework for FPGA-based Mass Spectrometry Clustering

Mass spectrometry-based proteomics is a key enabler for personalized healthcare, providing a deep dive into the complex protein compositions of biological systems. This technology has vast applications in biotechnology and biomedicine but faces significant computational bottlenecks. Current methodologies often require multiple hours or even days to process extensive datasets, particularly in the domain of spectral clustering. To tackle these inefficiencies, we introduce SpecHD, a hyperdimensional computing (HDC) framework supplemented by an FPGA-accelerated architecture with integrated near-storage preprocessing. Utilizing streamlined binary operations in an HDC environment, SpecHD capitalizes on the low-latency and parallel capabilities of FPGAs. This approach markedly improves clustering speed and efficiency, serving as a catalyst for real-time, high-throughput data analysis in future healthcare applications. Our evaluations demonstrate that SpecHD not only maintains but often surpasses existing clustering quality metrics while drastically cutting computational time. Specifically, it can cluster a large-scale human proteome dataset-comprising 25 million MS/MS spectra and 131 GB of MS data-in just 5 minutes. With energy efficiency exceeding 31x and a speedup factor that spans a range of 6x to 54x over existing state of-the-art solutions, SpecHD emerges as a promising solution for the rapid analysis of mass spectrometry data with great implications for personalized healthcare.

q-bio.QM↗

arXiv2023

Quantum K-theory Chevalley formulas in the parabolic case

We derive cancellation-free Chevalley-type multiplication formulas in the T-equivariant quantum K-theory of Grassmannians of type A and C, and also those of two-step flag manifolds of type A. They are obtained based on the uniform Chevalley formula in the T-equivariant quantum K-theory of arbitrary flag manifolds G/B, which was derived earlier in terms of the quantum alcove model, by the last three authors.

math.CO↗

arXiv2023

The isomorphism problem for Grassmannian Schubert varieties

We prove that Schubert varieties in potentially different Grassmannians are isomorphic as varieties if and only if their corresponding Young diagrams are identical up to a transposition. We also discuss a generalization of this result to Grassmannian Richardson varieties. In particular, we prove that Richardson varieties in potentially different Grassmannians are isomorphic as varieties if their corresponding skew diagrams are semi-isomorphic as posets, and we conjecture the converse. Here, two posets are said to be semi-isomorphic if there is a bijection between their sets of connected components such that the corresponding components are either isomorphic or opposite.

math.AG↗

arXiv2023

RAPIDx: High-performance ReRAM Processing in-Memory Accelerator for Sequence Alignment

Genome sequence alignment is the core of many biological applications. The advancement of sequencing technologies produces a tremendous amount of data, making sequence alignment a critical bottleneck in bioinformatics analysis. The existing hardware accelerators for alignment suffer from limited on-chip memory, costly data movement, and poorly optimized alignment algorithms. They cannot afford to concurrently process the massive amount of data generated by sequencing machines. In this paper, we propose a ReRAM-based accelerator, RAPIDx, using processing in-memory (PIM) for sequence alignment. RAPIDx achieves superior efficiency and performance via software-hardware co-design. First, we propose an adaptive banded parallelism alignment algorithm suitable for PIM architecture. Compared to the original dynamic programming-based alignment, the proposed algorithm significantly reduces the required complexity, data bit width, and memory footprint at the cost of negligible accuracy degradation. Then we propose the efficient PIM architecture that implements the proposed algorithm. The data flow in RAPIDx achieves four-level parallelism and we design an in-situ alignment computation flow in ReRAM, delivering $5.5$-$9.7\times$ efficiency and throughput improvements compared to our previous PIM design, RAPID. The proposed RAPIDx is reconfigurable to serve as a co-processor integrated into existing genome analysis pipeline to boost sequence alignment or edit distance calculation. On short-read alignment, RAPIDx delivers $131.1\times$ and $46.8\times$ throughput improvements over state-of-the-art CPU and GPU libraries, respectively. As compared to ASIC accelerators for long-read alignment, the performance of RAPIDx is $1.8$-$2.9\times$ higher.

cs.AR↗