arXiv subjects

Qi Meng

Publications and source records attributed to Qi Meng.

At least 37 records · Page 2Linked to original sources

arXiv2025

Generalized Gouy Rotation of Electron Vortex beams in uniform magnetic fields

The intrinsic rotation of electron vortex beams, governed by their phase structure, has been experimentally observed in magnetic fields by breaking the beam's cylindrical symmetry. However, conventional Landau states, which predict three fixed angular frequencies, cannot fully account for the existing experimental observations. To address this limitation, we introduce and derive the generalized Gouy rotation angle, which links the Gouy phase of an extended Landau state -- featuring a periodically oscillating beam width -- to the experimentally observed angular variation. In particular, this framework predicts a broader spectrum of angular frequencies and captures the reversal of rotation direction observed in electron vortex beams with negative topological charge. Calculations based on experimental parameters show good agreement with previously published data and are further validated here by numerical simulations using the Chebyshev method. Our results are, in principle, applicable to any system involving electron vortex beams in uniform magnetic fields, and provide a foundation for exploring vortex electrons in Glaser and other nonuniform magnetic fields.

quant-ph↗

arXiv2025

Riemannian Neural Geodesic Interpolant

Stochastic interpolants are efficient generative models that bridge two arbitrary probability density functions in finite time, enabling flexible generation from the source to the target distribution or vice versa. These models are primarily developed in Euclidean space, and are therefore limited in their application to many distribution learning problems defined on Riemannian manifolds in real-world scenarios. In this work, we introduce the Riemannian Neural Geodesic Interpolant (RNGI) model, which interpolates between two probability densities on a Riemannian manifold along the stochastic geodesics, and then samples from one endpoint as the final state using the continuous flow originating from the other endpoint. We prove that the temporal marginal density of RNGI solves a transport equation on the Riemannian manifold. After training the model's the neural velocity and score fields, we propose the Embedding Stochastic Differential Equation (E-SDE) algorithm for stochastic sampling of RNGI. E-SDE significantly improves the sampling quality by reducing the accumulated error caused by the excessive intrinsic discretization of Riemannian Brownian motion in the classical Geodesic Random Walk (GRW) algorithm. We also provide theoretical bounds on the generative bias measured in terms of KL-divergence. Finally, we demonstrate the effectiveness of the proposed RNGI and E-SDE through experiments conducted on both collected and synthetic distributions on S2 and SO(3).

cs.LG↗

arXiv2025

Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation

In scenarios with limited available data, training the function-to-function neural PDE solver in an unsupervised manner is essential. However, the efficiency and accuracy of existing methods are constrained by the properties of numerical algorithms, such as finite difference and pseudo-spectral methods, integrated during the training stage. These methods necessitate careful spatiotemporal discretization to achieve reasonable accuracy, leading to significant computational challenges and inaccurate simulations, particularly in cases with substantial spatiotemporal variations. To address these limitations, we propose the Monte Carlo Neural PDE Solver (MCNP Solver) for training unsupervised neural solvers via the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Compared to other unsupervised methods, MCNP Solver naturally inherits the advantages of the Monte Carlo method, which is robust against spatiotemporal variations and can tolerate coarse step size. In simulating the trajectories of particles, we employ Heun's method for the convection process and calculate the expectation via the probability density function of neighbouring grid points during the diffusion process. These techniques enhance accuracy and circumvent the computational issues associated with Monte Carlo sampling. Our numerical experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency compared to other unsupervised baselines. The source code will be publicly available at: https://github.com/optray/MCNP.

cs.LG↗

arXiv2025

HR-Extreme: A High-Resolution Dataset for Extreme Weather Forecasting

The application of large deep learning models in weather forecasting has led to significant advancements in the field, including higher-resolution forecasting and extended prediction periods exemplified by models such as Pangu and Fuxi. Despite these successes, previous research has largely been characterized by the neglect of extreme weather events, and the availability of datasets specifically curated for such events remains limited. Given the critical importance of accurately forecasting extreme weather, this study introduces a comprehensive dataset that incorporates high-resolution extreme weather cases derived from the High-Resolution Rapid Refresh (HRRR) data, a 3-km real-time dataset provided by NOAA. We also evaluate the current state-of-the-art deep learning models and Numerical Weather Prediction (NWP) systems on HR-Extreme, and provide a improved baseline deep learning model called HR-Heim which has superior performance on both general loss and HR-Extreme compared to others. Our results reveal that the errors of extreme weather cases are significantly larger than overall forecast error, highlighting them as an crucial source of loss in weather prediction. These findings underscore the necessity for future research to focus on improving the accuracy of extreme weather forecasts to enhance their practical utility.

cs.LG↗

arXiv2024

Provable Adaptivity of Adam under Non-uniform Smoothness

Adam is widely adopted in practical applications due to its fast convergence. However, its theoretical analysis is still far from satisfactory. Existing convergence analyses for Adam rely on the bounded smoothness assumption, referred to as the \emph{L-smooth condition}. Unfortunately, this assumption does not hold for many deep learning tasks. Moreover, we believe that this assumption obscures the true benefit of Adam, as the algorithm can adapt its update magnitude according to local smoothness. This important feature of Adam becomes irrelevant when assuming globally bounded smoothness. This paper studies the convergence of randomly reshuffled Adam (RR Adam) with diminishing learning rate, which is the major version of Adam adopted in deep learning tasks. We present the first convergence analysis of RR Adam without the bounded smoothness assumption. We demonstrate that RR Adam can maintain its convergence properties when smoothness is linearly bounded by the gradient norm, referred to as the \emph{$(L_0, L_1)$-smooth condition. We further compare Adam to SGD when both methods use diminishing learning rate. We refine the existing lower bound of SGD and show that SGD can be slower than Adam. To our knowledge, this is the first time that Adam and SGD are rigorously compared in the same setting and the advantage of Adam is revealed.

cs.LG↗

arXiv2024

MEFT: Memory-Efficient Fine-Tuning through Sparse Adapter

Parameter-Efficient Fine-tuning (PEFT) facilitates the fine-tuning of Large Language Models (LLMs) under limited resources. However, the fine-tuning performance with PEFT on complex, knowledge-intensive tasks is limited due to the constrained model capacity, which originates from the limited number of additional trainable parameters. To overcome this limitation, we introduce a novel mechanism that fine-tunes LLMs with adapters of larger size yet memory-efficient. This is achieved by leveraging the inherent activation sparsity in the Feed-Forward Networks (FFNs) of LLMs and utilizing the larger capacity of Central Processing Unit (CPU) memory compared to Graphics Processing Unit (GPU). We store and update the parameters of larger adapters on the CPU. Moreover, we employ a Mixture of Experts (MoE)-like architecture to mitigate unnecessary CPU computations and reduce the communication volume between the GPU and CPU. This is particularly beneficial over the limited bandwidth of PCI Express (PCIe). Our method can achieve fine-tuning results comparable to those obtained with larger memory capacities, even when operating under more limited resources such as a 24GB memory single GPU setup, with acceptable loss in training efficiency. Our codes are available at https://github.com/CURRENTF/MEFT.

cs.CL↗

arXiv2024

Mass Spectra of Full-Heavy and Double-Heavy Tetraquark States in the Conventional Quark Model

A comprehensive study of the $S$-wave heavy tetraquark states with identical quarks and antiquarks, specifically $QQ{\bar Q'}\bar Q'$ ($Q, Q'=c,b$), $QQ\bar s\bar s$/$\bar Q\bar Q ss$, and $QQ\bar q\bar q$/$\bar Q\bar Q qq$ ($q=u,d$), are studied in a unified constituent quark model. This model contains the one-gluon exchange and confinement potentials. The latter is modeled as the sum of all two-body linear potentials. We employ the Gaussian expansion method to solve the full four-body Schrödinger equations, and search bound and resonant states using the complex-scaling method. We then identify $3$ bound and $62$ resonant states. The bound states are all $QQ\bar q\bar q$ states with the isospin and spin-parity quantum numbers $I(J^P)=0(1^+)$: two bound $bb\bar{q}\bar{q}$ states with the binding energies, 153 MeV and 4 MeV below the $BB^*$ threshold, and a shallow $cc\bar{q}\bar{q}$ state at $-15$ MeV from the $DD^*$ threshold. The deeper $bb\bar q \bar q$ bound state aligns with the lattice QCD predictions, while $cc\bar q\bar q$ bound state, still has a much larger binding energy than the recently observed $T^+_{cc}$ by LHCb collaboration. No bound states are identified for the $QQ\bar Q'\bar Q'$, $QQ\bar s\bar s$ and $QQ\bar q\bar q$ with $I=1$. Our analysis shows that the bound $QQ\bar Q'\bar Q'$ states are more probable with a larger mass ratio, $m_Q/m_{Q'}$. Experimental investigation for these states is desired, which will enrich our understanding of hadron spectroscopy and probe insights into the confinement mechanisms within tetraquarks.

hep-ph↗

arXiv2024

On the Convergence of Adam under Non-uniform Smoothness: Separability from SGDM and Beyond

This paper aims to clearly distinguish between Stochastic Gradient Descent with Momentum (SGDM) and Adam in terms of their convergence rates. We demonstrate that Adam achieves a faster convergence compared to SGDM under the condition of non-uniformly bounded smoothness. Our findings reveal that: (1) in deterministic environments, Adam can attain the known lower bound for the convergence rate of deterministic first-order optimizers, whereas the convergence rate of Gradient Descent with Momentum (GDM) has higher order dependence on the initial function value; (2) in stochastic setting, Adam's convergence rate upper bound matches the lower bounds of stochastic first-order optimizers, considering both the initial function value and the final error, whereas there are instances where SGDM fails to converge with any learning rate. These insights distinctly differentiate Adam and SGDM regarding their convergence rates. Additionally, by introducing a novel stopping-time based technique, we further prove that if we consider the minimum gradient norm during iterations, the corresponding convergence rate can match the lower bounds across all problem hyperparameters. The technique can also help proving that Adam with a specific hyperparameter scheduler is parameter-agnostic, which hence can be of independent interest.

cs.LG↗

arXiv2024

Does Lorentz-symmetric design boost network performance in jet physics?

In the deep learning era, improving the neural network performance in jet physics is a rewarding task as it directly contributes to more accurate physics measurements at the LHC. Recent research has proposed various network designs in consideration of the full Lorentz symmetry, but its benefit is still not systematically asserted, given that there remain many successful networks without taking it into account. We conduct a detailed study on the Lorentz-symmetric design. We propose two generalized approaches for modifying a network - these methods are experimented on Particle Flow Network, ParticleNet, and LorentzNet, and exhibit a general performance gain. We also reveal that the notable improvement attributed to the "pairwise mass" feature in the network is due to its introduction of a structure that fully complies with Lorentz symmetry. We confirm that Lorentz-symmetry preservation serves as a strong inductive bias of jet physics, hence calling for attention to such general recipes in future network designs.

hep-ph↗

arXiv2024

Deciphering and integrating invariants for neural operator learning with various physical mechanisms

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose Physical Invariant Attention Neural Operator (PIANO) to decipher and integrate the physical invariants (PI) for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional layers. Compared to existing techniques, PIANO can reduce the relative error by 13.6\%-82.2\% on PDE forecasting tasks across varying coefficients, forces, or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO. The source code will be publicly available at: https://github.com/optray/PIANO.

cs.LG↗

arXiv2023

Doubly heavy tetraquarks including one-pion exchange potential

Spectrum of the doubly heavy tetraquarks is studied in a constituent quark model including one-pion exchange (OPE) potential. Central and tensor forces induced by OPE between two light quarks are considered. Our results show that $I(J^P)=0(1^+)$ compact bound states are shifted up because of the repulsive central force between $\bar{q}\bar{q}$. This effect possibly leads to the small binding energy in $T_{cc}$. In addition, a $I(J^P)=1(1^+)$ resonant state is reported with $ E=10641 \ \rm{MeV},Γ=15 \ \rm{MeV}$ and $ E=10640 \ \rm{MeV},Γ=15 \ \rm{MeV}$, without and with including OPE potential, respectively. The repulsive central force and attractive tensor force almost cancel with each other and leave a small energy difference when OPE potential is included.

nucl-th↗

arXiv2023

Short-range correlations and momentum distributions in mirror nuclei 3H and 3He

Motivated by recent high-energy electron and $\rm ^3H$ and $\rm ^3He$ nuclei scattering experiment in Jefferson Lab (Nature 609, 41 (2022)), the short-range correlations (SRCs) between nucleon pairs for 3-nucleon systems are microscopically studied using realistic $NN$ 2-body interaction and two-Gaussian type $NNN$ 3-body interaction. The wave functions of both $\rm ^3H$ and $\rm ^3He$ are obtained by solving 3-body Schrödinger equations using Gaussian expansion method (GEM). The differences of one-nucleon and nucleon-nucleon momentum distributions between $\rm ^3H$ and $\rm ^3He$ are analyzed in detail. The results show that the percentages of $pn$-SRC pairs are significantly enhanced as compared with those of $nn(pp)$-SRC ones in $\rm ^3H$ and $\rm ^3He$ nuclei, which is consistent with the experimental findings.

nucl-th↗

arXiv2023

Power-law Dynamic arising from machine learning

We study a kind of new SDE that was arisen from the research on optimization in machine learning, we call it power-law dynamic because its stationary distribution cannot have sub-Gaussian tail and obeys power-law. We prove that the power-law dynamic is ergodic with unique stationary distribution, provided the learning rate is small enough. We investigate its first exist time. In particular, we compare the exit times of the (continuous) power-law dynamic and its discretization. The comparison can help guide machine learning algorithm.

stat.ML↗

arXiv2023

NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the use of costly data and improve the generalization ability. However, these physics constraints, based on certain finite dimensional approximations over the function space, must resolve the smallest scaled physics to ensure the accuracy and stability of the simulation, resulting in high computational costs from large input, output, and neural networks. This paper proposes a general acceleration methodology called NeuralStagger by spatially and temporally decomposing the original learning tasks into several coarser-resolution subtasks. We define a coarse-resolution neural solver for each subtask, which requires fewer computational resources, and jointly train them with the vanilla physics-constrained loss by simply arranging their outputs to reconstruct the original solution. Due to the perfect parallelism between them, the solution is achieved as fast as a coarse-resolution neural solver. In addition, the trained solvers bring the flexibility of simulating with multiple levels of resolution. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations, which leads to an additional $10\sim100\times$ speed-up. Moreover, the experiment also shows that the learned model could be well used for optimal control.

cs.LG↗

arXiv2023

Complex-valued neural operator assisted soliton identification

The numerical determination of solitary states is an important topic for such research areas as Bose-Einstein condensates, nonlinear optics, plasma physics, etc. In this paper, we propose a data-driven approach for identifying solitons based on dynamical solutions of real-time differential equations. Our approach combines a machine-learning architecture called the complex-valued neural operator (CNO) with an energy-restricted gradient optimization. The former serves as a generalization of the traditional neural operator to the complex domain, and constructs a smooth mapping between the initial and final states; the latter facilitates the search for solitons by constraining the energy space. We concretely demonstrate this approach on the quasi-one-dimensional Bose-Einstein condensate with homogeneous and inhomogeneous nonlinearities. Our work offers a new idea for data-driven effective modeling and studies of solitary waves in nonlinear physical systems.

cond-mat.quant-gas↗

arXiv2022

Multilingual Speech Emotion Recognition With Multi-Gating Mechanism and Neural Architecture Search

Speech emotion recognition (SER) classifies audio into emotion categories such as Happy, Angry, Fear, Disgust and Neutral. While Speech Emotion Recognition (SER) is a common application for popular languages, it continues to be a problem for low-resourced languages, i.e., languages with no pretrained speech-to-text recognition models. This paper firstly proposes a language-specific model that extract emotional information from multiple pre-trained speech models, and then designs a multi-domain model that simultaneously performs SER for various languages. Our multidomain model employs a multi-gating mechanism to generate unique weighted feature combination for each language, and also searches for specific neural network structure for each language through a neural architecture search module. In addition, we introduce a contrastive auxiliary loss to build more separable representations for audio data. Our experiments show that our model raises the state-of-the-art accuracy by 3% for German and 14.3% for French.

cs.SD↗

arXiv2022

An Efficient Lorentz Equivariant Graph Neural Network for Jet Tagging

Deep learning methods have been increasingly adopted to study jets in particle physics. Since symmetry-preserving behavior has been shown to be an important factor for improving the performance of deep learning in many applications, Lorentz group equivariance - a fundamental spacetime symmetry for elementary particles - has recently been incorporated into a deep learning model for jet tagging. However, the design is computationally costly due to the analytic construction of high-order tensors. In this article, we introduce LorentzNet, a new symmetry-preserving deep learning model for jet tagging. The message passing of LorentzNet relies on an efficient Minkowski dot product attention. Experiments on two representative jet tagging benchmarks show that LorentzNet achieves the best tagging performance and improves significantly over existing state-of-the-art algorithms. The preservation of Lorentz symmetry also greatly improves the efficiency and generalization power of the model, allowing LorentzNet to reach highly competitive performance when trained on only a few thousand jets. Code and models are available at \url{https://github.com/sdogsq/LorentzNet-release}.

hep-ph↗

arXiv2022

$S$-wave fully charmed tetraquark resonant states

We calculate the mass spectrum of the $S$-wave fully-charmed tetraquark resonant states $cc\bar c\bar c $ in the nonrelativistic quark model, which successfully describes the charmonium spectrum. The four-body system is solved with the Gaussian expansion method. The complex scaling technique is used to identify the genuine resonances. With the nonrelativistic quark model, our results show the existence of two $cc\bar c\bar c$ resonances in each of the $J^{PC}=$ $0^{++}$, $1^{+-}$ and $2^{++}$ sectors, respectively. In the $S$-wave sector, no resonance is found at the energy region of the $X(6200)$ and $X(6600)$ states. The lower $0^{++}$ and $2^{++}$ resonances are located around $100$ MeV higher than the $X(6900)$ state observed in experiments but have the decay widths consistent with the experiment. The higher $0^{++}$ and $2^{++}$ resonances are found at around $7.2$ GeV with the widths of $60.6$ MeV and $91.2$ MeV, respectively, and they may be good candidates for the $X(7200)$ state.

hep-ph↗