arXiv subjects

Jianfeng Lu

Publications and source records attributed to Jianfeng Lu.

At least 91 records · Page 5Linked to original sources

arXiv2024

Regularized Stein Variational Gradient Flow

The Stein Variational Gradient Descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational Gradient Flow) only provides a constant-order approximation to the Wasserstein Gradient Flow corresponding to the KL-divergence minimization. In this work, we propose the Regularized Stein Variational Gradient Flow, which interpolates between the Stein Variational Gradient Flow and the Wasserstein Gradient Flow. We establish various theoretical properties of the Regularized Stein Variational Gradient Flow (and its time-discretization) including convergence to equilibrium, existence and uniqueness of weak solutions, and stability of the solutions. We provide preliminary numerical evidence of the improved performance offered by the regularization.

stat.ML↗

arXiv2024

LEAP: Optimization Hierarchical Federated Learning on Non-IID Data with Coalition Formation Game

Although Hierarchical Federated Learning (HFL) utilizes edge servers (ESs) to alleviate communication burdens, its model performance will be degraded by non-IID data and limited communication resources. Current works often assume that data is uniformly distributed, which however contradicts the heterogeneity of IoT. Solutions of additional model training to check the data distribution inevitably increases computational costs and the risk of privacy leakage. The challenges in solving these issues are how to reduce the impact of non-IID data without involving raw data and how to rationalize the communication resource allocation for addressing straggler problem. To tackle these challenges, we propose a novel optimization method based on coaLition formation gamE and grAdient Projection, called LEAP. Specifically, we combine edge data distribution with coalition formation game innovatively to adjust the correlations between clients and ESs dynamically, which ensures optimal correlations. We further capture the client heterogeneity to achieve the rational bandwidth allocation from coalition perception and determine the optimal transmission power within specified delay constraints at client level. Experimental results on four real datasets show that LEAP is able to achieve 20.62% improvement in model accuracy compared to the state-of-the-art baselines. Moreover, LEAP effectively reduce transmission energy consumption by at least about 2.24 times.

cs.GT↗

arXiv2024

Qubit Count Reduction by Orthogonally-Constrained Orbital Optimization for Variational Quantum Excited States Solvers

We propose a state-averaged orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for use on near-term quantum computers. Instead of parameterizing the orbital rotation operator in the conventional fashion as an exponential of an anti-hermitian matrix, we parameterize the orbital rotation as a general partial unitary matrix. Whereas conventional orbital optimization methods minimize the state-averaged energy using successive Newton steps of the second-order Taylor expansion of the energy, the method presented here optimizes the state-averaged energy using an orthogonally-constrained gradient projection method which does not require any expansion approximations. Through extensive benchmarking of the method on various small molecular systems, we find that the method is capable of producing more accurate results than fixed basis FCI while simultaneously using fewer qubits. In particular, we show that for $\mathrm{H_2}$, the method is capable of matching the accuracy of FCI in the cc-pVTZ basis (56 qubits) while only using 14 qubits.

physics.chem-ph↗

arXiv2024

One-dimensional Tensor Network Recovery

We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th order tensors. We prove that our algorithms can almost surely recover the correct graph or permutation when tensor entries can be observed without noise. We further establish the robustness of our algorithms against observational noise. The theoretical results are validated by numerical experiments.

math.NA↗

arXiv2024

Efficient posterior sampling for high-dimensional imbalanced logistic regression

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior computation are inefficient as $n$ and/or $p$ increase due to worsening time per step and mixing rates. One strategy is to use a gradient-based sampler to improve mixing while using data sub-samples to reduce per-step computational complexity. However, usual sub-sampling breaks down when applied to imbalanced data. Instead, we generalize piece-wise deterministic Markov chain Monte Carlo algorithms to include importance-weighted and mini-batch sub-sampling. These approaches maintain the correct stationary distribution with arbitrarily small sub-samples, and substantially outperform current competitors. We provide theoretical support and illustrate gains in simulated and real data applications.

stat.ME↗

arXiv2024

Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks

We study the convergence of stochastic gradient descent (SGD) for non-convex objective functions. We establish the local convergence with positive probability under the local Łojasiewicz condition introduced by Chatterjee in \cite{chatterjee2022convergence} and an additional local structural assumption of the loss function landscape. A key component of our proof is to ensure that the whole trajectories of SGD stay inside the local region with a positive probability. We also provide examples of neural networks with finite widths such that our assumptions hold.

cs.LG↗

arXiv2024

Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media

We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $\ell$ in an infinite heterogeneous medium, in a situation where the medium is only known in a box of diameter $L\gg\ell$ around the support of the charge. We propose a boundary condition that with overwhelming probability is (near) optimal with respect to scaling in terms of $\ell$ and $L$, in the setting where the medium is a sample from a stationary ensemble with a finite range of dependence (set to be unity and with the assumption that $\ell \gg 1$). The boundary condition is motivated by quantitative stochastic homogenization that allows for a multipole expansion [BGO20]. This work extends [LO21], the algorithm in which is optimal in two dimension, and thus we need to take quadrupoles, next to dipoles, into account. This in turn relies on stochastic estimates of second-order, next to first-order, correctors. These estimates are provided for finite range ensembles under consideration, based on an extension of the semi-group approach of [GO15].

math.AP↗

arXiv2024

Hyperspectral Image Denoising via Spatial-Spectral Recurrent Transformer

Hyperspectral images (HSIs) often suffer from noise arising from both intra-imaging mechanisms and environmental factors. Leveraging domain knowledge specific to HSIs, such as global spectral correlation (GSC) and non-local spatial self-similarity (NSS), is crucial for effective denoising. Existing methods tend to independently utilize each of these knowledge components with multiple blocks, overlooking the inherent 3D nature of HSIs where domain knowledge is strongly interlinked, resulting in suboptimal performance. To address this challenge, this paper introduces a spatial-spectral recurrent transformer U-Net (SSRT-UNet) for HSI denoising. The proposed SSRT-UNet integrates NSS and GSC properties within a single SSRT block. This block consists of a spatial branch and a spectral branch. The spectral branch employs a combination of transformer and recurrent neural network to perform recurrent computations across bands, allowing for GSC exploitation beyond a fixed number of bands. Concurrently, the spatial branch encodes NSS for each band by sharing keys and values with the spectral branch under the guidance of GSC. This interaction between the two branches enables the joint utilization of NSS and GSC, avoiding their independent treatment. Experimental results demonstrate that our method outperforms several alternative approaches. The source code will be available at https://github.com/lronkitty/SSRT.

eess.IV↗

arXiv2023

Learning Dense Flow Field for Highly-accurate Cross-view Camera Localization

This paper addresses the problem of estimating the 3-DoF camera pose for a ground-level image with respect to a satellite image that encompasses the local surroundings. We propose a novel end-to-end approach that leverages the learning of dense pixel-wise flow fields in pairs of ground and satellite images to calculate the camera pose. Our approach differs from existing methods by constructing the feature metric at the pixel level, enabling full-image supervision for learning distinctive geometric configurations and visual appearances across views. Specifically, our method employs two distinct convolution networks for ground and satellite feature extraction. Then, we project the ground feature map to the bird's eye view (BEV) using a fixed camera height assumption to achieve preliminary geometric alignment. To further establish content association between the BEV and satellite features, we introduce a residual convolution block to refine the projected BEV feature. Optical flow estimation is performed on the refined BEV feature map and the satellite feature map using flow decoder networks based on RAFT. After obtaining dense flow correspondences, we apply the least square method to filter matching inliers and regress the ground camera pose. Extensive experiments demonstrate significant improvements compared to state-of-the-art methods. Notably, our approach reduces the median localization error by 89%, 19%, 80% and 35% on the KITTI, Ford multi-AV, VIGOR and Oxford RobotCar datasets, respectively.

cs.CV↗

arXiv2023

Enhanced Fine-grained Motion Diffusion for Text-driven Human Motion Synthesis

The emergence of text-driven motion synthesis technique provides animators with great potential to create efficiently. However, in most cases, textual expressions only contain general and qualitative motion descriptions, while lack fine depiction and sufficient intensity, leading to the synthesized motions that either (a) semantically compliant but uncontrollable over specific pose details, or (b) even deviates from the provided descriptions, bringing animators with undesired cases. In this paper, we propose DiffKFC, a conditional diffusion model for text-driven motion synthesis with KeyFrames Collaborated, enabling realistic generation with collaborative and efficient dual-level control: coarse guidance at semantic level, with only few keyframes for direct and fine-grained depiction down to body posture level. Unlike existing inference-editing diffusion models that incorporate conditions without training, our conditional diffusion model is explicitly trained and can fully exploit correlations among texts, keyframes and the diffused target frames. To preserve the control capability of discrete and sparse keyframes, we customize dilated mask attention modules where only partial valid tokens participate in local-to-global attention, indicated by the dilated keyframe mask. Additionally, we develop a simple yet effective smoothness prior, which steers the generated frames towards seamless keyframe transitions at inference. Extensive experiments show that our model not only achieves state-of-the-art performance in terms of semantic fidelity, but more importantly, is able to satisfy animator requirements through fine-grained guidance without tedious labor.

cs.CV↗

arXiv2023

Efficient sampling from the Bingham distribution

We give a algorithm for exact sampling from the Bingham distribution $p(x)\propto \exp(x^\top A x)$ on the sphere $\mathcal S^{d-1}$ with expected runtime of $\operatorname{poly}(d, λ_{\max}(A)-λ_{\min}(A))$. The algorithm is based on rejection sampling, where the proposal distribution is a polynomial approximation of the pdf, and can be sampled from by explicitly evaluating integrals of polynomials over the sphere. Our algorithm gives exact samples, assuming exact computation of an inverse function of a polynomial. This is in contrast with Markov Chain Monte Carlo algorithms, which are not known to enjoy rapid mixing on this problem, and only give approximate samples. As a direct application, we use this to sample from the posterior distribution of a rank-1 matrix inference problem in polynomial time.

cs.LG↗

arXiv2023

Deep Equilibrium Based Neural Operators for Steady-State PDEs

Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and outputs its solution. However, the architectural design space, especially given structural knowledge of the PDE family of interest, is still poorly understood. We seek to remedy this gap by studying the benefits of weight-tied neural network architectures for steady-state PDEs. To achieve this, we first demonstrate that the solution of most steady-state PDEs can be expressed as a fixed point of a non-linear operator. Motivated by this observation, we propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE as the infinite-depth fixed point of an implicit operator layer using a black-box root solver and differentiates analytically through this fixed point resulting in $\mathcal{O}(1)$ training memory. Our experiments indicate that FNO-DEQ-based architectures outperform FNO-based baselines with $4\times$ the number of parameters in predicting the solution to steady-state PDEs such as Darcy Flow and steady-state incompressible Navier-Stokes. Finally, we show FNO-DEQ is more robust when trained with datasets with more noisy observations than the FNO-based baselines, demonstrating the benefits of using appropriate inductive biases in architectural design for different neural network based PDE solvers. Further, we show a universal approximation result that demonstrates that FNO-DEQ can approximate the solution to any steady-state PDE that can be written as a fixed point equation.

cs.LG↗

arXiv2023

On the convergence of Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem

We study the convergences of three projected Sobolev gradient flows to the ground state of the Gross-Pitaevskii eigenvalue problem. They are constructed as the gradient flows of the Gross-Pitaevskii energy functional with respect to the $H^1_0$-metric and two other equivalent metrics on $H_0^1$, including the iterate-independent $a_0$-metric and the iterate-dependent $a_u$-metric. We first prove the energy dissipation property and the global convergence to a critical point of the Gross-Pitaevskii energy for the discrete-time $H^1$ and $a_0$-gradient flow. We also prove local exponential convergence of all three schemes to the ground state.

math.NA↗

arXiv2023

Asymptotic analysis for Bloch electrons with Weyl nodes

In this paper, we study the semiclassical behavior of Bloch electrons in the presence of Weyl nodes, which are singular points in the band structure of certain materials. We carry out asymptotic analysis and present a rigorous derivation of the semiclassical asymptotic expansion of the current of Bloch electrons with the presence of Weyl nodes. The analysis shows that the current contains two parts, one independent of the Weyl nodes and the other a contribution from the singular points. This work provides a theoretical foundation towards a rigorous justification of recent scientific discoveries in Weyl semimetals. The main innovation of this paper is a new strategy to deal with the singular points with quantitative estimates, which may have broader applications in multiscale models with singularities.

math.AP↗

arXiv2023

Improving the Accuracy of Variational Quantum Eigensolvers With Fewer Qubits Using Orbital Optimization

Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as the Variational Quantum Eigensolver (VQE) have been limited to small molecules using minimal basis sets for this reason. In this work we propose incorporating an orbital optimization scheme into quantum eigensolvers wherein a parameterized partial unitary transformation is applied to the basis functions set in order to reduce the number of qubits required for a given problem. The optimal transformation is found by minimizing the ground state energy with respect to this partial unitary matrix. Through numerical simulations of small molecules up to 16 spin orbitals, we demonstrate that this method has the ability to greatly extend the capabilities of near-term quantum computers with regard to the electronic structure problem. We find that VQE paired with orbital optimization consistently achieves lower ground state energies than traditional VQE when using the same number of qubits and even frequently achieves lower ground state energies than VQE methods using more qubits.

physics.chem-ph↗

arXiv2023

Vector-wise Joint Diagonalization of Almost Commuting Matrices

This work aims to numerically construct exactly commuting matrices close to given almost commuting ones, which is equivalent to the joint approximate diagonalization problem. We first prove that almost commuting matrices generically have approximate common eigenvectors that are almost orthogonal to each other. Based on this key observation, we propose a fast and robust vector-wise joint diagonalization (VJD) algorithm, which constructs the orthogonal similarity transform by sequentially finding these approximate common eigenvectors. In doing so, we consider sub-optimization problems over the unit sphere, for which we present a Riemannian quasi-Newton method with rigorous convergence analysis. We also discuss the numerical stability of the proposed VJD algorithm. Numerical examples with applications in independent component analysis are provided to reveal the relation with Huaxin Lin's theorem and to demonstrate that our method compares favorably with the state-of-the-art Jacobi-type joint diagonalization algorithm.

math.NA↗

arXiv2023

Solution for SMART-101 Challenge of ICCV Multi-modal Algorithmic Reasoning Task 2023

In this paper, we present our solution to a Multi-modal Algorithmic Reasoning Task: SMART-101 Challenge. Different from the traditional visual question-answering datasets, this challenge evaluates the abstraction, deduction, and generalization abilities of neural networks in solving visuolinguistic puzzles designed specifically for children in the 6-8 age group. We employed a divide-and-conquer approach. At the data level, inspired by the challenge paper, we categorized the whole questions into eight types and utilized the llama-2-chat model to directly generate the type for each question in a zero-shot manner. Additionally, we trained a yolov7 model on the icon45 dataset for object detection and combined it with the OCR method to recognize and locate objects and text within the images. At the model level, we utilized the BLIP-2 model and added eight adapters to the image encoder VIT-G to adaptively extract visual features for different question types. We fed the pre-constructed question templates as input and generated answers using the flan-t5-xxl decoder. Under the puzzle splits configuration, we achieved an accuracy score of 26.5 on the validation set and 24.30 on the private test set.

cs.CV↗

arXiv2023

Diffusion Methods for Generating Transition Paths

In this work, we seek to simulate rare transitions between metastable states using score-based generative models. An efficient method for generating high-quality transition paths is valuable for the study of molecular systems since data is often difficult to obtain. We develop two novel methods for path generation in this paper: a chain-based approach and a midpoint-based approach. The first biases the original dynamics to facilitate transitions, while the second mirrors splitting techniques and breaks down the original transition into smaller transitions. Numerical results of generated transition paths for the Müller potential and for Alanine dipeptide demonstrate the effectiveness of these approaches in both the data-rich and data-scarce regimes.

physics.comp-ph↗