Jianfeng Lu

Conference Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition · January 1, 2025 Posterior sampling in high-dimensional spaces using generative models holds significant promise for various applications, including but not limited to inverse problems and guided generation tasks. Generating diverse posterior samples remains expensive, as ... Full text Cite

Towards characterizing the value of edge embeddings in Graph Neural Networks

Conference Proceedings of Machine Learning Research · January 1, 2025 Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design for GNNs remain ... Cite

What does guidance do? A fine-grained analysis in a simple setting

Conference Advances in Neural Information Processing Systems · January 1, 2024 The use of guidance in diffusion models was originally motivated by the premise that the guidance-modified score is that of the data distribution tilted by a conditional likelihood raised to some power. In this work we clarify this misconception by rigorou ... Cite

HeteRSGD: Tackling Heterogeneous Sampling Costs via Optimal Reweighted Stochastic Gradient Descent

Conference Proceedings of Machine Learning Research · January 1, 2023 One implicit assumption in current stochastic gradient descent (SGD) algorithms is the identical cost for sampling each component function of the finite-sum objective. However, there are applications where the costs differ substantially, for which SGD sche ... Cite

Convergence of score-based generative modeling for general data distributions

Conference Proceedings of Machine Learning Research · January 1, 2023 Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio. It is based on evolving an SDE that transforms white noise into a sample fro ... Cite

On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network

Conference Proceedings of Machine Learning Research · January 1, 2023 This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite the limited expr ... Cite

Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions

Conference Proceedings of Machine Learning Research · January 1, 2023 We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, ... Cite

Global optimality of Elman-type RNNs in the mean-field regime

Conference Proceedings of Machine Learning Research · January 1, 2023 We analyze Elman-type Recurrent Reural Networks (RNNs) and their training in the mean-field regime. Specifically, we show convergence of gradient descent training dynamics of the RNN to the corresponding mean-field formulation in the large width limit. We ... Cite

Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective

Conference Proceedings of Machine Learning Research · January 1, 2023 A burgeoning line of research leverages deep neural networks to approximate the solutions to high dimensional PDEs, opening lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of dimensionality. However, ... Cite

The probability flow ODE is provably fast

Conference Advances in Neural Information Processing Systems · January 1, 2023 We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling with an OU forward process. Our analysis is carried out in the wake of recent result ... Cite

Deep Equilibrium Based Neural Operators for Steady-State PDEs

Conference Advances in Neural Information Processing Systems · January 1, 2023 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 soluti ... Cite

ON REPRESENTING LINEAR PROGRAMS BY GRAPH NEURAL NETWORKS

Conference 11th International Conference on Learning Representations Iclr 2023 · January 1, 2023 Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML).In particular, the graph neural network (GNN) is considered a suitable ML model for optimization ... Cite

ON REPRESENTING MIXED-INTEGER LINEAR PROGRAMS BY GRAPH NEURAL NETWORKS

Conference 11th International Conference on Learning Representations Iclr 2023 · January 1, 2023 While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100-fold speedup in the past twenty years.Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating researchers to see ... Cite

MACHINE LEARNING FOR ELLIPTIC PDES: FAST RATE GENERALIZATION BOUND, NEURAL SCALING LAW AND MINIMAX OPTIMALITY

Conference Iclr 2022 10th International Conference on Learning Representations · January 1, 2022 In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To simplify the problem ... Cite

Convergence for score-based generative modeling with polynomial complexity

Conference Advances in Neural Information Processing Systems · January 1, 2022 Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM: drawing samples f ... Cite

On the Representation of Solutions to Elliptic PDEs in Barron Spaces

Conference Advances in Neural Information Processing Systems · January 1, 2021 Numerical solutions to high-dimensional partial differential equations (PDEs) based on neural networks have seen exciting developments. This paper derives complexity estimates of the solutions of d-dimensional second-order elliptic PDEs in the Barron space ... Cite

Random Coordinate Underdamped Langevin Monte Carlo

Conference Proceedings of Machine Learning Research · January 1, 2021 The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each iteration, an expensive operation if the dimension of the problem is high. We pro ... Cite

Efficient sampling from the Bingham distribution

Conference Proceedings of Machine Learning Research · January 1, 2021 We give a algorithm for exact sampling from the Bingham distribution p(x) ∝ exp(x⊺Ax) on the sphere Sd-1 with expected runtime of poly(d, λmax(A) - λmin(A)). The algorithm is based on rejection sampling, where th ... Cite

A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Partial Differential Equations

Conference Proceedings of Machine Learning Research · January 1, 2021 This paper concerns the a priori generalization analysis of the Deep Ritz Method (DRM) [W. E and B. Yu, 2017], a popular neural-network-based method for solving high dimensional partial differential equations. We derive the generalization error bounds of t ... Cite

Temporal-difference learning with nonlinear function approximation: lazy training and mean field regimes

Conference Proceedings of Machine Learning Research · January 1, 2021 We discuss the approximation of the value function for infinite-horizon discounted Markov Reward Processes (MRP) with wide neural networks trained with the Temporal-Difference (TD) learning algorithm. We first consider this problem under a certain scaling ... Cite

Random Coordinate Langevin Monte Carlo

Conference CONFERENCE ON LEARNING THEORY, VOL 134 · 2021 Link to item Cite

A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth

Conference Proceedings of Machine Learning Research · January 1, 2020 Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for training deep neural ne ... Cite

Large-scale benchmark of electronic structure solvers with the ELSI infrastructure

Conference ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY · March 31, 2019 Link to item Cite

ELSI: A unified software interface for Kohn-Sham electronic structure solvers

Conference ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY · March 18, 2018 Link to item Cite

CLASSIFICATION OF WHALE VOCALIZATIONS USING THE WEYL TRANSFORM

Conference 2015 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING (ICASSP) · 2015 Link to item Cite

Seismic modeling using the frozen Gaussian approximation

Conference SEG Technical Program Expanded Abstracts 2013 · 2013 We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The FGA method belongs to the category of ray-based beam methods. It decomposes the seismic wavefield into a set of Gaussian functions and propagates these functions along appropr ... Link to item Cite

Classification of whale vocalizations using the Weyl transform

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