Search Results for author:
Found 16 papers, 4 papers with code
Convergence Analysis of Probability Flow ODE for Score-based Generative Models
Score-based generative models have emerged as a powerful approach for sampling high-dimensional probability distributions.
Sampling via Gradient Flows in the Space of Probability Measures
Our third contribution is to study, and develop efficient algorithms based on Gaussian approximations of the gradient flows; this leads to an alternative to particle methods.
High-dimensional SGD aligns with emerging outlier eigenspaces
We rigorously study the joint evolution of training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices.
How Does Information Bottleneck Help Deep Learning?
In this paper, we provide the first rigorous learning theory for justifying the benefit of information bottleneck in deep learning by mathematically relating information bottleneck to generalization errors.
Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance
The flow in the Gaussian space may be understood as a Gaussian approximation of the flow.
PatchGT: Transformer over Non-trainable Clusters for Learning Graph Representations
Recently the Transformer structure has shown good performances in graph learning tasks.
Robustness Implies Generalization via Data-Dependent Generalization Bounds
This paper proves that robustness implies generalization via data-dependent generalization bounds.
Understanding End-to-End Model-Based Reinforcement Learning Methods as Implicit Parameterization
Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting.
Model-based Reinforcement Learning
reinforcement-learning
+1
Long Random Matrices and Tensor Unfolding
In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is "long": we allow the number of rows (columns) to grow polynomially in the number of columns (rows).
Improve Unscented Kalman Inversion With Low-Rank Approximation and Reduced-Order Model
The unscented Kalman inversion (UKI) presented in [1] is a general derivative-free approach to solving the inverse problem.
Numerical Analysis Numerical Analysis Optimization and Control
Spectrum of Random $d$-regular Graphs Up to the Edge
Consider the normalized adjacency matrices of random $d$-regular graphs on $N$ vertices with fixed degree $d\geq3$.
Probability Mathematical Physics Combinatorics Mathematical Physics 60B20, 05C80
Towards Understanding the Dynamics of the First-Order Adversaries
An acknowledged weakness of neural networks is their vulnerability to adversarial perturbations to the inputs.
Dynamics of Deep Neural Networks and Neural Tangent Hierarchy
However, it was observed in [5] that there is a performance gap between the kernel regression using the limiting NTK and the deep neural networks.
Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes
The theory developed in this paper only requires the practical degrees of over-parameterization unlike previous theories.
Every Local Minimum Value is the Global Minimum Value of Induced Model in Non-convex Machine Learning
Furthermore, as special cases of our general results, this article improves or complements several state-of-the-art theoretical results on deep neural networks, deep residual networks, and overparameterized deep neural networks with a unified proof technique and novel geometric insights.
Effect of Depth and Width on Local Minima in Deep Learning
In this paper, we analyze the effects of depth and width on the quality of local minima, without strong over-parameterization and simplification assumptions in the literature.
