相关论文: Mean-Field Analysis for Learning Subspace-Sparse P…
Deep learning models are often successfully trained using gradient descent, despite the worst case hardness of the underlying non-convex optimization problem. The key question is then under what conditions can one prove that optimization…
The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…
This work develops a mean-field analysis for the asymptotic behavior of deep BitNet-like architectures as smooth quantization parameters approach zero. We establish that empirical measures of latent weights converge weakly to solutions of…
State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…
The stochastic gradient descent (SGD) method is most widely used for deep neural network (DNN) training. However, the method does not always converge to a flat minimum of the loss surface that can demonstrate high generalization capability.…
Normalizing flows transform a latent distribution through an invertible neural network for a flexible and pleasingly simple approach to generative modelling, while preserving an exact likelihood. We propose FlowGMM, an end-to-end approach…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…
Let $f:\{-1,1\}^n$ be a polynomial with at most $s$ non-zero real coefficients. We give an algorithm for exactly reconstructing f given random examples from the uniform distribution on $\{-1,1\}^n$ that runs in time polynomial in $n$ and…
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which…
This is a sequel to our paper `On the kernel learning problem'. We identify a canonical choice of Riemannian gradient flow, to find the stationary points in the kernel learning problem. In the presence of Gaussian noise variables, this flow…
Learning in deep neural networks (DNNs) is implemented through minimizing a highly non-convex loss function, typically by a stochastic gradient descent (SGD) method. This learning process can effectively find good wide minima without being…
We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. More precisely, we construct a bijective transformation (a normalizing flow characterizing by neural networks) between a…
Many results in recent years established polynomial time learnability of various models via neural networks algorithms. However, unless the model is linear separable, or the activation is a polynomial, these results require very large…
Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in…
We introduce "AnnealSGD", a regularized stochastic gradient descent algorithm motivated by an analysis of the energy landscape of a particular class of deep networks with sparse random weights. The loss function of such networks can be…
In this work, we revisit several key design choices of modern Transformer-based approaches for feed-forward 3D Gaussian Splatting (3DGS) prediction. We argue that the common practice of regressing Gaussian means as depths along camera rays…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
Synchronous stochastic gradient descent (SGD) is the most common method used for distributed training of deep learning models. In this algorithm, each worker shares its local gradients with others and updates the parameters using the…
We consider the dynamics of gradient descent (GD) in overparameterized single hidden layer neural networks with a squared loss function. Recently, it has been shown that, under some conditions, the parameter values obtained using GD achieve…
The early phase of training of deep neural networks is critical for their final performance. In this work, we study how the hyperparameters of stochastic gradient descent (SGD) used in the early phase of training affect the rest of the…