Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Sonthalia, Rishi"'
Autor:
Li, Jiping, Sonthalia, Rishi
Random matrix theory has proven to be a valuable tool in analyzing the generalization of linear models. However, the generalization properties of even two-layer neural networks trained by gradient descent remain poorly understood. To understand the g
Externí odkaz:
http://arxiv.org/abs/2410.13991
This paper investigates the use of transformer architectures to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and engine
Externí odkaz:
http://arxiv.org/abs/2410.16295
A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model. Even for linear models, the effect is not fully understood for arbitrary learning rat
Externí odkaz:
http://arxiv.org/abs/2406.04425
We study the discrete dynamics of mini-batch gradient descent for least squares regression when sampling without replacement. We show that the dynamics and generalization error of mini-batch gradient descent depends on a sample cross-covariance matri
Externí odkaz:
http://arxiv.org/abs/2406.03696
We study the generalization capability of nearly-interpolating linear regressors: $\boldsymbol{\beta}$'s whose training error $\tau$ is positive but small, i.e., below the noise floor. Under a random matrix theoretic assumption on the data distributi
Externí odkaz:
http://arxiv.org/abs/2403.07264
There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of these methods often depend on traditional eigensolvers, which present lim
Externí odkaz:
http://arxiv.org/abs/2310.00729
Despite the importance of denoising in modern machine learning and ample empirical work on supervised denoising, its theoretical understanding is still relatively scarce. One concern about studying supervised denoising is that one might not always ha
Externí odkaz:
http://arxiv.org/abs/2305.17297
Autor:
Li, Xinyue, Sonthalia, Rishi
The relationship between the number of training data points, the number of parameters, and the generalization capabilities of models has been widely studied. Previous work has shown that double descent can occur in the over-parameterized regime and t
Externí odkaz:
http://arxiv.org/abs/2305.14689
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We character
Externí odkaz:
http://arxiv.org/abs/2305.14632
Autor:
Krenn, Mario, Buffoni, Lorenzo, Coutinho, Bruno, Eppel, Sagi, Foster, Jacob Gates, Gritsevskiy, Andrew, Lee, Harlin, Lu, Yichao, Moutinho, Joao P., Sanjabi, Nima, Sonthalia, Rishi, Tran, Ngoc Mai, Valente, Francisco, Xie, Yangxinyu, Yu, Rose, Kopp, Michael
Publikováno v:
Nature Machine Intelligence 5, 1326 (2023)
A tool that could suggest new personalized research directions and ideas by taking insights from the scientific literature could significantly accelerate the progress of science. A field that might benefit from such an approach is artificial intellig
Externí odkaz:
http://arxiv.org/abs/2210.00881