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08/25/2023
Six Lectures on Linearized Neural Networks
In these six lectures, we examine what can be learnt about the behavior ...
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02/21/2023
SGD learning on neural networks: leap complexity and saddle-to-saddle dynamics
We investigate the time complexity of SGD learning on fully-connected ne...
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04/21/2022
Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regression
We study the spectrum of inner-product kernel matrices, i.e., n × n matr...
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02/17/2022
The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networks
It is currently known how to characterize functions that neural networks...
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11/16/2021
Learning with convolution and pooling operations in kernel methods
Recent empirical work has shown that hierarchical convolutional kernels ...
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03/30/2021
Minimum complexity interpolation in random features models
Despite their many appealing properties, kernel methods are heavily affe...
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02/25/2021
Learning with invariances in random features and kernel models
A number of machine learning tasks entail a high degree of invariance: t...
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01/26/2021
Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration
Consider the classical supervised learning problem: we are given data (y...
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06/24/2020
When Do Neural Networks Outperform Kernel Methods?
For a certain scaling of the initialization of stochastic gradient desce...
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06/21/2019
Limitations of Lazy Training of Two-layers Neural Networks
We study the supervised learning problem under either of the following t...
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04/27/2019
Linearized two-layers neural networks in high dimension
We consider the problem of learning an unknown function f_ on the d-dime...
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02/16/2019
Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit
We consider learning two layer neural networks using stochastic gradient...
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03/25/2017
Solving SDPs for synchronization and MaxCut problems via the Grothendieck inequality
A number of statistical estimation problems can be addressed by semidefi...
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09/23/2015