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09/19/2023
Investigating the Catastrophic Forgetting in Multimodal Large Language Models
Following the success of GPT4, there has been a surge in interest in mul...
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12/23/2022
Principled and Efficient Transfer Learning of Deep Models via Neural Collapse
With the ever-growing model size and the limited availability of labeled...
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10/18/2022
Hidden State Variability of Pretrained Language Models Can Guide Computation Reduction for Transfer Learning
While transferring a pretrained language model, common approaches conven...
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10/04/2022
Are All Losses Created Equal: A Neural Collapse Perspective
While cross entropy (CE) is the most commonly used loss to train deep ne...
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09/19/2022
Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifold
When training overparameterized deep networks for classification tasks, ...
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03/02/2022
On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features
When training deep neural networks for classification tasks, an intrigui...
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02/28/2022
Robust Training under Label Noise by Over-parameterization
Recently, over-parameterized deep networks, with increasingly more netwo...
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09/23/2021
Rank Overspecified Robust Matrix Recovery: Subgradient Method and Exact Recovery
We study the robust recovery of a low-rank matrix from sparsely and gros...
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05/06/2021
A Geometric Analysis of Neural Collapse with Unconstrained Features
We provide the first global optimization landscape analysis of Neural Co...
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03/01/2021
Convolutional Normalization: Improving Deep Convolutional Network Robustness and Training
Normalization techniques have become a basic component in modern convolu...
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07/14/2020
From Symmetry to Geometry: Tractable Nonconvex Problems
As science and engineering have become increasingly data-driven, the rol...
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06/16/2020
Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization
Recent advances have shown that implicit bias of gradient descent on ove...
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01/20/2020
Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications
The problem of finding the sparsest vector (direction) in a low dimensio...
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12/05/2019
Analysis of the Optimization Landscapes for Overcomplete Representation Learning
We study nonconvex optimization landscapes for learning overcomplete rep...
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11/12/2019
Nonsmooth Optimization over Stiefel Manifold: Riemannian Subgradient Methods
Nonsmooth Riemannian optimization is a still under explored subfield of ...
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08/28/2019
Short-and-Sparse Deconvolution -- A Geometric Approach
Short-and-sparse deconvolution (SaSD) is the problem of extracting local...
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08/28/2019
A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution
We study the multi-channel sparse blind deconvolution (MCS-BD) problem, ...
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12/03/2017
Convolutional Phase Retrieval via Gradient Descent
We study the convolutional phase retrieval problem, which considers reco...
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02/22/2016
A Geometric Analysis of Phase Retrieval
Can we recover a complex signal from its Fourier magnitudes? More genera...
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11/15/2015
Complete Dictionary Recovery over the Sphere II: Recovery by Riemannian Trust-region Method
We consider the problem of recovering a complete (i.e., square and inver...
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11/11/2015
Complete Dictionary Recovery over the Sphere I: Overview and the Geometric Picture
We consider the problem of recovering a complete (i.e., square and inver...
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10/21/2015
When Are Nonconvex Problems Not Scary?
In this note, we focus on smooth nonconvex optimization problems that ob...
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04/26/2015
Complete Dictionary Recovery over the Sphere
We consider the problem of recovering a complete (i.e., square and inver...
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12/15/2014
Finding a sparse vector in a subspace: Linear sparsity using alternating directions
Is it possible to find the sparsest vector (direction) in a generic subs...
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01/16/2014