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07/23/2022
Boosting the Efficiency of Parametric Detection with Hierarchical Neural Networks
Gravitational wave astronomy is a vibrant field that leverages both clas...
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03/09/2022
Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization
Achieving invariance to nuisance transformations is a fundamental challe...
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01/05/2022
Testing matrix product states
Devising schemes for testing the amount of entanglement in quantum syste...
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11/15/2021
Quantum soundness of testing tensor codes
A locally testable code is an error-correcting code that admits very eff...
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11/01/2021
Unique Games hardness of Quantum Max-Cut, and a vector-valued Borell's inequality
The Gaussian noise stability of a function f:ℝ^n →{-1, 1} is the expecte...
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10/29/2021
Principal Component Pursuit for Pattern Identification in Environmental Mixtures
Environmental health researchers often aim to identify sources/behaviors...
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07/29/2021
Deep Networks Provably Classify Data on Curves
Data with low-dimensional nonlinear structure are ubiquitous in engineer...
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06/17/2021
Square Root Principal Component Pursuit: Tuning-Free Noisy Robust Matrix Recovery
We propose a new framework – Square Root Principal Component Pursuit – f...
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05/21/2021
ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction
This work attempts to provide a plausible theoretical framework that aim...
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04/08/2021
Generalized Approach to Matched Filtering using Neural Networks
Gravitational wave science is a pioneering field with rapidly evolving d...
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10/27/2020
Deep Networks from the Principle of Rate Reduction
This work attempts to interpret modern deep (convolutional) networks fro...
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09/27/2020
Quantum soundness of the classical low individual degree test
Low degree tests play an important role in classical complexity theory, ...
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08/25/2020
Deep Networks and the Multiple Manifold Problem
We study the multiple manifold problem, a binary classification task mod...
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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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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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01/13/2020
MIP*=RE
We show that the class MIP* of languages that can be decided by a classi...
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11/22/2019
Gemmini: An Agile Systolic Array Generator Enabling Systematic Evaluations of Deep-Learning Architectures
Advances in deep learning and neural networks have resulted in the rapid...
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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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06/06/2019
Complete Dictionary Learning via ℓ^4-Norm Maximization over the Orthogonal Group
This paper considers the fundamental problem of learning a complete (ort...
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04/11/2019
NEEXP in MIP*
We study multiprover interactive proof systems. The power of classical m...
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01/07/2019
On the Global Geometry of Sphere-Constrained Sparse Blind Deconvolution
Blind deconvolution is the problem of recovering a convolutional kernel ...
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01/02/2019
Geometry and Symmetry in Short-and-Sparse Deconvolution
We study the Short-and-Sparse (SaS) deconvolution problem of recovering ...
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06/01/2018
Structured Local Optima in Sparse Blind Deconvolution
Blind deconvolution is a ubiquitous problem of recovering two unknown si...
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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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03/29/2014
Scalable Robust Matrix Recovery: Frank-Wolfe Meets Proximal Methods
Recovering matrices from compressive and grossly corrupted observations ...
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07/22/2013
Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery
Recovering a low-rank tensor from incomplete information is a recurring ...
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07/04/2013
Toward Guaranteed Illumination Models for Non-Convex Objects
Illumination variation remains a central challenge in object detection a...
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11/05/2012
Efficient Point-to-Subspace Query in ℓ^1: Theory and Applications in Computer Vision
Motivated by vision tasks such as robust face and object recognition, we...
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08/02/2012
Efficient Point-to-Subspace Query in ℓ^1 with Application to Robust Object Instance Recognition
Motivated by vision tasks such as robust face and object recognition, we...
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11/03/2011
