Unfolded ISTA achieves linear convergence for sparse signal recovery.
problem Understanding and improving convergence of iterative algorithms in sparse signal recovery.
method Introducing weight structure and incorporating thresholding in the network.
result Unfolded ISTA can achieve linear convergence, better than sublinear convergence of ISTA/FISTA.
This paper optimizes step sizes for faster convergence in sparse coding.
problem Improving convergence rate of ISTA for sparse coding.
method Learning step sizes for ISTA using neural networks.
result A simple step size strategy can improve convergence rate of ISTA.
A-DLISTA and VLISTA learn dictionaries and sparse representations under varying sensing matrices.
problem Learning dictionaries and sparse representations under varying sensing matrices.
method Augmented Dictionary Learning ISTA (A-DLISTA) and Variational Learning ISTA (VLISTA).
result VLISTA provides a probabilistic way to jointly learn the dictionary distribution and the reconstruction algorithm.
New multi-layer algorithm improves CNN performance.
problem Efficiently modeling and processing information with parsimonious representations.
method Generalized Basis Pursuit to multi-layer setting, proposing ML-ISTA and ML-FISTA algorithms.
result Nested first order algorithms converge to solve the multi-layer problem.
Improved neural network reconstruction from sparse measurements with theoretical guarantees.
problem Improving neural network performance in sparse signal reconstruction from few measurements.
method Combining iterative reconstruction algorithms with neural networks, analyzing generalization properties, and deriving a generalization bound.
result Theoretical guarantees for neural network reconstruction from compressive linear measurements, with generalization error scaling logarithmically in the number of layers and linearly in the number of measurements.
Proposes a novel neural architecture for sparse coding using learned greedy pursuit.
problem Lack of interpretability in neural network architectures for sparse coding.
method Unfolded and learned version of Orthogonal Matching Pursuit (OMP) algorithm.
result Demonstrates flexibility and efficiency of the Learned Greedy Method (LGM) in various experiments.
In this paper, we propose a novel recurrent neural network architecture for speech separation. This architecture is constructed by unfolding the iterations of a sequential iterative soft-thresholding algorithm (ISTA) that solves the optimization problem for sparse nonnegative matrix factorization (NMF) of spectrograms.…
Paper analyzes adaptive ISTA with MAD for LASSO problem.
problem Finding solutions to LASSO problems without tuning λ. method Adaptive ISTA with median absolute deviation (MAD) for estimating noise level.
result Local linear convergence and global convergence of the algorithm.
Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simpl…
The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing L1-regularized co…
Paper shows linear convergence of ISTA and FISTA for ill-conditioned images.
problem Solving linear inverse problems with sparse representation in signal and image processing.
method Revisits iterative shrinkage-thresholding algorithms (ISTA) and improves their convergence properties.
result Linear convergence of ISTA and FISTA for strongly convex smooth parts, even in ill-conditioned cases.
The paper accelerates ISTA and FISTA algorithms for composite optimization problems.
problem Improving convergence rates of ISTA and FISTA for composite optimization.
method Improved proximal subgradient norm minimization using Lyapunov function.
result Convergence rates of ISTA and FISTA are accelerated.
This review summarizes five Lasso optimization algorithms.
problem Optimizing the Lasso objective function.
method Five representative algorithms: ISTA, FISTA, CGDA, SLA, PFA.
result Comparison of convergence rates and strengths/weaknesses.
New models explain residual and dilated dense neural networks using sparse coding.
problem Lack of theoretical understanding of residual and dilated dense neural networks.
method Proposed Res-CSC and MSD-CSC models, derived mathematical relationships, implemented ISTA.
result Mathematical understanding of residual and dilated dense neural networks.
New method for unbinned, profiled unfolding in particle physics.
problem Traditional unfolding methods are limited in the number of unfolded variables and cannot profile nuisance parameters.
method Proposes a machine learning-based method that allows for unbinned differential cross sections and profiles nuisance parameters.
result Demonstrates the method with Gaussian examples and a simulated Higgs boson cross section measurement.
New method unfolds distribution moments directly from data without binning.
problem Deconvolving detector distortions in particle physics.
method Uses machine learning, inspired by GANs, to unfold moments directly.
result More precise than bin-based approaches and comparable to unbinned methods.
OmniFold simultaneously unfolds all observables using machine learning.
problem Traditional unfolding methods are limited to individual observables and do not incorporate all detector information.
method OmniFold iteratively reweights a simulated dataset using machine learning to handle all available information.
result OmniFold enables the simultaneous measurement of all observables, including those not yet invented.
Study families of Lie algebroids on complex spaces, introducing unfoldings.
problem Investigate singular holomorphic Lie algebroids on complex analytic spaces.
method Introduce and study unfoldings of Lie algebroids, showing a correspondence with holomorphic flat connections.
result Existence of a one-to-one correspondence between transversal unfoldings and holomorphic flat connections.
Abstract reviews Kähler geometry of complex projective spaces using reduction and unfolding.
problem Describing the Kähler geometry of complex projective spaces.
method Reduction and unfolding procedures associated with a momentum map.
result Describes Kähler geometry of complex projective spaces.
Study on unfolding maps of surfaces in 3D space, proving versality conditions.
problem Investigating the versality of rotation unfolding of folding maps for surfaces in R3. method Introducing and analyzing the rotation unfolding of folding maps, proving versality conditions in terms of geometry.
result Proved conditions for the rotation unfolding to be versal, showing diffeomorphic type of tangent plane locus.
New deep-unfolded network improves video background separation.
problem Video foreground-background separation.
method Deep unfolding of an iterative RPCA algorithm with adaptive learning.
result Proposed network outperforms state-of-the-art in video foreground-background separation.
Unfolding paths in Outer space accumulate on a simplex, not converge.
problem Understanding accumulation points in Outer space.
method Constructing an unfolding path in Outer space.
result Unfolding paths accumulate on a 1-simplex, not converge.
The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.
problem Phase transitions in singular values and vectors of large random matrices.
method Analysis of singular values and vectors of long rectangular random matrices, and tensor unfolding algorithm for asymmetric rank-one spiked tensor models.
result An exact threshold for tensor unfolding to detect signals, independent of unfolding procedure.
We show that every convex polyhedron admits a simple edge unfolding after an affine transformation. In particular there exists no combinatorial obstruction to a positive resolution of Durer's unfoldability problem, which answers a question of Croft, Falconer, and Guy. Among other techniques, the proof employs a topolog…
A simple self-supervised model for tensor RPCA using deep unfolding.
problem Tensor robust principal component analysis (RPCA) challenges in practical applications.
method Deep unfolding with only four hyperparameters.
result Competitive or superior performance compared to supervised methods, even in data-starved scenarios.
A new machine learning method handles nuisance parameters for better unfolding in particle physics.
problem Improving statistical correction of cross sections in complex particle physics detectors.
method Profile OmniFold, a machine learning-based Expectation-Maximization procedure that incorporates nuisance parameters.
result Demonstrated the effectiveness of Profile OmniFold on both simulated and real data.
In a previous work we proved the uniqueness and functoriality of primary unfoldings on simple Thom-Mather spaces, which is a functor to the category of smooth manifolds. In this article we extend these results for any stratified Thom-Mather pseudomanifold with arbitary finite length, through a new kind of intermediate …
A pseudo-edge graph of a convex polyhedron K is a 3-connected embedded graph in K whose vertices coincide with those of K, whose edges are distance minimizing geodesics, and whose faces are convex. We construct a convex polyhedron K in Euclidean 3-space with a pseudo-edge graph with respect to which K is not unfoldable…
Paper proposes efficient algorithm for non-convex rank minimization.
problem Efficiently solving rank minimization problems with non-convex penalties.
method Iterative Shrinkage-Thresholding Algorithm (ISTA) for non-convex weighted and reweighted nuclear norm.
result Proves convergence to critical point with rate O(1/T) and outperforms state-of-the-art methods. Unified framework for spectral methods, kernel learning, and manifold unfolding.
problem Tackles the unification and optimization of spectral dimensionality reduction methods.
method Unified spectral methods as kernel PCA, kernel learning by SDP, and detailed explanation of MVU variants.
result Unified understanding and optimization of manifold learning techniques.
This is mainly a survey article on the recent development of the theory of graph-like Legendrian unfoldings and its applications. The notion of big Legendrian submanifolds was introduced by Zakalyukin for describing the wave front propagations. Graph-like Legendrian unfoldings belong to a special class of big Legendria…
Deep unfolding accelerates MCMC-based COP solvers.
problem Optimizing combinatorial problems with MCMC and gradient descent.
method Combines MCMC and gradient descent, trains step sizes, uses variance estimation for non-differentiable MCMC.
result Significantly accelerates convergence speed for COPs.
New algorithms accelerate SVGD convergence using deep unfolding.
problem Improving the speed of SVGD convergence.
method Integrating deep unfolding into SVGD for parameter learning.
result Proposed algorithms achieve faster convergence in various tasks.
Chebyshev steps improve convergence in deep-unfolded gradient descent.
problem Improving convergence speed in iterative algorithms.
method Introducing Chebyshev steps to bound convergence rate of gradient descent.
result Chebyshev steps lead to asymptotically optimal convergence rate.
In this paper, we introduce the notions of map-germs of pedal unfolding type and normalized Legendrian map-germs; and then we show that the fundamental theorem of calculus provides a natural one to one correspondence between Whitney umbrellas of pedal unfolding type and normalized swallowtails.
Develops a Thom-Mather theory for corank 1 frontals.
problem Characterizing and constructing stable unfoldings of corank 1 frontals.
method Thom-Mather theory, frontal stability, versality of unfoldings, reduction method.
result Classification of stable frontal multigerms and corank 1 stable frontals.
Let Y be a closed and oriented 3-manifold. We define different versions of unfolded Seiberg-Witten Floer spectra for Y. These invariants generalize Manolescu's Seiberg-Witten Floer spectrum for rational homology 3-spheres. We also compute some examples when Y is a Seifert space.
ULES embeds dynamic networks with stability guarantees.
problem Stability of time-varying node embeddings in evolving networks.
method Unfolded Laplacian Spectral Embedding (ULSE) using normalized Laplacian operators.
result ULES satisfies cross-sectional and longitudinal stability under dynamic stochastic block model.
Branched covers are applied frequently in topology - most prominently in the construction of closed oriented PL d-manifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d<=4. On the other hand, Izmestiev and Joswig described how to obtain a simplic…
Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the underlying submanifold is isometric to a convex subset, and we provide some simple e…
New method uses Wasserstein loss for data unfolding, offering better accuracy than classical techniques.
problem Removing noise or artifacts from measurements in physics experiments.
method Alternative formulation using Wasserstein loss, developing a convergent algorithm.
result Optimal transport approach offers robust, accurate performance compared to classical techniques, especially in cases with significant binning artifacts.
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about the true distribution from theory or previous experiments is used for Monte-Car…
This paper develops a novel deep recurrent neural network for sequential signal reconstruction.
problem Sequential signal reconstruction from low-dimensional measurements.
method Unfolding a reweighted ℓ1-ℓ1 minimization algorithm to design a deep recurrent neural network. result The proposed reweighted-RNN significantly outperforms existing RNN models in sequential frame reconstruction.
A new method for unfolding histograms without matrix inversion.
problem Matrix inversion in experimental physics, especially in high-energy particle physics.
method Sampling many distributions, folding them through the response matrix, and choosing the closest one to the data.
result Performs as well as traditional methods in well-defined inverse problems and outperforms them in ill-defined ones.
A very simple heuristic approach to the unfolding problem will be described. An iterative algorithm starts with an empty histogram and every iteration aims to add one entry to this histogram. The entry to be added is selected according to a criteria which includes a χ2 test and a regularization. After a relatively s…
This article is devoted to the study of smooth desingularization, which are customary employed in the definition of De Rham Intersection Cohomology with differential forms. In this paper we work with the category of Thom-Mather simple spaces. We construct a functor which sends each Thom-Mather simple space into a smoot…
Extends invariants to 4-manifolds with boundary.
problem Defining invariants for 4-manifolds with boundary.
method Using unfolded Seiberg-Witten Floer spectra.
result Detailed proof of gluing theorem for relative invariants.
A framework for stable dynamic network embeddings using static methods.
problem Dynamic network embedding in a nascent field.
method Using static network embedding methods on dilated unfolded adjacency matrices.
result Stable embeddings that preserve latent node behavior across time.