arXiv research

New deep-unfolded network improves video background separation.

A simple self-supervised model for tensor RPCA using deep unfolding.

Deep unfolding accelerates MCMC-based COP solvers.

New algorithms accelerate SVGD convergence using deep unfolding.

Chebyshev steps improve convergence in deep-unfolded gradient descent.

This paper develops a novel deep recurrent neural network for sequential signal reconstruction.

The paper interprets learned step sizes in deep-unfolded gradient descent.

In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding of a numerical algorithm into a neural network form, resulting in a substantial …

Deep-RLS uses deep learning to improve PCA for better source separation.

Machine learning, and more specifically deep learning, have shown remarkable performance in sensing, communications, and inference. In this paper, we consider the application of the deep unfolding technique in the problem of signal reconstruction from its one-bit noisy measurements. Namely, we propose a model-based mac…

A new deep learning model improves phase retrieval performance.

Deep learning aids ADMM-based decoding for binary linear codes.

OmniFold uses deep learning to deconvolve high-dimensional simulations.

Model-based methods and deep neural networks have both been tremendously successful paradigms in machine learning. In model-based methods, problem domain knowledge can be built into the constraints of the model, typically at the expense of difficulties during inference. In contrast, deterministic deep neural networks a…

Model-based machine learning improves communication systems.

LargeMvC-Net improves scalability of multi-view clustering.

We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such, our network leverages by design that signals have a sparse representation and t…

DeepFPC uses neural networks to recover sparse signals from quantized measurements.

New method for unbinned, profiled unfolding in particle physics.

New method unfolds distribution moments directly from data without binning.

OmniFold simultaneously unfolds all observables using machine learning.

Study families of Lie algebroids on complex spaces, introducing unfoldings.

Study on unfolding maps of surfaces in 3D space, proving versality conditions.

Novel LRMC tackles missing data and outliers in large-scale low-rank data recovery.

Unfolding paths in Outer space accumulate on a simplex, not converge.

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.…

The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.

The paper develops generalization bounds for deep compound Gaussian neural networks.

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…

Proposes a novel neural architecture for sparse coding using learned greedy pursuit.

Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented subwavelength spatial resolution by relying on super-resolution techniques. A t…

A new machine learning method handles nuisance parameters for better unfolding in particle physics.

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…

Unified framework for spectral methods, kernel learning, and manifold unfolding.

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…

We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the Kähler geometry of a finite dimensional complex projective spaces.

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.

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.

Survey of deep learning methods for inverse problems, highlighting theoretical challenges.

In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the power of neural networks. In this work, we study unfolded ISTA (Iterative Shrinkage…

Recently, the paradigm of unfolding iterative algorithms into finite-length feed-forward neural networks has achieved a great success in the area of sparse recovery. Benefit from available training data, the learned networks have achieved state-of-the-art performance in respect of both speed and accuracy. However, the …

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…

Paper proposes online learning for MIMO channel estimation using neural networks.

New method uses Wasserstein loss for data unfolding, offering better accuracy than classical techniques.