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Transformer-based large language models are in some respects limited by the quadratic time and space computational complexity of attention. We introduce the Toeplitz MLP Mixer (TMM), a transformer-like architecture that swaps attention for…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
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…
Dynamic Metasurface Antenna (DMA) is a cutting-edge antenna technology offering scalable and sustainable solutions for large antenna arrays. The effectiveness of DMAs stems from their inherent configurable analog signal processing…
The inverse Toeplitz eigenvalue problem (ToIEP) concerns finding a vector that specifies the real-valued symmetric Toeplitz matrix with the prescribed set of eigenvalues. Since phase "calibration" errors in uniform linear antenna arrays…
It was recently shown that low rank matrix completion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target…
This paper focuses on the resolution of infinite-dimensional Toeplitz Block LMIs, which are frequently encountered in the context of stability analysis and control design problems formulated in the harmonic framework. We propose a…
Unrolled deep neural networks have attracted significant attention for their success in various practical applications. In this paper, we explore an application of deep unrolling in the direction of arrival (DoA) estimation problem when…
Deep neural networks have emerged as very successful tools for image restoration and reconstruction tasks. These networks are often trained end-to-end to directly reconstruct an image from a noisy or corrupted measurement of that image. To…
Drawing on theoretical insights, we advocate an error-based thresholding (EBT) mechanism for learned ISTA (LISTA), which utilizes a function of the layer-wise reconstruction error to suggest a specific threshold for each observation in the…
Can one recover a matrix efficiently from only matrix-vector products? If so, how many are needed? This paper describes algorithms to recover matrices with known structures, such as tridiagonal, Toeplitz, Toeplitz-like, and hierarchical…
In this paper, we consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. Specifically, we treat sensing problems with model mismatch where one wishes to recover a sparse…
We consider the parametric data model employed in applications such as line spectral estimation and direction-of-arrival estimation. We focus on the stochastic maximum likelihood estimation (MLE) framework and offer approaches to estimate…
Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…
This paper proposes a set of piecewise Toeplitz matrices as the linear mapping/sensing operator $\mathcal{A}: \mathbf{R}^{n_1 \times n_2} \rightarrow \mathbf{R}^M$ for recovering low rank matrices from few measurements. We prove that such…
It is promising to solve linear inverse problems by unfolding iterative algorithms (e.g., iterative shrinkage thresholding algorithm (ISTA)) as deep neural networks (DNNs) with learnable parameters. However, existing ISTA-based unfolded…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
In this paper we consider algorithm unfolding for the Multiple Measurement Vector (MMV) problem in the case where only few training samples are available. Algorithm unfolding has been shown to empirically speed-up in a data-driven way the…
The objective of deep metric learning (DML) is to learn embeddings that can capture semantic similarity and dissimilarity information among data points. Existing pairwise or tripletwise loss functions used in DML are known to suffer from…
Image restoration is a long-standing low-level vision problem, e.g., deblurring and deraining. In the process of image restoration, it is necessary to consider not only the spatial details and contextual information of restoration to ensure…