Related papers: Random Paraunitary Projections
Products of random transfer matrices are applied to low dimensional disordered systems to evaluate numerically extensive quantities such as entropy and overlap probability distribution. The main advantage is the possibility to avoid…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…
We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
In this letter, a permutation enhanced parallel reconstruction architecture for compressive sampling is proposed. In this architecture, a measurement matrix is constructed from a block-diagonal sensing matrix and the sparsifying basis of…
For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to…
It is a significant challenge to predict the network topology from a small amount of dynamical observations. Different from the usual framework of the node-based reconstruction, two optimization approaches (i.e., the global and partitioned…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…
The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
Programmable structures are systems whose undeformed geometries and material property distributions are deliberately designed to achieve prescribed deformed configurations under specific loading conditions. Inflatable structures are a…
Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…