Related papers: Spiky Rank and Its Applications to Rigidity and Ci…
In this paper we study various versions of extension complexity for polygons through the study of factorization ranks of their slack matrices. In particular, we develop a new asymptotic lower bound for their nonnegative rank, shortening the…
As the demand for compute power in traditional neural networks has increased significantly, spiking neural networks (SNNs) have emerged as a potential solution to increasingly power-hungry neural networks. By operating on 0/1 spikes emitted…
We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of…
Spiking neural networks (SNNs) are gaining popularity in deep learning due to their low energy budget on neuromorphic hardware. However, they still face challenges in lacking sufficient robustness to guard safety-critical applications such…
For energy-efficient computation in specialized neuromorphic hardware, we present spiking neural coding, an instantiation of a family of artificial neural models grounded in the theory of predictive coding. This model, the first of its…
For an $N \times N$ matrix $A$, its rank-$r$ rigidity, denoted $\mathcal{R}_A(r)$, is the minimum number of entries of $A$ that one must change to make its rank become at most $r$. Determining the rigidity of interesting explicit families…
In this paper we parameterize non-negative matrices of sum one and rank at most two. More precisely, we give a family of parameterizations using the least possible number of parameters. We also show how these parameterizations relate to a…
The nonnegative and positive semidefinite (PSD-) ranks are closely connected to the nonnegative and positive semidefinite extension complexities of a polytope, which are the minimal dimensions of linear and SDP programs which represent this…
The spiking neural network, known as the third generation neural network, is an important network paradigm. Due to its mode of information propagation that follows biological rationality, the spiking neural network has strong energy…
One of the most interesting and still growing scientific fields is neuromorphic engineering, which is focused on studying and designing hardware and software with the purpose of mimicking the basic principles of biological nervous systems.…
Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing…
The SPIKE family of linear system solvers provides parallelism using a block tridiagonal partitioning. Typically SPIKE-based solvers are applied to banded systems, resulting in structured off-diagonal blocks with non-zeros elements…
Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…
The rank of a finite algebraic structure with a single binary operation is the minimum number of elements needed to express every other element under the closure of the operation. In the case of groups, the previous best algorithm for…
Stability arguments are often used to prevent learning algorithms from having ever increasing activity and weights that hinder generalization. However, stability conditions can clash with the sparsity required to augment the energy…
In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric cases, where the metric aims to quantify the complexity of the nonconvex optimization…
The rank metric measures the distance between two matrices by the rank of their difference. Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a…