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Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
This paper presents a first-order {distributed continuous-time algorithm} for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size,…
A distributed discrete-time algorithm is proposed for multi-agent networks to achieve a common least squares solution of a group of linear equations, in which each agent only knows some of the equations and is only able to receive…
The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…
One of the defining features of living systems is their adaptability to changing environmental conditions. This requires organisms to extract temporal and spatial features of their environment, and use that information to compute the…
We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be use to…
Many science and engineering applications involve solving a linear least-squares system formed from some field measurements. In the distributed cyber-physical systems (CPS), often each sensor node used for measurement only knows partial…
This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression…
The paper addresses the model reduction problem by least squares moment matching for continuous-time, linear, time-invariant systems. The basic idea behind least squares moment matching is to approximate a transfer function by ensuring that…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
Do neural networks, trained on well-understood algorithmic tasks, reliably rediscover known algorithms for solving those tasks? Several recent studies, on tasks ranging from group arithmetic to in-context linear regression, have suggested…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…
Full scale simulations of neuronal network models of the brain are challenging due to the high density of connections between neurons. This contribution reports run times shorter than the simulated span of biological time for a full scale…
There is extensive evidence that biological neural networks encode information in the precise timing of the spikes generated and transmitted by neurons, which offers several advantages over rate-based codes. Here we adopt a vector space…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We…
While cyclic scheduling is involved in numerous real-world applications, solving the derived problem is still of exponential complexity. This paper focuses specifically on modelling the manufacturing application as a cyclic job shop problem…