1 citations · 2 across the 7 of their papers we have counts for
7 papers
An explicit operator explains end-to-end computation in the modern neural networks used for sequence and language modeling
Anif N. Shikder, Ramit Dey, Sayantan Auddy +6
We establish a mathematical correspondence between state space models, a state-of-the-art architecture for capturing long-range dependencies in data, and an exactly solvable nonlin…
A mathematical language for linking fine-scale structure in spikes from hundreds to thousands of neurons with behaviour
Alexandra N. Busch, Roberto C. Budzinski, Federico W. Pasini +8
Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, character…
On prime Cayley graphs
Maria Chudnovsky, Michal Cizek, Logan Crew +4
The decomposition of complex networks into smaller, interconnected components is a central challenge in network theory with a wide range of potential applications. In this paper, w…
An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network
Roberto C. Budzinski, Alexandra N. Busch, Samuel Mestern +7
We study a complex-valued neural network (cv-NN) with linear, time-delayed interactions. We report the cv-NN displays sophisticated spatiotemporal dynamics, including partially syn…
Spectral perturbation by rank- matrices
Jonathan L. Merzel, Ján Mináč, Tung T. Nguyen +1
Let and designate matrices with coefficients in a field . In this paper, we completely answer the following question: For fixed, what are the possible ch…
On the joins of group rings
Sunil K. Chebolu, Jonathan L. Merzel, Ján Mináč +4
Given a collection of finite groups and a ring , we define a subring of the ring ( that encompasses all the individual group…
Joins of normal matrices, their spectrum, and applications
Jan Mináč, Lyle Muller, Tung T. Nguyen +1
Motivated by studies of oscillator networks, we study the spectrum of the join of several normal matrices with constant row sums. We apply our results to compute the characteristic…