Related papers: Transient amplification in balanced neural network…
Modern deep neural networks display striking examples of rich internal computational structure. Uncovering principles governing the development of such structure is a priority for the science of deep learning. In this paper, we explore the…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…
We study the phenomena of topological amplification in arrays of parametric oscillators. We find two phases of topological amplification, both with directional transport and exponential gain with the number of sites, and one of them…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
In this paper, we study wave transmission in a rotating fluid with multiple alternating convectively stable and unstable layers. We have discussed wave transmissions in two different circumstances: cases where the wave is propagative in…
Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is…
A direct transient growth analysis for three-dimensional perturbations to flow past a periodic array of T-106/300 low-pressure turbine fan blades is presented. The methodology is based on a singular value decomposition of the flow evolution…
The construction of biologically plausible models of neural circuits is crucial for understanding the computational properties of the nervous system. Constructing functional networks composed of separate excitatory and inhibitory neurons…
An exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact…
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…
Analytical results are presented for the structure of networks that evolve via a preferential-attachment-random-deletion (PARD) model in the regime of overall network growth and in the regime of overall contraction. The phase transition…
Real-world visual data often exhibits a long-tailed distribution, where some ''head'' classes have a large number of samples, yet only a few samples are available for ''tail'' classes. Such imbalanced distribution causes a great challenge…
Understanding how transient dynamics unfold in response to localized inputs is central to predicting and controlling signal propagation in network systems, including neural processing, epidemic intervention, and power-grid resilience.…
Linear max-plus systems describe the behavior of a large variety of complex systems. It is known that these systems show a periodic behavior after an initial transient phase. Assessment of the length of this transient phase provides…
Recurrent neural network-based reinforcement learning systems are capable of complex motor control tasks such as locomotion and manipulation, however, much of their underlying mechanisms still remain difficult to interpret. Our aim is to…
Transient responses in disordered systems typically show a heavy-tail relaxation behavior: the decay time constant increases as time increases, revealing a spectral distribution of time constants. The asymptotic value of such transients is…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
Using the transfer-matrix approach and solving time-domain differential equations, we analyze the loss compensation mechanism in multilayer systems composed of an absorbing transparent conductive oxide and dielectric doped with an active…