Related papers: Activation Saturation and Floquet Spectrum Collaps…
We investigate the asymptotic behaviour of networks of interacting non-linear Hawkes processes modeling a homogeneous population of neurons in the large population limit. In particular, we prove a functional central limit theorem for the…
Most existing expressivity theories for neural networks assume exact real arithmetic, whereas practical neural networks are executed under finite-precision floating-point arithmetic with implementation-dependent execution semantics. Recent…
The solution to the BFKL equation grows like a power of center of mass energy, s, violating unitarity conditions at high energies. The growth of the cross section can be tamed by taking into account multiple pomeron exchanges. This is known…
We consider time-harmonic incompressible flow with a spatially resolved complex viscosity field $\mu^*(\mathbf{x},\omega)$ and, at fixed forcing frequency $\omega>0$, its constitutive phase texture…
This paper aims to understand the training solution, which is obtained by the back-propagation algorithm, of two-layer neural networks whose hidden layer is composed of the units with smooth activation functions, including the usual sigmoid…
As modern deep learning architectures grow in complexity, representational ambiguity emerges as a critical barrier to their interpretability and reliable merging. For ReLU networks, identical functional mappings can be achieved through…
In this paper, we construct neural networks with ReLU, sine and $2^x$ as activation functions. For general continuous $f$ defined on $[0,1]^d$ with continuity modulus $\omega_f(\cdot)$, we construct ReLU-sine-$2^x$ networks that enjoy an…
The $f^{-\gamma}$ sloped current noise power spectra, observed in organic semiconductors, have been interpreted within a {\em variable range hopping} mechanism of the fluctuations. The relative current noise power spectral density ${\cal…
Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents. We consider a linear system of differential equations with a time-periodic coefficient matrix. Assuming that the coefficient matrix depends…
We study Schr\"odinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The expansion is in $\lambda^{-\delta}$ with $\delta\in(0,1)$ for most of the…
The effect of structural constriction on molecular mobility is investigated by broadband dielectric spectroscopy (BDS) within three types of molecular arrangements: monomers, oligomers and self-assembled monolayers (SAMs). While disordered…
We consider the self-energy and quasiparticle spectrum, for both electrons interacting with phonons, and composite fermions interacting with gauge fluctuations. In both cases we incorporate the singular structure arising from Landau level…
We theoretically studied the Floquet state of gated bilayer graphene, which is irradiated by normally incident focused Gaussian beam with orbital angular momentum (OAM). According to the Floquet theory, in-plane and out-of-plane electric…
We consider the capacity of \emph{treelike committee machines} (TCM) neural networks. Relying on Random Duality Theory (RDT), \cite{Stojnictcmspnncaprdt23} recently introduced a generic framework for their capacity analysis. An upgrade…
We investigate the excitation spectrum of strongly correlated sodium cobaltate within a realistic many-body description beyond dynamical mean-field theory (DMFT). At lower doping around $x$=0.3, rather close to Mott-critical half-filling,…
In this paper, we report the excitation of coherent density and potential fluctuations induced by magnetohydrodynamic (MHD) activity in the edge plasma region of ADITYA-U Tokamak. When the amplitude of the MHD mode, mainly the m/n = 2/1,…
The $1/f$-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitute evidences of criticality in neuronal systems. Recent in vitro studies…
We study the approximation properties of shallow neural networks with an activation function which is a power of the rectified linear unit. Specifically, we consider the dependence of the approximation rate on the dimension and the…
In the previous work hep-ph/0112140, hep-ph/0204277, we showed that while the nonlinear QCD evolution equation of Balitsky and Kovchegov (BK) leads to saturation of the scattering amplitude locally in impact parameter space, it does not…
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural…