Related papers: Activation Saturation and Floquet Spectrum Collaps…
It is well-known that overparametrized neural networks trained using gradient-based methods quickly achieve small training error with appropriate hyperparameter settings. Recent papers have proved this statement theoretically for highly…
Using the Ogata-Shiba wave function, the spectral functions of the one-dimensional infinite U Hubbard model are calculated for various concentrations. It is shown that the ``shadow band'' feature due to 2k_F fluctuations becomes more…
We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive…
We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on the parameter omega. We assume that the spectrum of H is discrete, {h_m (m = 1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian operator,…
The influence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic…
The stochastic Hodgkin-Huxley neurons considered in this paper replace time-constant deterministic input $a dt$ of the classical deterministic model by increments $\vartheta dt + dX_t$ of a stochastic process: $X$ is Ornstein-Uhlenbeck with…
We study the growth of the operator entanglement entropy (EE) of the time evolution operator in chaotic, many-body localized and Floquet systems. In the random field Heisenberg model we find a universal power law growth of the operator EE…
Results are presented for the occupation probabilities and current densities of bulk and edge states of half-filled graphene in a cylindrical geometry, and irradiated by a circularly polarized laser. It is assumed that the system is closed,…
We study a purely inhibitory neural network model where neurons are represented by their state of inhibition. The study we present here is partially based on the work of Cottrell \cite{Cot} and Fricker et al. \cite{FRST}. The spiking rate…
In recent years, deep neural networks (DNNs) achieved unprecedented performance in many low-level vision tasks. However, state-of-the-art results are typically achieved by very deep networks, which can reach tens of layers with tens of…
We prove new upper and lower bounds on the VC-dimension of deep neural networks with the ReLU activation function. These bounds are tight for almost the entire range of parameters. Letting $W$ be the number of weights and $L$ be the number…
We study the energy dependence of the saturation momentum in the context of the collinearly improved Leading and Next to Leading BFKL evolution, and in the presence of saturation boundaries. We find that the logarithmic derivative of the…
Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in…
We study the charge noise $S_Q$ in Josephson qubits produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate. The TLS are driven by an alternating electric field of angular frequency $\Omega$ and…
This paper addresses inverse problems (in a broad sense) for two classes of multivariate neural network (NN) operators, with particular emphasis on saturation results, and both analytical and semi-analytical inverse theorems. One of the key…
In this paper, we introduce the Hyperbolic Tangent Exponential Linear Unit (TeLU), a novel neural network activation function, represented as $f(x) = x{\cdot}tanh(e^x)$. TeLU is designed to overcome the limitations of conventional…
Activation functions are essential to deep learning networks. Popular and versatile activation functions are mostly monotonic functions, some non-monotonic activation functions are being explored and show promising performance. But by…
We present extensive experiments training and testing hidden units in deep networks that emit only a predefined, static, number of discretized values. These units provide benefits in real-world deployment in systems in which memory and/or…
We investigate the training and generalization errors of overparameterized neural networks (NNs) with a wide class of leaky rectified linear unit (ReLU) functions. More specifically, we carefully upper bound both the convergence rate of the…
The widespread application of artificial neural networks has prompted researchers to experiment with FPGA and customized ASIC designs to speed up their computation. These implementation efforts have generally focused on weight…