In this paper we s h o w that the loading problem for a 3-node architecture with sigmoidal activation is NP-hard if the input dimension varies, if the classiication is performed with a certain accuracy, and if the output weights are restricted.

For the minimal O(N) sigma model, which is defined to be generated by the O(N) scalar auxiliary field alone, all n-point functions, till order 1/N included, can be expressed by elementary functions without logarithms. Consequently, the conformal composite fields of m auxiliary fields possess at the same order such dimensions, which are m times the dimension of the auxiliary field plus the order...

Visual Cryptography (VC), proposed by Naor and Shamir, has numerous uses, including visual authentication and identification, image encryption and steganography for security purpose, and. In this paper Contrast the visual information based on pseudo randomization and pixel reversal using sigmoid function is also proposed. Keywords— Information hiding, Information Security, Halftone image, Visua...

We report the first realization of a biomolecular AND gate function with double-sigmoid response (sigmoid in both inputs). Two enzyme biomarker inputs activate the gate output signal, which can then be used as indicating liver injury, but only when both of these inputs have elevated pathophysiological concentrations, effectively corresponding to logic-1 of the binary gate functioning. At lower,...

Mixture models constitute a popular type of probabilistic neural networks which model the density of a dataset using a convex combination of statistical distributions, with the Gaussian distribution being the one most commonly used. In this work we propose a new probability density function, called the Π-sigmoid, from its ability to form the shape of the letter “Π” by appropriately combining tw...

We study the power of deep neural networks (DNNs) with sigmoid activation function. Recently, it was shown that DNNs approximate any d-dimensional, smooth function on a compact set rate order W?p?d, where W is number nonzero weights in network and p smoothness Unfortunately, these rates only hold for special class sparsely connected DNNs. ask ourselves if we can show same approximation simpler ...

This paper examines the circuit complexity of feedforward neural networks having sigmoid activation function. The starting point is the complexity class NN defined in [18]. First two additional complexity classes NN∆ k and NN∆,ε k having less restrictive conditions (than NN) concerning fan-in and accuracy are defined. We then prove several relations among these three classes and well establishe...

We describe a general technique for estimating the intractable quantities that occur in a wide variety of largescale probabilistic models. The technique transforms intractable sums into integrals which are subsequently approximated via saddle point methods. When applied to sigmoid and noisy-OR networks, the technique yields a generic mean-field approximation as well as a second order Gaussian a...