Vector Operations in Neural Network Computations

Visual motion information is useful for many complex tasks in the biological and robotic systems. Models for motion processing in the biological systems have been studied to use conventional symmetric quadrature functions with Gabor filters. This paper proposes a model of the another bio-inspired asymmetric neural networks. The prominent features are the nonlinear characteristics as the squaring and rectification functions, which are observed in the retinal and visual cortex networks. In this paper, the asymmetric network with Gabor filters is compared with that of the conventional symmetric networks. It is shown that the biological asymmetric network with nonlinearities is effective for detecting the inputted phase information and directional movements from the network computations. The responses to the frequency characteristics and to the complex motion stimulus are computed in the asymmetric networks, which are not derived for the conventional energy model.

To make clear the mechanism of the visual movement is important in the visual system. The prominent feature is the nonlinear characteristics as the squaring and rectification functions, which are observed in the retinal and visual cortex networks. Conventional model for motion processing in cortex, is the use of symmetric quadrature functions with Gabor filters. This paper proposes a new motion sensing processing model in the asymmetric networks. To make clear the behavior of the asymmetric nonlinear network, white noise analysis and Wiener kernels are applied. It is shown that the biological asymmetric network with nonlinearities is effective and general for generating the directional movement from the network computations. The qualitative analysis is performed between the asymmetrical network and the conventional quadrature model. The results are applicable to the V1 and MT model of the neural networks in the cortex.

The author discusses a problem of motion perception in the neural network of the catfish retina. Linear and nonlinear information are crucial to visual processing in the catfish retinal network. Horizontal and bipolar cell responses are linearly related to the input modulation of light, while amacrine cells work as a nonlinear function of squaring. These cells make an asymmetrical nonlinear network. The author solves a problem of motion perception in the catfish retinal-like network. It is shown that this asymmetrical neural network is sensitive to the directional moving stimulus. The conditions of the directional movement are shown by the equations of Wiener kernels in the asymmetrical neural network. It is also shown that a symmetrical neural network cannot determine the equations for the moving stimulus. >

The prominent feature is the nonlinear characteristics as the squaring and rectification functions, which are observed in the retinal and visual cortex networks. Conventional model for motion processing in cortex, uses a symmetric quadratic functions with Gabor filters. This paper proposes a new motion processing model in the asymmetric networks. First, the asymmetric network is analyzed using Wiener kernels. It is shown that the asymmetric network with nonlinearities is effective and general for generating the directional movement compared with the conventional quadratic model. Second, independence maximization of data is an important issue in computational neural networks. To make clear the characteristics of the asymmetric network with Gabor functions, orthogonality is computed, which shows independent characteristics of the asymmetric network without maximizing optimization of independence in the quadratic model. The orthogonal analyses for the independence of the asymmetric networks are applied to the V1 and MT neural networks to generate independent subspaces by using selective Gabor functions.

To make clear the mechanism of the visual movement is important in he visual system. The prominent feature is the nonlinear characteristics as the squaring and rectification functions, which are observed in the retinal and visual cortex networks. Many popular models for motion processing in cortex, is the use of symmetric quadrature functions with Gabor filters. This paper proposes a new motion sensing processing model in the asymmetric networks. To make clear the behavior of the asymmetric nonlinear network, white noise analysis and Wiener kernels are applied. It is shown that the biological asymmetric network with nonlinearities is effective and superior for generating the directional movement from the network computations. The directive equations for the stimulus were derived by applying the white noise analysis and kernels to characterize stimulus changes. The results are applicable to the V1 and MT model of the neural networks in the cortex.

We show that for asymmetric neural networks the symmetric degree η of the synaptic coupling can be related to the two main network parameters, the storage capacity α and another designing parameter κ by the formula η = ακ2. Such a relation has been well verified by the simulations of our neural network designing. The formula suggests that we cannot improve the network performances by tuning the parameters α and κ simultaneously. The result may provide useful information for optimizing the designing of asymmetric neural networks.

The efficient and high throughput multicast communication in interconnection networks is known as a fundamental but hard problem. In the literature, most of the related works handle multicast communication within limited operating conditions and low throughput. Recently, a new multicast scheme, known as qualified groups QG, was proposed in [2] and has shown promising performance characteristics. However, this scheme has been examined only, so far, under deterministic routing and symmetric networks. In order to examine the QG in more realistic and different scenarios, this paper makes two major contributions. Firstly, the QG is generalised here to handling multicast communication in symmetric, asymmetric and different network sizes. Secondly, unlike most existing multicast algorithms the present study proposes a new adaptive multicast algorithm that maintains good performance levels for various system sizes. Our experiments show that the QG exhibits significant improvement in both throughput and multicast latency.

Using a generalized version of the signal-to-noise analysis, we study local instabilities of trajectories for the parallel dynamics of an extremely diluted, symmetric, Hopfield neural network. In order to reach a better understanding of the structure of the attractors of this model, a revision of the asymmetric version is performed in the case of zero and non-zero temperatures. New unexpected dynamical behaviours are found. Moreover, despite accepted beliefs, both analytical and numerical deviations between the dynamical properties of the two models (symmetric and asymmetric) can be exhibited. We show that, in some range of parameters, the diluted symmetric network exhibits strong dynamical oscillations of the neuronal activity, similar to those observed in synchronized networks. Furthermore, a deeper knowledge of the structure near attractors is achieved from this stability/instability analysis thanks to explicit analytical formulae for a two-step parallel dynamics for a symmetric network.

To make clear the mechanism of the visual movement is important in the visual system. The problem is how to perceive vectors of the optic flow in the network. First, the biological asymmetric network with nonlinear ties is analyzed for generating the vector from the point of the network computations. The results are applicable to the V1 and MT model of the neural networks in the cortex. The stimulus with a mixture distribution is applied to evaluate their network processing ability for the movement direction and its velocity, which generate the vector. Second, it is shown that the vector is emphasized in the MT than the V1. The characterized equation is derived in the network computations, which evaluates the vector properties of processing ability of the network. The movement velocity is derived, which is represented in Wiener kernels. The operations of vectors are shown in the divisive normalization network, which will create curl or divergence vectors in the higher neural network as MST area.

Memristor-coupled asymmetric neural networks: Bionic modeling, chaotic dynamics analysis and encryption application

This paper presents new necessary and sufficient conditions for absolute stability of asymmetric neural networks. The main result is based on a solvable Lie algebra condition, which generalizes existing results for symmetric and normal neural networks. An exponential convergence estimate of the neural networks is also obtained. Further, it is demonstrated how to generate larger sets of weight matrices for absolute stability of the neural networks from known normal weight matrices through simple procedures. The approach is nontrivial in the sense that non-normal matrices can possibly be contained in the resulting weight matrix set. And the results also provide finite checking for robust stability of neural networks in the presence of parameter uncertainties.

This paper deals not only with pointwise and uniform convergence but also Y-valued fractional approximation results by univariate symmetrized neural network (SNN) operators on Banach space Y,.. Moreover, our main motivation in this work is to compare the convergence results obtained by classical neural network (NN) operators and symmetric neural network (SNN) operators and try to convert them into numerical examples and graphs through computer programming language Python codes. As a result of this experimental study conducted under the regime of certain parameters, the convergence speed and results of SNN operators are superior to those of classical NN operators.

The classical interchange (permutation) of atoms of similar identity does not have an effect on the overall potential energy. In this study, we present feed-forward neural network structures that provide permutation symmetry to the potential energy surfaces of molecules. The new feed-forward neural network structures are employed to fit the potential energy surfaces for two illustrative molecules, which are H(2)O and ClOOCl. Modifications are made to describe the symmetric interchange (permutation) of atoms of similar identity (or mathematically, the permutation of symmetric input parameters). The combined-function-derivative approximation algorithm (J. Chem. Phys. 2009, 130, 134101) is also implemented to fit the neural-network potential energy surfaces accurately. The combination of our symmetric neural networks and the function-derivative fitting effectively produces PES fits using fewer numbers of training data points. For H(2)O, only 282 configurations are employed as the training set; the testing root-mean-squared and mean-absolute energy errors are respectively reported as 0.0103 eV (0.236 kcal/mol) and 0.0078 eV (0.179 kcal/mol). In the ClOOCl case, 1693 configurations are required to construct the training set; the root-mean-squared and mean-absolute energy errors for the ClOOCl testing set are 0.0409 eV (0.943 kcal/mol) and 0.0269 eV (0.620 kcal/mol), respectively. Overall, we find good agreements between ab initio and NN prediction in term of energy and gradient errors, and conclude that the new feed-forward neural-network models advantageously describe the molecules with excellent accuracy.

Digital image halftoning is treated as an optimization problem to which neural networks provide an efficient parallel solution. An image distortion measure is introduced in which the gray-tone image is approximated by a filtered version of the halftoned image. This distortion measure is minimized by using a near-neighborhood-connected symmetric neural network. The filter used in the distortion measure is estimated on the basis of a training set of gray-tone and bilevel images. This filter is then used for the reconstruction of a gray-tone image from its halftoned version. The above procedure, combined with a postprocessing of the reconstructed image by a nonlinear edge-preserving noise-smoothing filter, provides images of good quality. >

Gene Networks with Transcriptional Bursting Recapitulate Rare Transient Coordinated High Expression States in Cancer.