R.P. Lippmann, An introduction to computing with neural nets. IEEE Magazine on Acoustics, Signal and Speech Processing 4 (1987) 4--22  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... in the hidden layer is substituted by the classical sigmoid function, and the situation of separation in the output is considered, or (b) c = 2380 and the threshold activation function is substituted by the semilinear activation function commonly used in the neural net literature (e.g. see [6, 10, 13, 21]) As in [4] the above reductions use example sets where some of the examples occur more than once. In Section 3.3, we discuss how these multiplicities can be avoided. In Section 3.4, we consider the situation where the number of examples is restricted with respect to the number of hidden neurons, ....

....factors concerning the L reduction are the same as in Theorem 9, we obtain the same approximation bound. 2 3.2. 2 The (n; 2; 1) flin; Hg net In this section, we consider the approximability of the loading problem with the semilinear activation function commonly used in the neural net literature [6, 10, 13, 21]. This activation function is defined as: lin(x) 0 if x 0 x if 0 x 1 It is continuous and captures the linearity of the sigmoidal activation at the origin as well as the asymptotic behavior of the sigmoid for large values. The following result is of interest since it is not necessary ....

R. Lippmann, An introduction to computing with neural nets, IEEE Acoustics, Speech, and Signal Processing Magazine, pp. 4-22, 1987.

....represents the learned weight of a synapse. This learned weight will suffer a deviation from synapse to synapse, due to the mismatch in the transistors that constitute multipliers M3 and resistors fl. The deviation of the final learned weight depends on the duty cycle of the signal used. Fig. 11 shows the result of several Monte Carlo Hspice simulations of the learning circuit for different duty cycles. The deviation in the steady state weight voltage (w(mV) I I [ igmatVeigh 0 120.00 Fig. 11. Weight deviations (ou. as a function of nominal weight for the learning circuit of Fig. 7. ....

....The deviation of the final learned weight depends on the duty cycle of the signal used. Fig. 11 shows the result of several Monte Carlo Hspice simulations of the learning circuit for different duty cycles. The deviation in the steady state weight voltage (w(mV) I I [ igmatVeigh 0 120.00 Fig. 11. Weight deviations (ou. as a function of nominal weight for the learning circuit of Fig. 7. obtained from Monte Carlo Hspice simulations. is represented as a function of the mean weight voltage for each Monte Carlo simulation. In order to estimate the weights deviation crw from the nominal ....

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R.P. Lippmann, "An introduction to computing with neural nets," ILEE ASSP Mag.. Apr. 1987.

....the processing nodes. The most popular learning algorithm for MLPs is the error backpropagation (EBP) algorithm [7] MLPs have been widely studied and applied to solve cloud detection problems (see e.g. 5] It is well known that MLPs are able to construct arbitrary decision boundaries [8], and therefore are applicable to cloud detection. In the context of cloud detection, the number of inputs to the networks is determined by the number of features in a pixel. Similarly, the number of outputs is equal to the number of classes. The number of hidden nodes is a fi ee parameter and its ....

.... the normalized outputs of the RBF networks (2) or the scaled outputs of the MLPs (3) Note that this rule makes use of the notion that the network s outputs are the estimate of the a posteriori probabilities, i.e. y( p(Cl) where P( denotes a priori probability and C denotes the kth class [8]. Here, the decision criterion can be written as: then a 6 cloudy class If Zl z2 then a 6 clear class (5) where 6 [ 1, 1] is a decision threshold. A decision is made for each input vector, and the error rate is the proportion of incorrect labeling decisions to the total number of ....

R. P. Lippmann. An introduction to computing with neural nets. IEEE ASSP Magazine, 4:4-22, 1987.

....types of neural network called multilayer feedforward networks. These are static networks where the network outputs depend only on the current inputs, not on any past inputs or outputs. While feedforward networks have found applications in pattern classification and functional interpolations [31,32,48], they are subjected to a constraint that temporal information cannot be stored naturally (unless encoded explicitly, e.g. through the use of tapped delay inputs [74,78] To circumvent the above drawback, recurrent neural networks (RNNs) have been introduced by a number of researchers, e.g. ....

R. P. Lippmann. An introduction to computing with neural nets. IEEE Acoustics, Speech, and Signal Processing Magazine, pages 4--22, 1987.

....be made adaptive in compressing various image contents such as those described in the last section. 2.3. Vector quantization neural networks Since neural networks are capable of learning from input information and optimizing itself to obtain the appropriate environment for a wide range of tasks [38], a family of learning algorithms has been developed for vector quantization. For all the learning algorithms, the basic structure is similar which can be illustrated in Fig. 5. The input vector is constructed from a K dimensional space. M neurones are designed in Fig. 5 to compute the vector ....

R.P. Lippmann, An introduction to computing with neural nets, IEEE ASSP Mag. (April 1987) 4}21.

.... in the hidden layer is substituted by the classical sigmoid function, and the situation of separation in the output is considered, or (b) c = 2380 and the threshold activation function is substituted by the semilinear activation function commonly used in the neural net literature (e.g. see [6,11,14,22]) As in [4] the above reductions use example sets where some of the examples occur more than once. In Section 3.3, we discuss how these multiplicities can be avoided. In Section 3.4, we consider the situation where the number of examples is restricted with respect to the number of hidden neurons, ....

....concerning the L reduction are the same as in Theorem 9, we obtain the same approximation bound. 2 3.2. 2 The (n; 2; 1) flin; Hg net In this section, we consider the approximability of the loading problem with the semilinear activation function which is commonly used in the neural net literature [6,11,14,22]. This activation function is defined as: lin(x) 0 if x 0 x if 0 x 1 It is continuous and captures the linearity of the sigmoidal activation at the origin as well as the asymptotic behavior of the sigmoid for large values. The following result is of ....

R. Lippmann, An introduction to computing with neural nets, IEEE Acoustics, Speech, and Signal Processing Magazine 4(2) (1987) 4--22.

....training methods, learn parameters, or network structure, comparably few work has been done towards using activation functions other than the logistic function. It has been shown that a two hidden layer MLP with sigmoidal activation function can implement arbitrary convex decision boundaries [1]. Moreover, such an MLP is capable of forming an arbitrarily close approximation to any continous nonlinear mapping [2] However, common to these theorems is that the number of neurons in the layers is at best bounded, but can be extremely large for practical purposes. e.g. for a one hidden layer ....

Lippmann, R.P.: An introduction to computing with neural nets. IEEE Acoustics, Speech and Signal Processing 4 (1987) 4-22

....connected. From engineering viewpoint, time varying behaviors are probably of greater importance among the nonlinear dynamic behaviors that recurrent neural networks manifest. Many authors have studied recurrent neural network models of various types of perceptual processes and applications [1], 2] 31, 41, 5] 61, 71. One of the dynamic behaviors concerned by many works [8] 9] 10] 11] 12] is that the existence and the location of equilibrium points, and with the qualitative properties of the equilibria. The stability analysis and applications of a class of single ....

....= x R xict i 1,i = 1, n for Ct= Ct,Ct2, Ct, r P In an N neurons Winner Take All case, C = r2, rn , where 1, Vj : k, k = 1, n, is the desired Otr =loj = output. If we define the T matrix in system (2) as 1, i=j 0 l n, l i,j n, T = ii system (2) becomes MAXNET [1]. We will mainly analysis the performance of MAXNET with saturation function. o Figure 2. A geometric interpretation of stable equilibrium From (4) we have 0, and (5) 0. It s a contradiction. Note that MAXNET with other type ofpiecewise nonlinear function may achieve the desired output O ....

. Richard P. Lippmann, "An Introduction to Computing with Neural Nets", IEEE ASSP Magazine, IEEE Acoustics, Speech, and Signal Processing Society, Vol. 4, No. 2, pp. 4-22, April 1987.

....training methods, learn parameters, or network structure, comparably few work has been done towards using activation functions other than the logistic function. It has been shown that a two hidden layer MLP with sigmoidal activation function can implement arbitrary convex decision boundaries [6]. Moreover, such an MLP is capable of forming an arbitrarily close approximation to any continous nonlinear mapping [4] However, common to these theorems is that the number of neurons in the layers is at best bounded, but can be extremely large for practical purposes. e.g. for a one ....

R. P. Lippmann. An introduction to computing with neural nets. IEEE Acoustics, Speech and Signal Processing, 4(2):4-22, March 1987.

....5472; E mail pizzi(u ibd.nrc.ca 0933 3657, t,5, 9 50 1995 Elsevier Science B.V. All rights reserved SSDI 0933 3657(94)00027 1 68 N. Pizzi t t al. Artificial Itltelligence itl Medicine 7 (1995) 07 79 1. Introduction 1.1. Artificial neural networks An artificial neural network (ANN) [2,6,9] is a self adaptive massively parallel machine learning system composed of layers of processing elements (PEs) used primarily for pattern recognition problems. APE is a construct composed of a set of inputs and corresponding weights (input connection strengths) that are combined to produce a ....

R.P. Lippmann, An introduction to computing with neural nets, IEEE ,4SSP Mag. 4 (1987) 4-22.

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R.P. Lippmann, An introduction to computing with neural nets. IEEE Magazine on Acoustics, Signal and Speech Processing 4 (1987) 4--22

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R. P. Lippmann, "An introduction to computing with neural nets," IEEE ASSP Mag., pp. 4--22, Apr. 1987.

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R. P. Lippmann, "An introduction to computing with neural nets," IEEE Acoust., Speech, Signal Processing Mag., vol. 4, pp. 4--22, Apr. 1987.

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Lippmann, R..P., 'An introduction to computing with Neural nets', IEEE ASSP Magagine, April

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R. P. Lippmann, An Introduction to Computing with Neural Nets, IEEE ASSP Mag. 4 (1987), 4-22.

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R. P. Lippmann, "An introduction to computing with neural nets," IEEE ASSP Magazine, pp. 4--22, Apr. 1987.

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R. Lippmann. An introduction to computing with neural nets. IEEE ASSP Magazine, 4(22), 1987.

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Lippmann, R. P. An introduction to computing with neural nets. IEEE ASSP Magazine, Vol. 3, No. 4, pp. 4-22, 1987.

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R. Lippmann. An introduction to computing with neural nets. IEEE ASSP Magazine, 4(22), 1987.

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R. P. Lippmann, "An Introduction to Computing with Neural Nets", IEEE Acoustics, Speech, and Signal Processing Magazine, April 1987, pp. 4-22.

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R.P. Lippmann,"An introduction to computing with neural nets", IEEE Acoustic, Speech and Signal Processing Magazine, pp. 4-22, April 1987.

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R.L. Lippmann. An introduction to computing with neural nets. IEEE ASSP Magazine, 4:4--22, 1987.

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R.P. Lippmann, An introduction to computing with neural nets, IEEE ASSP Mag. (April 1987) 4--22.

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R.P. Lippmann, "An introduction to computing with neural nets," IEEE ASSP Magazine, vol. 4, no. 87, pp 4-23, 1987.

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Lippmann R. P.: An Introduction to Computing with Neural Nets, IEEE ASSP Magazine, Vol. 4, 1987, pp. 4-22.

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