Chapter_17

# Chapter_17 - CHAPTER 17 17.1 (a) The complementary error...

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334 CHAPTER 17 17.1 (a) The complementary error function qualifies as a sigmoid function for two reasons: 1. The function is a monotonically increasing function of x , with For equals the total area under the probability density function of a Gaussian variable with zero mean and unit variable; this area is unity by definition. 2. The function ϕ ( x ) is continuously differentiable: (b) The inverse tangent function also qualifies as a sigmoid function for two reasons: 1. 2. ϕ ( x ) is continuously differentiable: The complementary error function and the inverse tangent function differ from each other in the following respects: ϕ x () 1 2 π ---------- e t 2 t d x = ϕ∞ 0 = ϕ 0 0.5 = 1 = x ∞ϕ , = d ϕ dx ------ 1 2 π e x 2 2 = ϕ x 2 π -- x 1 tan = 1 = ϕ 0 0 = +1 = d ϕ 2 π 1 1 x 2 + ------------------ =

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335 The complementary error function is unipolar (nonsymmetric). The inverse tangent function is bipolar (antisymmetric). 17.2 The incorporation of a momentum modifies the update rule for sympatic weight w kj as follows: (1) where α = momentum constant η = learning-rate parameter ε ( n ) = cost function to be minimized n = iteration number Equation (1) represents a first-order difference equation in . Solving it for
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## Chapter_17 - CHAPTER 17 17.1 (a) The complementary error...

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