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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 + ------------------ =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online