- What Is A Multilayer Network A Network With More Than One Layer Is Called A Multilayer Network Input First Layer Secon 1 (206.61 KiB) Viewed 42 times
- What Is A Multilayer Network A Network With More Than One Layer Is Called A Multilayer Network Input First Layer Secon 2 (129.52 KiB) Viewed 42 times
- What Is A Multilayer Network A Network With More Than One Layer Is Called A Multilayer Network Input First Layer Secon 3 (57.65 KiB) Viewed 42 times
Thank you!
What is a Multilayer Network? A network with more than one layer is called a multilayer network. Input First Layer Second Layer Third Layer a 22 P RX1 W W slx11 n' W 52x1 f2 50 x 50x1 n n S'XR $2x f + # + * S2 x 1 f3 50x1f b b- b R stx 1 SI $2x1 S2 59x1 S3 al=f(Wp+b) a = f(W2a'+b) a=f(Wa2+b) a = f( Wf(W2f(Wip+b)+b) + b) In a multilayer network, the first layer has R inputs and S1 neurons. Therefore, w1 is a (S1 x R), because we have R inputs for each neuron. The bias b1 is a (51 x 1) vector, because we have 1 bias per neuron. n- and al are also (51 x 1) vectors, because we have 1 output for each neuron. The second layer has 51 inputs and S2 neurons. Therefore, W2 is a (S? x 54), because we have S1 inputs for each neuron. The bias b2 is a (S2 x 1) vector, because we have 1 bias per neuron. n2 and a2 are also (52 x 1) vectors, because we have 1 output for each neuron. The third layer has X inputs and X neurons. Therefore, W3 is a (X), because we have X inputs for each neuron. The bias b3 is a (x) vector, because we have 1 bias per neuron. n3 and a3 are also (x) vectors, because we have 1 output for each neuron. In this lab, we will implement a two layer network, depicted in the figure below. We will start by implementing each layer separately then visualizing the network output when we change the values of W and b. Input Log-Sigmoid Layer Linear Layer ni w1.1 a ΣΗ . W211 712 a2 р ΣΗ al b2 "파 12 n12 W12. Σ b12 1.2 al = logsig(W1p+b) a2 = purelin (W241+52) Q1. Implement the first layer and name it "logsiglayer". The function takes the following parameters: W1, p and b?. W is the weight matrix, p is the input and b is the bias. The layer computes the output, given the input, using the following formula. [2 marks] a1 = logsig(wp+b) Q2. Implement the second layer and name it "linearlaver". The function takes the following parameters: W?, ał and b2. W is the weight matrix, a is the input and b is the bias. The layer computes the output, given the input, using the following formula. [1 marks)
a? = purelin(W2 a++b) Q3. Let the network has the following values. wi,1 = 10, w21 = 10, b) = -10, b) = 10, win = 1, wi2 = 1, b2 = 0. Plot the output of the network. To do so, follow the steps below: 1. Set the weight and bias values as given above 2. Let p (the input) be between -2 and 2. 3. Pass the input p to layer 1, to get a1 (the output of the first layer). 4. Pass a1 to layer 2, to get a2 (the output of the second layer). 5. Plot p vs a2. [2 marks] 2. To do so, follow the steps below: 1. Use the weight and bias values as given previously 2. For each value of p, compute by hand the following: a. a1 = logsig(W1p+b+) b. a? = purelin(W2 a++b) 3. Report the values you got by hand and from your python code in the table below. [2 marks] ||||0|1| р a2 (from code) a2 (by hand) -2 0 ? -1 0.5 ? 1 ? 1.5 ? 2 ? Q4. Test the effect of changing b, and plot the results. To do so, follow the steps below: 1. Set the weight and bias values as given previously 2. Let bį be between 0 s bis 20 3. For each value of b1, repeat: a. Let p (the input) be between -2 and 2. b. Pass the input p to layer 1, to get a1 (the output of the first layer). C. Pass a1 to layer 2, to get a 2 (the output of the second layer). d. Plot p vs a 2. 4. What changes does bị have on the network output? [2 marks] Q5. Repeat the same for bż. What changes does bị have on the network output? [2 marks]
Q6. Test the effect of changing W1,1, and plot the results. To do so, follow the steps below: 1. Set the weight and bias values as given previously 2. Let W1,1 be between -1 < W1,1 S1 3. For each value of W1.1, repeat: a. Let p (the input) be between -2 and 2. b. Pass the input p to layer 1, to get a1 (the output of the first layer). C. Pass a1 to layer 2, to get a 2 (the output of the second layer). d. Plot p vs a2. 4. What changes does W1,1 have on the network output? [2 marks] Q7. Repeat the same for Wị,1. What changes does Wị,1 have on the network output? [2 marks]