1. First write out the jacobians as matrices with lots of (unknown) partial derivatives.
2. Work out what each of those partial derivatives is. (The partial derivates are just standard calc 1
derivatives).
1. First write out the jacobians as matrices with lots of (unknown) partial derivatives.
2. Work out what each of those partial derivatives is. (The partial derivates are just standard calc 1
derivatives).
1 Multi-layer Perceptrons Next week you will create, train, and test a fully connected neural
network (a.k.a. MLP). Your MLP will have 64 neurons in its hidden layer and 10 neurons in its
output layer. Each neuron should have a bias variable. The hidden layers will use a sigmoid
activation function. The output layer will apply a soft-max function across the 10 neurons. See
Figure 1. Figure 1: Network Architecture 1.1 Derive the Jacobians The Jacobian of a multivariate,
vector-valued function f:RnRm, is a matrix J=x1f1x1fmxnf1xnfm.With some slight abuse of
notation, let's call this Jacobian xf. Derive the following Jacobian matrices and indicate the
dimensions of each. Hint: Vectorize the matrices W1 and W2. 1. b2a2 2. W2a2 3. f1a2 4. a1f1 5. b
1a1 6. W1a1 As an example, the Jacobian a2L is a 110 matrix with elements a2L=[y^1y1,y^2y2,y^
10y10].
1 First write out the jacobians as matrices with lots of u.pdf
1. 1. First write out the jacobians as matrices with lots of (unknown) partial derivatives.
2. Work out what each of those partial derivatives is. (The partial derivates are just standard calc 1
derivatives).
1. First write out the jacobians as matrices with lots of (unknown) partial derivatives.
2. Work out what each of those partial derivatives is. (The partial derivates are just standard calc 1
derivatives).
1 Multi-layer Perceptrons Next week you will create, train, and test a fully connected neural
network (a.k.a. MLP). Your MLP will have 64 neurons in its hidden layer and 10 neurons in its
output layer. Each neuron should have a bias variable. The hidden layers will use a sigmoid
activation function. The output layer will apply a soft-max function across the 10 neurons. See
Figure 1. Figure 1: Network Architecture 1.1 Derive the Jacobians The Jacobian of a multivariate,
vector-valued function f:RnRm, is a matrix J=x1f1x1fmxnf1xnfm.With some slight abuse of
notation, let's call this Jacobian xf. Derive the following Jacobian matrices and indicate the
dimensions of each. Hint: Vectorize the matrices W1 and W2. 1. b2a2 2. W2a2 3. f1a2 4. a1f1 5. b
1a1 6. W1a1 As an example, the Jacobian a2L is a 110 matrix with elements a2L=[y^1y1,y^2y2,y^
10y10]
![1. First write out the jacobians as matrices with lots of (unknown) partial derivatives.
2. Work out what each of those partial derivatives is. (The partial derivates are just standard calc 1
derivatives).
1. First write out the jacobians as matrices with lots of (unknown) partial derivatives.
2. Work out what each of those partial derivatives is. (The partial derivates are just standard calc 1
derivatives).
1 Multi-layer Perceptrons Next week you will create, train, and test a fully connected neural
network (a.k.a. MLP). Your MLP will have 64 neurons in its hidden layer and 10 neurons in its
output layer. Each neuron should have a bias variable. The hidden layers will use a sigmoid
activation function. The output layer will apply a soft-max function across the 10 neurons. See
Figure 1. Figure 1: Network Architecture 1.1 Derive the Jacobians The Jacobian of a multivariate,
vector-valued function f:RnRm, is a matrix J=x1f1x1fmxnf1xnfm.With some slight abuse of
notation, let's call this Jacobian xf. Derive the following Jacobian matrices and indicate the
dimensions of each. Hint: Vectorize the matrices W1 and W2. 1. b2a2 2. W2a2 3. f1a2 4. a1f1 5. b
1a1 6. W1a1 As an example, the Jacobian a2L is a 110 matrix with elements a2L=[y^1y1,y^2y2,y^
10y10]](https://image.slidesharecdn.com/1firstwriteoutthejacobiansasmatriceswithlotsofu-230320103317-0f23eca9/85/1-First-write-out-the-jacobians-as-matrices-with-lots-of-u-pdf-1-320.jpg)
