I'm trying to Implement a Recurrent Neural Network using Numpy in python. I'm trying to implement a Many-to-One RNN, for a classification problem. I'm a little fuzzy on the psuedo code, especially on the BPTT concept. I'm comfortable with the forward pass ( not entirely sure if my implementation is correct ) but really confused with back ward pass, and I need some advice from experts in this field.
I did check out related posts :
1) Implementing RNN in numpy
2) Output for RNN
3) How can I build RNN
But I feel my issue is with understanding the psuedo code / concept first up, code in those posts is complete and have reached further stage than mine.
My Implementation is inspired from the tutorial:
WildML RNN from scratch
I did implement a Feed-Forward Neural Network following part of tutorial from the same author, but I'm really confused with this implementation of his. Andrew Ng's RNN video suggests 3 different weights ( Weights for activation, Input and Output layers ) but the above tutorial only has two sets of weights ( correct me if I'm wrong ).
The nomenclature in my code follows that of Andrew Ng's RNN pseudo code ...
I'm reshaping my input samples in to 3D ( batch_size, n_time steps, n_ dimensions ) ... Once , I reshape my samples I'm doing forward pass on each sample seperately ...
Here's my code:
def RNNCell(X, lr, y=None, n_timesteps=None, n_dimensions=None, return_sequence = None, bias = None):
'''Simple function to compute forward and bakward passes for a Many-to-One Recurrent Neural Network Model.
This function Reshapes X,Y in to 3D array of shape (batch_size, n_timesteps, n_ dimensions) and then performs
recurrent operations on each sample of the data for n_timesteps'''
# If user has specified some target variable
if len(y) != 0:
# No. of unique values in the target variables will be the dimesions for the output layer
_,n_unique = np.unique(y, return_counts=True)
else:
# If there's no target variable given, then dimensions of target variable by default is 2
n_unique = 2
# Weights of Vectors to multiply with input samples
Wx = np.random.uniform(low = 0.0,
high = 0.3,
size = (n_dimensions, n_dimensions))
# Weights of Vectors to multiply with resulting activations
Wy = np.random.uniform(low = 0.0,
high = 0.3,
size = (n_dimensions, n_timesteps))
# Weights of Vectors to multiple with activations of previous time steps
Wa = np.random.randn(n_dimensions, n_dimensions)
# List to hold activations of each time step
activations = {'a-0' : np.zeros(shape=(n_timesteps-1, n_dimensions),
dtype=float)}
# List to hold Yhat at each time step
Yhat = []
try:
# Reshape X to align with the shape of RNN architecture
X = np.reshape(X, newshape=(len(X), n_timesteps, n_dimensions))
except:
return "Sorry can't reshape and array in to your shape"
def Forward_Prop(sample):
# Outputs at the last time step
Ot = 0
# In each time step
for time_step in range(n_timesteps+1):
if time_step < n_timesteps:
# activation G ( Wa.a<t> + X<t>.Wx )
activations['a-' + str(time_step+1)] = ReLu( np.dot( activations['a-' + str(time_step)], Wa )
+ np.dot( sample[time_step, :].reshape(1, n_dimensions) , Wx ) )
# IF it's the last time step then use softmax activation function
elif time_step == n_timesteps:
# Wy.a<t> and appending that to Yhat list
Ot = softmax( np.dot( activations['a-' + str(time_step)], Wy ) )
# Return output probabilities
return Ot
def Backward_Prop(Yhat):
# List to hold errors for the last layer
error = []
for ind in range(len(Yhat)):
error.append( y[ind] - Yhat[ind] )
error = np.array(error)
# Calculating Delta for the output layer
delta_out = error * lr
#* relu_derivative(activations['a-' + str(n_timesteps)])
# Calculating gradient for the output layer
grad_out = np.dot(delta_out.reshape(len(X), n_timesteps),
activations['a-' + str(n_timesteps)])
# I'm basically stuck at this point
# Adjusting weights for the output layer
Wy = Wy - (lr * grad_out.reshape((n_dimesions, n_timesteps)))
for sample in X:
Yhat.append( Forward_Prop(sample) )
Backward_Prop(Yhat)
return Yhat
# DUMMY INPUT DATA
X = np.random.random_integers(low=0, high = 5, size = (10, 10 ));
# DUMMY LABELS
y = np.array([[0],
[1],
[1],
[1],
[0],
[0],
[1],
[1],
[0],
[1]])
I understand that my BPTT implementation is wrong, but I'm not thinking clearly and I need some experts' perspective on where exactly I'm missing the trick. I don't expect a detailed debugging of my code, I only require a high level overview of the pseudo code on back propagation ( assuming my forward prop is correct ). I think my fundamental problem can also be with the way I'm doing my forward pass on each sample individually.
I'm stuck on this problem since 3 days now, and it's really frustrating not being able to think clearly. I'd be really grateful if someone could point me in the right direction and clear my confusion. Thank you for your time in advance !! I really appreciate it once again !
Related
I am creating a basic, and also my first neural network on handwritten digit recognition without any framework (like Tensorflow, PyTorch...) using the Backpropagation algorithm.
My NN has 784 inputs and 10 outputs. So for the last layer, I have to use Softmax.
Because of some memory errors, I have right now my images in shape (300, 784) and my labels in shape (300, 10)
After that I am calculating loss from Categorical Cross-entropy.
Now we are getting to my problem. In Backpropagation, I need manually compute the first derivative of an activation function. I am doing it like this:
dAl = -(np.divide(Y, Al) - np.divide(1 - Y, 1 - Al))
#Y = test labels
#Al - Activation value from my last layer
And after that my Backpropagation can start, so the last layer is softmax.
def SoftmaxDerivative(dA, Z):
#Z is an output from np.dot(A_prev, W) + b
#Where A_prev is an activation value from previous layer
#W is weight and b is bias
#dA is the derivative of an activation function value
x = activation_functions.softmax(dA)
s = x.reshape(-1,1)
dZ = np.diagflat(s) - np.dot(s, s.T)
return dZ
1. Is this function working properly?
In the end, I would like to compute derivatives of weights and biases, So I am using this:
dW = (1/m)*np.dot(dZ, A_prev.T)
#m is A_prev.shape[1] -> 10
db = (1/m)*np.sum(dZ, axis = 1, keepdims = True)
BUT it fails on dW, because dZ.shape is (3000, 3000) (compare to A_prev.shape, which is (300,10))
So from this I assume, that there are only 3 possible outcomes.
My Softmax backward is wrong
dW is wrong
I have some other bug completely somewhere else
Any help would be really appreciated!
I faced the same problem recently. I'm not sure but maybe this question will help you: Softmax derivative in NumPy approaches 0 (implementation)
I need to apply ZCA whitening in PyTorch. I think I have found a way this can be done by using transforms.LinearTransformation and I have found a test in the PyTorch repo which gives some insight into how this is done (see final code block or link below)
https://github.com/pytorch/vision/blob/master/test/test_transforms.py
I am struggling to work out how I apply something like this myself.
Currently I have transforms along the lines of:
transform_test = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize(np.array([125.3, 123.0, 113.9]) / 255.0,
np.array([63.0, 62.1, 66.7]) / 255.0),
])
The documents say they way to use LinearTransformation is as follows:
torchvision.transforms.LinearTransformation(transformation_matrix, mean_vector)
whitening transformation: Suppose X is a column vector zero-centered
data. Then compute the data covariance matrix [D x D] with
torch.mm(X.t(), X), perform SVD on this matrix and pass it as
transformation_matrix.
I can see from the tests I linked above and copied below that they are using torch.mm to calculate what they call a principal_components:
def test_linear_transformation(self):
num_samples = 1000
x = torch.randn(num_samples, 3, 10, 10)
flat_x = x.view(x.size(0), x.size(1) * x.size(2) * x.size(3))
# compute principal components
sigma = torch.mm(flat_x.t(), flat_x) / flat_x.size(0)
u, s, _ = np.linalg.svd(sigma.numpy())
zca_epsilon = 1e-10 # avoid division by 0
d = torch.Tensor(np.diag(1. / np.sqrt(s + zca_epsilon)))
u = torch.Tensor(u)
principal_components = torch.mm(torch.mm(u, d), u.t())
mean_vector = (torch.sum(flat_x, dim=0) / flat_x.size(0))
# initialize whitening matrix
whitening = transforms.LinearTransformation(principal_components, mean_vector)
# estimate covariance and mean using weak law of large number
num_features = flat_x.size(1)
cov = 0.0
mean = 0.0
for i in x:
xwhite = whitening(i)
xwhite = xwhite.view(1, -1).numpy()
cov += np.dot(xwhite, xwhite.T) / num_features
mean += np.sum(xwhite) / num_features
# if rtol for std = 1e-3 then rtol for cov = 2e-3 as std**2 = cov
assert np.allclose(cov / num_samples, np.identity(1), rtol=2e-3), "cov not close to 1"
assert np.allclose(mean / num_samples, 0, rtol=1e-3), "mean not close to 0"
# Checking if LinearTransformation can be printed as string
whitening.__repr__()
How do I apply something like this? do I use it where I define my transforms or apply it in my training loop where I am iterating over my training loop?
Thanks in advance
ZCA whitening is typically a preprocessing step, like center-reduction, which basically aims at making your data more NN-friendly (additional info below). As such, it is supposed to be applied once, right before training.
So right before you starts training your model with a given dataset X, compute the whitened dataset Z, which is simply the multiplication of X with the ZCA matrix W_zca that you can learn to compute here. Then train your model on the whitened dataset.
Finally, you should have something that looks like this
class MyModule(torch.nn.Module):
def __init__(self):
super(MyModule,self).__init__()
# Feel free to use something more useful than a simple linear layer
self._network = torch.nn.Linear(...)
# Do your stuff
...
def fit(self, inputs, labels):
""" Trains the model to predict the right label for a given input """
# Compute the whitening matrix and inputs
self._zca_mat = compute_zca(inputs)
whitened_inputs = torch.mm(self._zca_mat, inputs)
# Apply training on the whitened data
outputs = self._network(whitened_inputs)
loss = torch.nn.MSEloss()(outputs, labels)
loss.backward()
optimizer.step()
def forward(self, input):
# You always need to apply the zca transform before forwarding,
# because your network has been trained with whitened data
whitened_input = torch.mm(self._zca_mat, input)
predicted_label = self._network.forward(whitened_input)
return predicted_label
Additional info
Whitening your data means decorrelating its dimensions so that the correlation matrix of the whitened data is the identity matrix. It is a rotation-scaling operation (thus linear), and there are actually an infinity of possible ZCA transforms. To understand the maths behind ZCA, read this
So, I'm using Michael Nielson's machine learning book as a reference for my code (it is basically identical): http://neuralnetworksanddeeplearning.com/chap1.html
The code in question:
def backpropagate(self, image, image_value) :
# declare two new numpy arrays for the updated weights & biases
new_biases = [np.zeros(bias.shape) for bias in self.biases]
new_weights = [np.zeros(weight_matrix.shape) for weight_matrix in self.weights]
# -------- feed forward --------
# store all the activations in a list
activations = [image]
# declare empty list that will contain all the z vectors
zs = []
for bias, weight in zip(self.biases, self.weights) :
print(bias.shape)
print(weight.shape)
print(image.shape)
z = np.dot(weight, image) + bias
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# -------- backward pass --------
# transpose() returns the numpy array with the rows as columns and columns as rows
delta = self.cost_derivative(activations[-1], image_value) * sigmoid_prime(zs[-1])
new_biases[-1] = delta
new_weights[-1] = np.dot(delta, activations[-2].transpose())
# l = 1 means the last layer of neurons, l = 2 is the second-last, etc.
# this takes advantage of Python's ability to use negative indices in lists
for l in range(2, self.num_layers) :
z = zs[-1]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
new_biases[-l] = delta
new_weights[-l] = np.dot(delta, activations[-l-1].transpose())
return (new_biases, new_weights)
My algorithm can only get to the first round backpropagation before this error occurs:
File "D:/Programming/Python/DPUDS/DPUDS_Projects/Fall_2017/MNIST/network.py", line 97, in stochastic_gradient_descent
self.update_mini_batch(mini_batch, learning_rate)
File "D:/Programming/Python/DPUDS/DPUDS_Projects/Fall_2017/MNIST/network.py", line 117, in update_mini_batch
delta_biases, delta_weights = self.backpropagate(image, image_value)
File "D:/Programming/Python/DPUDS/DPUDS_Projects/Fall_2017/MNIST/network.py", line 160, in backpropagate
z = np.dot(weight, activation) + bias
ValueError: shapes (30,50000) and (784,1) not aligned: 50000 (dim 1) != 784 (dim 0)
I get why it's an error. The number of columns in weights doesn't match the number of rows in the pixel image, so I can't do matrix multiplication. Here's where I'm confused -- there are 30 neurons used in the backpropagation, each with 50,000 images being evaluated. My understanding is that each of the 50,000 should have 784 weights attached, one for each pixel. But when I modify the code accordingly:
count = 0
for bias, weight in zip(self.biases, self.weights) :
print(bias.shape)
print(weight[count].shape)
print(image.shape)
z = np.dot(weight[count], image) + bias
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
count += 1
I still get a similar error:
ValueError: shapes (50000,) and (784,1) not aligned: 50000 (dim 0) != 784 (dim 0)
I'm just really confuzzled by all the linear algebra involved and I think I'm just missing something about the structure of the weight matrix. Any help at all would be greatly appreciated.
It looks like the issue is in your changes to the original code.
I’be downloaded example from the link you provided and it works without any errors:
Here is full source code I used:
import cPickle
import gzip
import numpy as np
import random
def load_data():
"""Return the MNIST data as a tuple containing the training data,
the validation data, and the test data.
The ``training_data`` is returned as a tuple with two entries.
The first entry contains the actual training images. This is a
numpy ndarray with 50,000 entries. Each entry is, in turn, a
numpy ndarray with 784 values, representing the 28 * 28 = 784
pixels in a single MNIST image.
The second entry in the ``training_data`` tuple is a numpy ndarray
containing 50,000 entries. Those entries are just the digit
values (0...9) for the corresponding images contained in the first
entry of the tuple.
The ``validation_data`` and ``test_data`` are similar, except
each contains only 10,000 images.
This is a nice data format, but for use in neural networks it's
helpful to modify the format of the ``training_data`` a little.
That's done in the wrapper function ``load_data_wrapper()``, see
below.
"""
f = gzip.open('../data/mnist.pkl.gz', 'rb')
training_data, validation_data, test_data = cPickle.load(f)
f.close()
return (training_data, validation_data, test_data)
def load_data_wrapper():
"""Return a tuple containing ``(training_data, validation_data,
test_data)``. Based on ``load_data``, but the format is more
convenient for use in our implementation of neural networks.
In particular, ``training_data`` is a list containing 50,000
2-tuples ``(x, y)``. ``x`` is a 784-dimensional numpy.ndarray
containing the input image. ``y`` is a 10-dimensional
numpy.ndarray representing the unit vector corresponding to the
correct digit for ``x``.
``validation_data`` and ``test_data`` are lists containing 10,000
2-tuples ``(x, y)``. In each case, ``x`` is a 784-dimensional
numpy.ndarry containing the input image, and ``y`` is the
corresponding classification, i.e., the digit values (integers)
corresponding to ``x``.
Obviously, this means we're using slightly different formats for
the training data and the validation / test data. These formats
turn out to be the most convenient for use in our neural network
code."""
tr_d, va_d, te_d = load_data()
training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]
training_results = [vectorized_result(y) for y in tr_d[1]]
training_data = zip(training_inputs, training_results)
validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]
validation_data = zip(validation_inputs, va_d[1])
test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]
test_data = zip(test_inputs, te_d[1])
return (training_data, validation_data, test_data)
def vectorized_result(j):
"""Return a 10-dimensional unit vector with a 1.0 in the jth
position and zeroes elsewhere. This is used to convert a digit
(0...9) into a corresponding desired output from the neural
network."""
e = np.zeros((10, 1))
e[j] = 1.0
return e
class Network(object):
def __init__(self, sizes):
"""The list ``sizes`` contains the number of neurons in the
respective layers of the network. For example, if the list
was [2, 3, 1] then it would be a three-layer network, with the
first layer containing 2 neurons, the second layer 3 neurons,
and the third layer 1 neuron. The biases and weights for the
network are initialized randomly, using a Gaussian
distribution with mean 0, and variance 1. Note that the first
layer is assumed to be an input layer, and by convention we
won't set any biases for those neurons, since biases are only
ever used in computing the outputs from later layers."""
self.num_layers = len(sizes)
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
self.weights = [np.random.randn(y, x)
for x, y in zip(sizes[:-1], sizes[1:])]
def feedforward(self, a):
"""Return the output of the network if ``a`` is input."""
for b, w in zip(self.biases, self.weights):
a = sigmoid(np.dot(w, a)+b)
return a
def SGD(self, training_data, epochs, mini_batch_size, eta,
test_data=None):
"""Train the neural network using mini-batch stochastic
gradient descent. The ``training_data`` is a list of tuples
``(x, y)`` representing the training inputs and the desired
outputs. The other non-optional parameters are
self-explanatory. If ``test_data`` is provided then the
network will be evaluated against the test data after each
epoch, and partial progress printed out. This is useful for
tracking progress, but slows things down substantially."""
if test_data: n_test = len(test_data)
n = len(training_data)
for j in xrange(epochs):
random.shuffle(training_data)
mini_batches = [
training_data[k:k+mini_batch_size]
for k in xrange(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, eta)
if test_data:
print "Epoch {0}: {1} / {2}".format(
j, self.evaluate(test_data), n_test)
else:
print "Epoch {0} complete".format(j)
def update_mini_batch(self, mini_batch, eta):
"""Update the network's weights and biases by applying
gradient descent using backpropagation to a single mini batch.
The ``mini_batch`` is a list of tuples ``(x, y)``, and ``eta``
is the learning rate."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]
def backprop(self, x, y):
"""Return a tuple ``(nabla_b, nabla_w)`` representing the
gradient for the cost function C_x. ``nabla_b`` and
``nabla_w`` are layer-by-layer lists of numpy arrays, similar
to ``self.biases`` and ``self.weights``."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# backward pass
delta = self.cost_derivative(activations[-1], y) * \
sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
# Note that the variable l in the loop below is used a little
# differently to the notation in Chapter 2 of the book. Here,
# l = 1 means the last layer of neurons, l = 2 is the
# second-last layer, and so on. It's a renumbering of the
# scheme in the book, used here to take advantage of the fact
# that Python can use negative indices in lists.
for l in xrange(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
def evaluate(self, test_data):
"""Return the number of test inputs for which the neural
network outputs the correct result. Note that the neural
network's output is assumed to be the index of whichever
neuron in the final layer has the highest activation."""
test_results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in test_data]
return sum(int(x == y) for (x, y) in test_results)
def cost_derivative(self, output_activations, y):
"""Return the vector of partial derivatives \partial C_x /
\partial a for the output activations."""
return (output_activations-y)
#### Miscellaneous functions
def sigmoid(z):
"""The sigmoid function."""
return 1.0/(1.0+np.exp(-z))
def sigmoid_prime(z):
"""Derivative of the sigmoid function."""
return sigmoid(z)*(1-sigmoid(z))
training_data, validation_data, test_data = load_data_wrapper()
net = Network([784, 30, 10])
net.SGD(training_data, 30, 10, 3.0, test_data=test_data)
Additional info:
However, I would recommend using one of existing frameworks, for example - Keras to don't reinvent the wheel
Also, it was checked with python 3.6:
Kudos on digging into Nielsen's code. It's a great resource to develop thorough understanding of NN principles. Too many people leap ahead to Keras without knowing what goes on under the hood.
Each training example doesn't get its own weights. Each of the 784 features does. If each example got its own weights then each weight set would overfit to its corresponding training example. Also, if you later used your trained network to run inference on a single test example, what would it do with 50,000 sets of weights when presented with just one handwritten digit? Instead, each of the 30 neurons in your hidden layer learns a set of 784 weights, one for each pixel, that offers high predictive accuracy when generalized to any handwritten digit.
Import network.py and instantiate a Network class like this without modifying any code:
net = network.Network([784, 30, 10])
..which gives you a network with 784 input neurons, 30 hidden neurons and 10 output neurons. Your weight matrices will have dimensions [30, 784] and [10, 30], respectively. When you feed the network an input array of dimensions [784, 1] the matrix multiplication that gave you an error is valid because dim 1 of the weight matrix equals dim 0 of the input array (both 784).
Your problem is not implementation of backprop but rather setting up a network architecture appropriate for the shape of your input data. If memory serves Nielsen leaves backprop as a black box in chapter 1 and doesn't dive into it until chapter 2. Keep at it, and good luck!
My question is at the bottom, but first I will explain what I am attempting to achieve.
I have an example I am trying to implement on my own model. I am creating an adversarial image, in essence I want to graph how the image score changes when the epsilon value changes.
So let's say my model has already been trained, and in this example I am using the following model...
x = tf.placeholder(tf.float32, shape=[None, 784])
...
...
# construct model
logits = tf.matmul(x, W) + b
pred = tf.nn.softmax(logits) # Softmax
Next, let us assume I extract an array of images of the number 2 from the mnist data set, and I saved it in the following variable...
# convert into a numpy array of shape [100, 784]
labels_of_2 = np.concatenate(labels_of_2, axis=0)
So now, in the example that I have, the next step is to try different epsilon values on every image...
# random epsilon values from -1.0 to 1.0
epsilon_res = 101
eps = np.linspace(-1.0, 1.0, epsilon_res).reshape((epsilon_res, 1))
labels = [str(i) for i in range(10)]
num_colors = 10
cmap = plt.get_cmap('hsv')
colors = [cmap(i) for i in np.linspace(0, 1, num_colors)]
# Create an empty array for our scores
scores = np.zeros((len(eps), 10))
for j in range(len(labels_of_2)):
# Pick the image for this iteration
x00 = labels_of_2[j].reshape((1, 784))
# Calculate the sign of the derivative,
# at the image and at the desired class
# label
sign = np.sign(im_derivative[j])
# Calculate the new scores for each
# adversarial image
for i in range(len(eps)):
x_fool = x00 + eps[i] * sign
scores[i, :] = logits.eval({x: x_fool,
keep_prob: 1.0})
Now we can graph the images using the following...
# Create a figure
plt.figure(figsize=(10, 8))
plt.title("Image {}".format(j))
# Loop through the score functions for each
# class label and plot them as a function of
# epsilon
for k in range(len(scores.T)):
plt.plot(eps, scores[:, k],
color=colors[k],
marker='.',
label=labels[k])
plt.legend(prop={'size':8})
plt.xlabel('Epsilon')
plt.ylabel('Class Score')
plt.grid('on')
For the first image the graph would look something like the following...
Now Here Is My Question
Let's say the model I trained used a batch_size of 100, in that case the following line would not work...
scores[i, :] = logits.eval({x: x_fool,
keep_prob: 1.0})
In order for this to work, I would need to pass an array of 100 images to the model, but in this instance x_fool is just one image of size (1, 784).
I want to graph the effect of different epsilon values on class scores for any one image, but how can I do so when I need calculate the score of 100 images at a time (since my model was trained on a batch_size of 100)?
You can choose to not choose a batch size by setting it to None. That way, any batch size can be used.
However, keep in mind that this non-choice could com with a moderate penalty.
This fixes it if you start again from scratch. If you start from an existing trained network with a batch size of 100, you can create a test network that is similar to your starting network except for the batch size. You can set the batch size to 1, or again, to None.
I realised the problem was not with the batch_size but with the format of the image I was attempting to pass to the model. As user1735003 pointed out, the batch_size does not matter.
The reason I could not pass the image to the model was because I was passing it as so...
x_fool = x00 + eps[i] * sign
scores[i, :] = logits.eval({x: x_fool})
The problem with this is that the shape of the image is simply (784,) whereas the placeholder needs to accept an array of images of shape shape=[None, 784], so what needs to be done is to reshape the image.
x_fool = labels_of_2[0].reshape((1, 784)) + eps[i] * sign
scores[i, :] = logits.eval({x:x_fool})
Now my image is shape (1, 784) which can now be accepted by the placeholder.
I read all posts in the net adressing the issue where people forgot to change the target vector to a matrix, and as a problem remains after this change, I decided to ask my question here. Workarounds are mentioned below, but new problems show and I am thankful for suggestions!
Using a convolution network setup and binary crossentropy with sigmoid activation function, I get a dimension mismatch problem, but not during the training data, only during validation / test data evaluation. For some strange reason, of of my validation set vectors get his dimension switched and I have no idea, why. Training, as mentioned above, works fine. Code follows below, thanks a lot for help (and sorry for hijacking the thread, but I saw no reason for creating a new one), most of it copied from the lasagne tutorial example.
Workarounds and new problems:
Removing "axis=1" in the valAcc definition helps, but validation accuracy remains zero and test classification always returns the same result, no matter how many nodes, layers, filters etc. I have. Even changing training set size (I have around 350 samples for each class with 48x64 grayscale images) does not change this. So something seems off
Network creation:
def build_cnn(imgSet, input_var=None):
# As a third model, we'll create a CNN of two convolution + pooling stages
# and a fully-connected hidden layer in front of the output layer.
# Input layer using shape information from training
network = lasagne.layers.InputLayer(shape=(None, \
imgSet.shape[1], imgSet.shape[2], imgSet.shape[3]), input_var=input_var)
# This time we do not apply input dropout, as it tends to work less well
# for convolutional layers.
# Convolutional layer with 32 kernels of size 5x5. Strided and padded
# convolutions are supported as well; see the docstring.
network = lasagne.layers.Conv2DLayer(
network, num_filters=32, filter_size=(5, 5),
nonlinearity=lasagne.nonlinearities.rectify,
W=lasagne.init.GlorotUniform())
# Max-pooling layer of factor 2 in both dimensions:
network = lasagne.layers.MaxPool2DLayer(network, pool_size=(2, 2))
# Another convolution with 16 5x5 kernels, and another 2x2 pooling:
network = lasagne.layers.Conv2DLayer(
network, num_filters=16, filter_size=(5, 5),
nonlinearity=lasagne.nonlinearities.rectify)
network = lasagne.layers.MaxPool2DLayer(network, pool_size=(2, 2))
# A fully-connected layer of 64 units with 25% dropout on its inputs:
network = lasagne.layers.DenseLayer(
lasagne.layers.dropout(network, p=.25),
num_units=64,
nonlinearity=lasagne.nonlinearities.rectify)
# And, finally, the 2-unit output layer with 50% dropout on its inputs:
network = lasagne.layers.DenseLayer(
lasagne.layers.dropout(network, p=.5),
num_units=1,
nonlinearity=lasagne.nonlinearities.sigmoid)
return network
Target matrices for all sets are created like this (training target vector as an example)
targetsTrain = np.vstack( (targetsTrain, [[targetClass], ]*numTr) );
...and the theano variables as such
inputVar = T.tensor4('inputs')
targetVar = T.imatrix('targets')
network = build_cnn(trainset, inputVar)
predictions = lasagne.layers.get_output(network)
loss = lasagne.objectives.binary_crossentropy(predictions, targetVar)
loss = loss.mean()
params = lasagne.layers.get_all_params(network, trainable=True)
updates = lasagne.updates.nesterov_momentum(loss, params, learning_rate=0.01, momentum=0.9)
valPrediction = lasagne.layers.get_output(network, deterministic=True)
valLoss = lasagne.objectives.binary_crossentropy(valPrediction, targetVar)
valLoss = valLoss.mean()
valAcc = T.mean(T.eq(T.argmax(valPrediction, axis=1), targetVar), dtype=theano.config.floatX)
train_fn = function([inputVar, targetVar], loss, updates=updates, allow_input_downcast=True)
val_fn = function([inputVar, targetVar], [valLoss, valAcc])
Finally, here the two loops, training and test. The first is fine, the second throws the error, excerpts below
# -- Neural network training itself -- #
numIts = 100
for itNr in range(0, numIts):
train_err = 0
train_batches = 0
for batch in iterate_minibatches(trainset.astype('float32'), targetsTrain.astype('int8'), len(trainset)//4, shuffle=True):
inputs, targets = batch
print (inputs.shape)
print(targets.shape)
train_err += train_fn(inputs, targets)
train_batches += 1
# And a full pass over the validation data:
val_err = 0
val_acc = 0
val_batches = 0
for batch in iterate_minibatches(valset.astype('float32'), targetsVal.astype('int8'), len(valset)//3, shuffle=False):
[inputs, targets] = batch
[err, acc] = val_fn(inputs, targets)
val_err += err
val_acc += acc
val_batches += 1
Erorr (excerpts)
Exception "unhandled ValueError"
Input dimension mis-match. (input[0].shape[1] = 52, input[1].shape[1] = 1)
Apply node that caused the error: Elemwise{eq,no_inplace}(DimShuffle{x,0}.0, targets)
Toposort index: 36
Inputs types: [TensorType(int64, row), TensorType(int32, matrix)]
Inputs shapes: [(1, 52), (52, 1)]
Inputs strides: [(416, 8), (4, 4)]
Inputs values: ['not shown', 'not shown']
Again, thanks for help!
so it seems the error is in the evaluation of the validation accuracy.
When you remove the "axis=1" in your calculation, the argmax goes on everything, returning only a number.
Then, broadcasting steps in and this is why you would see the same value for the whole set.
But from the error you have posted, the "T.eq" op throws the error because it has to compare a 52 x 1 with a 1 x 52 vector (matrix for theano/numpy).
So, I suggest you try to replace the line with:
valAcc = T.mean(T.eq(T.argmax(valPrediction, axis=1), targetVar.T))
I hope this should fix the error, but I haven't tested it myself.
EDIT:
The error lies in the argmax op that is called.
Normally, the argmax is there to determine which of the output units is activated the most.
However, in your setting you only have one output neuron which means that the argmax over all output neurons will always return 0 (for first arg).
This is why you have the impression your network gives you always 0 as output.
By replacing:
valAcc = T.mean(T.eq(T.argmax(valPrediction, axis=1), targetVar.T))
with:
binaryPrediction = valPrediction > .5
valAcc = T.mean(T.eq(binaryPrediction, targetVar.T)
you should get the desired result.
I'm just not sure, if the transpose is still necessary or not.