I am implementing the paper Deep multiscale convolutional feature learning for weakly supervised localization of chest pathologies in X-ray images
According to my understanding the layer relevance weights belong to the last layer of each dense block.
I tried implementing the weight constraints as shown below:
def weight_constraints(self):
weights= {'feat1': self.model.features.denseblock2.denselayer12.conv2.weight.data,
'feat2':self.model.features.denseblock3.denselayer24.conv2.weight.data,
'feat3':self.model.features.denseblock4.denselayer16.conv2.weight.data}
sum(weights.values()) == 1
for i in weights.keys():
w = weights[i]
w1 = w.clamp(min= 0)
weights[i] = w1
return weights
weights= self.weight_constraints()
for i in weights.keys():
w = weights[i]
l = logits[i]
p = torch.matmul(w , l[0])
sum = sum + p
where logits is a dictionary which contains out of FC layer from each block as shown in the diagram.
logits = {'feat1': [tensor([[-0.0630]], ...ackward0>)], 'feat2': [tensor([[-0.0323]], ...ackward0>)], 'feat3': [tensor([[-8.2897e-06...ackward0>)]}
I get the following error :
mat1 and mat2 shapes cannot be multiplied (12288x3 and 1x1)
Is this the right approach?
The paper states
The
logit response from all the layers have same dimension (equal to the number of
category for classification) and now can be combined using class specific convex
combination to obtain the probability score for the class pc.
The function matmul you used perfroms matrix multiplications, it requires mat1.shape[-1] == mat2.shape[-2].
If you assume sum(w)==1, and torch.all(w > 0), you could compute the convex combination of l as (w * l).sum(-1) that is multiply w and l element-wise, broadcasting over the batch dimensions of l, and requiring w.shape[-1] == l.shape[-1] (presumably 3).
If you want to stick with matmul you can add one dimension to w and l, and perform the vector product as a matrix multiplication: torch.matmul(w[...,None,:], l[..., :, None]).
I wonder if I want to implement dropout by myself, is something like the following sufficient (taken from Implementing dropout from scratch):
class MyDropout(nn.Module):
def __init__(self, p: float = 0.5):
super(MyDropout, self).__init__()
if p < 0 or p > 1:
raise ValueError("dropout probability has to be between 0 and 1, " "but got {}".format(p))
self.p = p
def forward(self, X):
if self.training:
binomial = torch.distributions.binomial.Binomial(probs=1-self.p)
return X * binomial.sample(X.size()) * (1.0/(1-self.p))
return X
My concern is even if the unwanted weights are masked out (either through this way or by using a mask tensor), there can still be gradient flow through the 0 weights (https://discuss.pytorch.org/t/custom-connections-in-neural-network-layers/3027/9). Is my concern valid?
DropOut does not mask the weights - it masks the features.
For linear layers implementing y = <w, x> the gradient w.r.t the parameters w is x. Therefore, if you set entries in x to zero - it will amount to no update for the corresponding weight in the adjacent linear layer.
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
I have a RGB image of shape (256,256,3) and I have a weight mask of shape (256,256). How do I perform the element-wise multiplication between them with Keras? (all channels share the same mask)
You need a Reshape so both tensors have the same number of dimensions, and a Multiply layer
mask = Reshape((256,256,1))(mask)
out = Multiply()([image,mask])
If you have variable shapes, you can use a single Lambda layer like this:
import keras.backend as K
def multiply(x):
image,mask = x
mask = K.expand_dims(mask, axis=-1) #could be K.stack([mask]*3, axis=-1) too
return mask*image
out = Lambda(multiply)([image,mask])
As an alternative you can do this using a Lambda layer (as in #DanielMöller's answer you need to add a third axis to the mask):
from keras import backend as K
out = Lambda(lambda x: x[0] * K.expand_dims(x[1], axis=-1))([image, mask])
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!