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Custom loss function for out of distribution detection using CNN in Tensorflow 2.0+

My question is in reference to the paper Learning Confidence for Out-of-Distribution Detection in Neural Networks.
I need help in creating a custom loss function in tensorflow 2.0+ as per the paper to get confident prediction from the CNN on a in distribution (if the image belongs to train categories) image while a low prediction for an out of distribution (any random image) image. The paper suggests adding a confidence estimation branch to any conventional feedforward architecture in parallel with the original class prediction branch (refer to image below)
In order to define the loss function, the softmax prediction probabilities are adjusted by interpolating between the original predictions(pi) and the target probability distribution y, where the degree of interpolation is indicated by the network’s confidence(c):
pi'= c · pi + (1 − c)yi and the final loss is :
I need help in implementing this along with the loss function in Tensorflow 2.0+, below is what I could think of, from my knowledge:
import tensorflow.keras.backend as k
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
from tensorflow.keras.applications import ResNet50
#Defining custom loss function
def custom_loss(c):
def loss(y_true, y_pred):
interpolated_p = c*y_pred+ (1-c)*y_true
return -k.reduce_sum((k.log(interpolated_p) * y_true), axis=-1) - k.log(c)
return loss
#Defining model strcuture using resnet50
basemodel = ResNet50(weights = "imagenet",include_top = False)
headmodel = basemodel.output
headmodel = layers.AveragePooling2D(pool_size = (7,7))(headmodel)
#Add a sigmoid layer to the pooling output
conf_branch = layers.Dense(1,activation = "sigmoid",name = "confidence_branch")(headmodel)
# Add a softmax layer after the pooling output
softmax_branch = layers.Dense(10,activation = "softmax",name = "softmax_branch")(headmodel)
# Instantiate an end-to-end model predicting both confidence and class prediction
model = keras.Model(
inputs=basemodel.input,
outputs=[softmax_branch, conf_branch],
)
model.compile(loss=custom_loss(c=conf_branch.output), optimizer='rmsprop')
Appreciate any help on this ! Thanks !

The following is the code I wrote for the keras implementation:
num_classes = 10
basemodel = ResNet50(weights = "imagenet",include_top = False)
headmodel = basemodel.output
headmodel = layers.AveragePooling2D(pool_size = (7,7))(headmodel)
conf_branch = layers.Dense(1,activation = "sigmoid",name="confidence_branch")(headmodel)
softmax_branch = layers.Dense(num_classes,activation = "softmax",name = "softmax_branch")(headmodel)
output = Concatenate(axis=-1)([softmax_branch , conf_branch])
def custom_loss(y_true, y_pred, budget=0.3):
with tf.compat.v1.variable_scope("LAMBDA", reuse=tf.compat.v1.AUTO_REUSE):
LAMBDA = tf.compat.v1.get_variable("LAMBDA", dtype=tf.float32, initializer=tf.constant(0.1))
pred_original = y_pred[:, 0:num_classes]
confidence = y_pred[:, num_classes]
eps = 1e-12
pred_original = tf.clip_by_value(pred_original, 0. + eps, 1. - eps)
confidence = tf.clip_by_value(confidence, 0. + eps, 1. - eps)
b = np.random.uniform(size=y_true.shape[0], low=0.0, high=1.0)
conf = confidence * b + (1 - b)
conf = tf.expand_dims(conf, axis=-1)
pred_new = pred_original * conf + y_true * (1 - conf)
xentropy_loss = tf.reduce_mean(-tf.reduce_sum(y_true * tf.math.log(pred_new), axis=-1))
confidence_loss = tf.reduce_mean(-tf.math.log(confidence))
total_loss = xentropy_loss + LAMBDA * confidence_loss
def true_func():
return LAMBDA / 1.01
def false_func():
return LAMBDA / 0.99
LAMBDA_NEW = tf.cond(budget > confidence_loss, true_func, false_func)
LAMBDA.assign(LAMBDA_NEW)
# tf.print(LAMBDA)
return total_loss
def accuracy(y_true, y_pred):
y_pred = y_pred[:, :num_classes]
correct_pred = tf.equal(tf.argmax(y_pred, 1), tf.argmax(y_true, 1))
accuracy = tf.reduce_mean(tf.cast(correct_pred, tf.float32))
return accuracy
model = Model(inputs=basemodel.input, outputs=output)
optimizer = keras.optimizers.Adam(learning_rate=0.001)
model.compile(loss=custom_loss, optimizer=optimizer, metrics=[accuracy])

Why does regularization in pytorch and scratch code does not match and what is the formula used for regularization in pytorch?

I have been trying to do L2 regularization on a binary classification model in PyTorch but when I match the results of PyTorch and scratch code it doesn't match,
Pytorch code:
class LogisticRegression(nn.Module):
def __init__(self,n_input_features):
super(LogisticRegression,self).__init__()
self.linear=nn.Linear(4,1)
self.linear.weight.data.fill_(0.0)
self.linear.bias.data.fill_(0.0)
def forward(self,x):
y_predicted=torch.sigmoid(self.linear(x))
return y_predicted
model=LogisticRegression(4)
criterion=nn.BCELoss()
optimizer=torch.optim.SGD(model.parameters(),lr=0.05,weight_decay=0.1)
dataset=Data()
train_data=DataLoader(dataset=dataset,batch_size=1096,shuffle=False)
num_epochs=1000
for epoch in range(num_epochs):
for x,y in train_data:
y_pred=model(x)
loss=criterion(y_pred,y)
loss.backward()
optimizer.step()
optimizer.zero_grad()
Scratch Code:
def sigmoid(z):
s = 1/(1+ np.exp(-z))
return s
def yinfer(X, beta):
return sigmoid(beta[0] + np.dot(X,beta[1:]))
def cost(X, Y, beta, lam):
sum = 0
sum1 = 0
n = len(beta)
m = len(Y)
for i in range(m):
sum = sum + Y[i]*(np.log( yinfer(X[i],beta)))+ (1 -Y[i])*np.log(1-yinfer(X[i],beta))
for i in range(0, n):
sum1 = sum1 + beta[i]**2
return (-sum + (lam/2) * sum1)/(1.0*m)
def pred(X,beta):
if ( yinfer(X, beta) > 0.5):
ypred = 1
else :
ypred = 0
return ypred
beta = np.zeros(5)
iterations = 1000
arr_cost = np.zeros((iterations,4))
print(beta)
n = len(Y_train)
for i in range(iterations):
Y_prediction_train=np.zeros(len(Y_train))
Y_prediction_test=np.zeros(len(Y_test))
for l in range(len(Y_train)):
Y_prediction_train[l]=pred(X[l,:],beta)
for l in range(len(Y_test)):
Y_prediction_test[l]=pred(X_test[l,:],beta)
train_acc = format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100)
test_acc = 100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100
arr_cost[i,:] = [i,cost(X,Y_train,beta,lam),train_acc,test_acc]
temp_beta = np.zeros(len(beta))
''' main code from below '''
for j in range(n):
temp_beta[0] = temp_beta[0] + yinfer(X[j,:], beta) - Y_train[j]
temp_beta[1:] = temp_beta[1:] + (yinfer(X[j,:], beta) - Y_train[j])*X[j,:]
for k in range(0, len(beta)):
temp_beta[k] = temp_beta[k] + lam * beta[k] #regularization here
temp_beta= temp_beta / (1.0*n)
beta = beta - alpha*temp_beta
graph of the losses
graph of training accuracy
graph of testing accuracy
Can someone please tell me why this is happening?
L2 value=0.1

Great question. I dug a lot through PyTorch documentation and found the answer. The answer is very tricky. Basically there are two ways to calculate regulalarization. (For summery jump to the last section).
The PyTorch uses the first type (in which regularization factor is not divided by batch size).
Here's a sample code which demonstrates that:
import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np
import torch.optim as optim
class model(nn.Module):
def __init__(self):
super().__init__()
self.linear = nn.Linear(1, 1)
self.linear.weight.data.fill_(1.0)
self.linear.bias.data.fill_(1.0)
def forward(self, x):
return self.linear(x)
model = model()
optimizer = optim.SGD(model.parameters(), lr=0.1, weight_decay=1.0)
input = torch.tensor([[2], [4]], dtype=torch.float32)
target = torch.tensor([[7], [11]], dtype=torch.float32)
optimizer.zero_grad()
pred = model(input)
loss = F.mse_loss(pred, target)
print(f'input: {input[0].data, input[1].data}')
print(f'prediction: {pred[0].data, pred[1].data}')
print(f'target: {target[0].data, target[1].data}')
print(f'\nMSEloss: {loss.item()}\n')
loss.backward()
print('Before updation:')
print('--------------------------------------------------------------------------')
print(f'weight [data, gradient]: {model.linear.weight.data, model.linear.weight.grad}')
print(f'bias [data, gradient]: {model.linear.bias.data, model.linear.bias.grad}')
print('--------------------------------------------------------------------------')
optimizer.step()
print('After updation:')
print('--------------------------------------------------------------------------')
print(f'weight [data]: {model.linear.weight.data}')
print(f'bias [data]: {model.linear.bias.data}')
print('--------------------------------------------------------------------------')
which outputs:
input: (tensor([2.]), tensor([4.]))
prediction: (tensor([3.]), tensor([5.]))
target: (tensor([7.]), tensor([11.]))
MSEloss: 26.0
Before updation:
--------------------------------------------------------------------------
weight [data, gradient]: (tensor([[1.]]), tensor([[-32.]]))
bias [data, gradient]: (tensor([1.]), tensor([-10.]))
--------------------------------------------------------------------------
After updation:
--------------------------------------------------------------------------
weight [data]: tensor([[4.1000]])
bias [data]: tensor([1.9000])
--------------------------------------------------------------------------
Here m = batch size = 2, lr = alpha = 0.1, lambda = weight_decay = 1.
Now consider tensor weight which has value = 1 and grad = -32
case1(type1 regularization):
weight = weight - lr(grad + weight_decay.weight)
weight = 1 - 0.1(-32 + 1(1))
weight = 4.1
case2(type2 regularization):
weight = weight - lr(grad + (weight_decay/batch size).weight)
weight = 1 - 0.1(-32 + (1/2)(1))
weight = 4.15
From the output we can see that updated weight = 4.1000. That concludes PyTorch uses type1 regularization.
So finally In your code you are following type2 regularization. So just change some last lines to this:
# for k in range(0, len(beta)):
# temp_beta[k] = temp_beta[k] + lam * beta[k] #regularization here
temp_beta= temp_beta / (1.0*n)
beta = beta - alpha*(temp_beta + lam * beta)
And also PyTorch loss functions doesn't include regularization term(implemented inside optimizers) so also remove regularization terms inside your custom cost function.
In summary:
Pytorch use this Regularization function:
Regularization is implemented inside Optimizers (weight_decay parameter).
PyTorch Loss functions doesn't include Regularization term.
Bias is also regularized if Regularization is used.
To use Regularization try:
torch.nn.optim.optimiser_name(model.parameters(), lr, weight_decay=lambda).

How to accumulate gradients for large batch sizes in Keras

I am working with a very memory demanding CNN model for a task of classification.
This poses a big limit on the batch size that I can use during training.
One solution is to accumulate the gradients during training, meaning that the weights of the model are not updated after every single batch. Instead the same weights are used for several batches, while the gradients from each batch are accumulated and than averaged for a single weight-update action.
I'm using a Tensorflow backend Keras and I'm pretty sure that Keras has no off-the-shelf function/method to achieve this.
How can it be done for a Keras/tensorflow model?

As was mentioned in the question, there is no off-the-shelf function/method to achieve this with Keras/Tensorflow. However this can be done by writing a custom optimizer for Keras.
The main idea is to use a flag to determine whether to update the weights during each batch.
The following implementation is based on this github post by "alexeydevederkin" and it is an accumulating Adam optimizer:
import keras.backend as K
from keras.legacy import interfaces
from keras.optimizers import Optimizer
class AdamAccumulate(Optimizer):
def __init__(self, lr=0.001, beta_1=0.9, beta_2=0.999,
epsilon=None, decay=0., amsgrad=False, accum_iters=1, **kwargs):
if accum_iters < 1:
raise ValueError('accum_iters must be >= 1')
super(AdamAccumulate, self).__init__(**kwargs)
with K.name_scope(self.__class__.__name__):
self.iterations = K.variable(0, dtype='int64', name='iterations')
self.lr = K.variable(lr, name='lr')
self.beta_1 = K.variable(beta_1, name='beta_1')
self.beta_2 = K.variable(beta_2, name='beta_2')
self.decay = K.variable(decay, name='decay')
if epsilon is None:
epsilon = K.epsilon()
self.epsilon = epsilon
self.initial_decay = decay
self.amsgrad = amsgrad
self.accum_iters = K.variable(accum_iters, K.dtype(self.iterations))
self.accum_iters_float = K.cast(self.accum_iters, K.floatx())
#interfaces.legacy_get_updates_support
def get_updates(self, loss, params):
grads = self.get_gradients(loss, params)
self.updates = [K.update_add(self.iterations, 1)]
lr = self.lr
completed_updates = K.cast(K.tf.floordiv(self.iterations, self.accum_iters), K.floatx())
if self.initial_decay > 0:
lr = lr * (1. / (1. + self.decay * completed_updates))
t = completed_updates + 1
lr_t = lr * (K.sqrt(1. - K.pow(self.beta_2, t)) / (1. - K.pow(self.beta_1, t)))
# self.iterations incremented after processing a batch
# batch: 1 2 3 4 5 6 7 8 9
# self.iterations: 0 1 2 3 4 5 6 7 8
# update_switch = 1: x x (if accum_iters=4)
update_switch = K.equal((self.iterations + 1) % self.accum_iters, 0)
update_switch = K.cast(update_switch, K.floatx())
ms = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params]
vs = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params]
gs = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params]
if self.amsgrad:
vhats = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params]
else:
vhats = [K.zeros(1) for _ in params]
self.weights = [self.iterations] + ms + vs + vhats
for p, g, m, v, vhat, tg in zip(params, grads, ms, vs, vhats, gs):
sum_grad = tg + g
avg_grad = sum_grad / self.accum_iters_float
m_t = (self.beta_1 * m) + (1. - self.beta_1) * avg_grad
v_t = (self.beta_2 * v) + (1. - self.beta_2) * K.square(avg_grad)
if self.amsgrad:
vhat_t = K.maximum(vhat, v_t)
p_t = p - lr_t * m_t / (K.sqrt(vhat_t) + self.epsilon)
self.updates.append(K.update(vhat, (1 - update_switch) * vhat + update_switch * vhat_t))
else:
p_t = p - lr_t * m_t / (K.sqrt(v_t) + self.epsilon)
self.updates.append(K.update(m, (1 - update_switch) * m + update_switch * m_t))
self.updates.append(K.update(v, (1 - update_switch) * v + update_switch * v_t))
self.updates.append(K.update(tg, (1 - update_switch) * sum_grad))
new_p = p_t
# Apply constraints.
if getattr(p, 'constraint', None) is not None:
new_p = p.constraint(new_p)
self.updates.append(K.update(p, (1 - update_switch) * p + update_switch * new_p))
return self.updates
def get_config(self):
config = {'lr': float(K.get_value(self.lr)),
'beta_1': float(K.get_value(self.beta_1)),
'beta_2': float(K.get_value(self.beta_2)),
'decay': float(K.get_value(self.decay)),
'epsilon': self.epsilon,
'amsgrad': self.amsgrad}
base_config = super(AdamAccumulate, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
It can be used in the following way:
opt = AdamAccumulate(lr=0.001, decay=1e-5, accum_iters=5)
model.compile( loss='categorical_crossentropy', # Loss function
optimizer=opt, # Optimization technique
metrics=['accuracy']) # Accuracy matrix
model.fit(X_train, y_train, batch_size = 10)
In this example, the model processes 10 samples in every iteration ("batch_size"), but the update to the weights only happens after accumulating 5 such batches ("accum_iters"). So the actual batch size for updating the weights is 50.

We have published an open-source tool to automatically add gradient accumulation support in Keras models we implemented at Run:AI to help us with batch sizing issues.
Using gradient accumulation in our models allowed us to use large batch sizes while being limited by GPU memory. It specifically allowed us running neural networks with large batch sizes using only a single GPU.
The project is available at https://github.com/run-ai/runai/tree/master/runai/ga along with explanations and examples you can use right out of the box.
Using this tool, all you have to do is add a single line of code to your Python script, and you can add gradient accumulation support to your optimizer.
The Python package is available at PyPI and can be installed using the command: pip install runai.
Adding gradient accumulation support to Keras models is extremely easy. First, import the package to your code: import runai.ga. Then, you have to create a gradient accumulation optimizer. There are two ways to do so:
1. Wrap an existing Keras optimizer
You can take any Keras optimizer - whether it's a built-in one (SGD, Adam, etc...) or a custom optimizer with your algorithm implementation - and add gradient accumulation support to it using the next line:
optimizer = runai.ga.keras.optimizers.Optimizer(optimizer, steps=STEPS)
Where optimizer is your optimizer, and STEPS is the number of steps you want to accumulate gradients over.
2. Create a gradient accumulation version of any of the built-ins optimizers
There are gradient accumulation versions of all built-in optimizers (SGD, Adam, etc...) available in the package. They can be created using this line:
optimizer = runai.ga.keras.optimizers.Adam(steps=STEPS)
Here, we create a gradient accumulation version of Adam optimizer, and we accumulate gradients over STEPS steps.
More information, explanations, and examples are available in GitHub.
In addition to the open-source tool itself, we have published a series of 3 articles on Towards Data Science (Medium), where we explained issues when using large batch sizes, what is gradient accumulation and how can it help in solving these issues, how it works, and how we implemented it. Here are links to the articles:
The problem of batch sizing and limited GPU memory
What is Gradient Accumulation and how does it help?
How-to guide to using the gradient accumulation mechanism and how we implemented it
Let us know if the tool helped you in using gradient accumulation in your own Keras models.
We are here to give any support and help with the problems you encounter when using it in your own models.

A more convenient way is to inject some changes into the existing optimizer.
class AccumOptimizer(Optimizer):
"""Inheriting Optimizer class, wrapping the original optimizer
to achieve a new corresponding optimizer of gradient accumulation.
# Arguments
optimizer: an instance of keras optimizer (supporting
all keras optimizers currently available);
steps_per_update: the steps of gradient accumulation
# Returns
a new keras optimizer.
"""
def __init__(self, optimizer, steps_per_update=1, **kwargs):
super(AccumOptimizer, self).__init__(**kwargs)
self.optimizer = optimizer
with K.name_scope(self.__class__.__name__):
self.steps_per_update = steps_per_update
self.iterations = K.variable(0, dtype='int64', name='iterations')
self.cond = K.equal(self.iterations % self.steps_per_update, 0)
self.lr = self.optimizer.lr
self.optimizer.lr = K.switch(self.cond, self.optimizer.lr, 0.)
for attr in ['momentum', 'rho', 'beta_1', 'beta_2']:
if hasattr(self.optimizer, attr):
value = getattr(self.optimizer, attr)
setattr(self, attr, value)
setattr(self.optimizer, attr, K.switch(self.cond, value, 1 - 1e-7))
for attr in self.optimizer.get_config():
if not hasattr(self, attr):
value = getattr(self.optimizer, attr)
setattr(self, attr, value)
# Cover the original get_gradients method with accumulative gradients.
def get_gradients(loss, params):
return [ag / self.steps_per_update for ag in self.accum_grads]
self.optimizer.get_gradients = get_gradients
def get_updates(self, loss, params):
self.updates = [
K.update_add(self.iterations, 1),
K.update_add(self.optimizer.iterations, K.cast(self.cond, 'int64')),
]
# gradient accumulation
self.accum_grads = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params]
grads = self.get_gradients(loss, params)
for g, ag in zip(grads, self.accum_grads):
self.updates.append(K.update(ag, K.switch(self.cond, ag * 0, ag + g)))
# inheriting updates of original optimizer
self.updates.extend(self.optimizer.get_updates(loss, params)[1:])
self.weights.extend(self.optimizer.weights)
return self.updates
def get_config(self):
iterations = K.eval(self.iterations)
K.set_value(self.iterations, 0)
config = self.optimizer.get_config()
K.set_value(self.iterations, iterations)
return config
usage:
opt = AccumOptimizer(Adam(), 10) # 10 is accumulative steps
model.compile(loss='mse', optimizer=opt)
model.fit(x_train, y_train, epochs=10, batch_size=10)
reference: https://github.com/bojone/accum_optimizer_for_keras

how can i Develop Deep sparse Autoencoder cost function in TensorFlow?

I have developed deep sparse auto encoders cost function with Tensorflow and I have download the autoencoder structure from the following link:
https://github.com/aymericdamien/TensorFlow-Examples/blob/master/examples/3_NeuralNetworks/autoencoder.py .
I have the following cost function in simple AutoEncoder:
loss = tf.reduce_mean(tf.pow(y_true - y_pred, 2))
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)
I have developed sparsity in AutoEncoders by using the following mathematical functions:
I have developed these mathematical function with the following code:
learning_rate = 0.01
training_epochs = 1000
batch_size = 256
display_step = 1
examples_to_show = 10
lambda_ = 3e-3
beta = 3
Nv = batch_size
def KL_divergence(x1, y1):
return x1* tf.log(x1 / y1) + (1 - x1) * tf.log((1 - x1) / (1 - y1))
#Weights
W1 = sum(tf.reduce_sum(tf.abs(var)**2) for var in tf.trainable_variables() if
'encoder_' in var.name)
W2 = sum(tf.reduce_sum(tf.abs(var)**2) for var in tf.trainable_variables() if
'decoder_' in var.name)
## Sparsity
rho_hat = (1+tf.reduce_mean(encoder(X),axis=0))/2
rho = np.tile(sparsity_param, n_output)
cost = tf.reduce_sum(tf.pow(y_true - y_pred, 2))/(2*Nv) + (lambda_/2)*(W1+W2)
+ beta * tf.reduce_sum(KL_divergence(rho,rho_hat))
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)
the name of paper that i have used the mathematical functions:
"Visualization of Driving Behavior Based on Hidden Feature Extraction by Using Deep Learning"
Thanks

Hi I have developed the final version of Deep sparse AutoEncoder with the following python code:
it is ok and ready for using:
from __future__ import division, print_function, absolute_import
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
def next_batch(num, data, labels):
'''
Return a total of `num` random samples and labels.
'''
idx = np.arange(0 , len(data))
np.random.shuffle(idx)
idx = idx[:num]
data_shuffle = [data[ i] for i in idx]
labels_shuffle = [data[ i] for i in idx]
return np.asarray(data_shuffle), np.asarray(labels_shuffle)
# Parameters
learning_rate = 0.01
training_epochs = 1000
batch_size = 256
display_step = 1
examples_to_show = 10
lambda_ = 3e-3
beta = 3
# tf Graph input (only pictures)
X = tf.placeholder("float", [None, n_input])
# Network Parameters
n_input = 60 # number of input layers
n_hidden_1 = 30 # 1st layer num features
n_hidden_2 = 10 # 2nd layer num features
n_output = 3 # output layer num features
sparsity_param = 0.05
weights = {
'encoder_h1': tf.Variable(tf.random_normal([n_input, n_hidden_1])),
'encoder_h2': tf.Variable(tf.random_normal([n_hidden_1, n_hidden_2])),
'encoder_h3': tf.Variable(tf.random_normal([n_hidden_2, n_output])),
'decoder_h1': tf.Variable(tf.random_normal([n_output, n_hidden_2])),
'decoder_h2': tf.Variable(tf.random_normal([n_hidden_2, n_hidden_1])),
'decoder_h3': tf.Variable(tf.random_normal([n_hidden_1, n_input])),
}
biases = {
'encoder_b1': tf.Variable(tf.random_normal([n_hidden_1])),
'encoder_b2': tf.Variable(tf.random_normal([n_hidden_2])),
'encoder_b3': tf.Variable(tf.random_normal([n_output])),
'decoder_b1': tf.Variable(tf.random_normal([n_hidden_2])),
'decoder_b2': tf.Variable(tf.random_normal([n_hidden_1])),
'decoder_b3': tf.Variable(tf.random_normal([n_input])),
}
# Building the encoder
def encoder(x):
# Encoder Hidden layer with sigmoid activation #1
layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights['encoder_h1']),
biases['encoder_b1']))
# Decoder Hidden layer with sigmoid activation #2
layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights['encoder_h2']),
biases['encoder_b2']))
# Decoder Hidden layer with sigmoid activation #3
layer_3 = tf.nn.sigmoid(tf.add(tf.matmul(layer_2, weights['encoder_h3']),
biases['encoder_b3']))
return layer_3
# Building the decoder
def decoder(x):
# Encoder Hidden layer with sigmoid activation #1
layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights['decoder_h1']),
biases['decoder_b1']))
# Decoder Hidden layer with sigmoid activation #2
layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights['decoder_h2']),
biases['decoder_b2']))
# Decoder Hidden layer with sigmoid activation #3
layer_3 = tf.nn.sigmoid(tf.add(tf.matmul(layer_2, weights['decoder_h3']),
biases['decoder_b3']))
return layer_3
def KL_divergence(x1, y1):
return x1* tf.log(x1 / y1) + (1 - x1) * tf.log((1 - x1) / (1 - y1))
# Construct model
Nv = batch_size
encoder_op = encoder(X)
decoder_op = decoder(encoder_op)
#Weights
W1 = sum(tf.reduce_sum(tf.abs(var)**2) for var in tf.trainable_variables() if 'encoder_' in var.name)
W2 = sum(tf.reduce_sum(tf.abs(var)**2) for var in tf.trainable_variables() if 'decoder_' in var.name)
# Prediction
y_pred = decoder_op
# Targets (Labels) are the input data.
y_true = X
## Sparsity
rho_hat = tf.reduce_mean(encoder(X),axis=0)
#rho_hat = (1+tf.reduce_mean(encoder(X),axis=0))/2
rho = np.tile(sparsity_param, n_output)
# Define loss and optimizer, minimize the squared error
size = tf.shape(tf.pow(y_true - y_pred, 2))
cost = tf.reduce_sum(tf.pow(y_true - y_pred, 2))/(2*Nv) + (lambda_/2)*(W1+W2) + beta * tf.reduce_sum(KL_divergence(rho,rho_hat))
#(lambda_/2)*(tf.reduce_sum(W1**2) + tf.reduce_sum(W1**2))
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)
# Initializing the variables
init = tf.global_variables_initializer()
# Launch the graph
with tf.Session() as sess:
sess.run(init)
total_batch = int(len(data)/batch_size)
# Training cycle
for epoch in range(training_epochs):
# Loop over all batches
for i in range(total_batch):
batch_xs, batch_ys = next_batch(batch_size,data[:,0:60], data[:,60:] )
# Run optimization op (backprop) and cost op (to get loss value)
_, c = sess.run([optimizer, cost], feed_dict={X: batch_xs})
# Display logs per epoch step
if epoch % display_step == 0:
print("Epoch:", '%04d' % (epoch+1),
"cost=", "{:.9f}".format(c))
print("Optimization Finished!")
tr, label = next_batch(200000,data[:,0:60], data[:,60:])
encode_decode = sess.run(
encoder_op, feed_dict={X: tr})

Here is the code for a 3 layer sparse autoencoder, implemented in Tensorflow 2.1.
The input and the output, in this case, are 1D arrays (496).
I would like to give credit to Dr. Zhiwei Lin at Ulster University for providing the initial implementation on github
https://github.com/zhiweiuu/sparse-autoencoder-tensorflow/blob/master/SparseAutoEncoder.py
I have wrapped it in a class, where each layer is now an instance variable. This makes it easier to get different outputs for each layer.
You will notice that I have used only the first layer output for the sparsity constraint.
This architecture is similar to the one used in this article: https://pubmed.ncbi.nlm.nih.gov/29302382/
My implementation is simple and the training and it can be improved :)
to train the model
model = my_model() then you loop for i in range(1000): model.network_learn(X,Y)
class my_model:
def __init__(self):
xavier=tf.keras.initializers.GlorotUniform()
self.l1 = tf.keras.layers.Dense(496,kernel_initializer=xavier,activation=tf.nn.sigmoid,input_shape=(496,))
self.l2 = tf.keras.layers.Dense(496,kernel_initializer=xavier,activation=tf.nn.sigmoid)
self.l3 = tf.keras.layers.Dense(496,kernel_initializer=xavier,activation=tf.nn.sigmoid)
self.train_op = tf.keras.optimizers.SGD(learning_rate=0.01)
self.rho = 0.05
self.alpha= 0.001
self.beta = 4
def kl_divergence(self, rho, rho_hat):
return rho * tf.math.log(rho) - rho * tf.math.log(rho_hat) + (1 - rho) * tf.math.log(1 - rho) - (1 - rho) * tf.math.log(1 - rho_hat)
def run(self,X):
out1=self.l1(X)
out2=self.l2(out1)
out3 = self.l3(out2)
return out3
def get_loss(self,X,Y):
rho_hat = tf.reduce_mean(self.l1(X),axis=0)
kl = self.kl_divergence(self.rho,rho_hat)
out1=self.l1(X)
out2=self.l2(out1)
X_prime=self.l3(out2)
diff = X-X_prime
W1 = self.l1.variables[0]
W2 = self.l2.variables[0]
W3 = self.l3.variables[0]
cost= 0.5*tf.reduce_mean(tf.reduce_sum(diff**2,axis=1)) \
+0.5*self.alpha*(tf.nn.l2_loss(W1) + tf.nn.l2_loss(W2) + tf.nn.l2_loss(W3)) \
+self.beta*tf.reduce_sum(kl)
return cost
return tf.math.square(boom2-Y)
def get_grad(self,X,Y):
with tf.GradientTape() as tape:
tape.watch(self.l1.variables)
tape.watch(self.l2.variables)
tape.watch(self.l3.variables)
L = self.get_loss(X,Y)
g = tape.gradient(L, [self.l1.variables[0],self.l1.variables[1],self.l2.variables[0],self.l2.variables[1],self.l3.variables[0],self.l3.variables[1]])
return g
def network_learn(self,X,Y):
g = self.get_grad(X,Y)
self.train_op.apply_gradients(zip(g, [self.l1.variables[0],self.l1.variables[1],self.l2.variables[0],self.l2.variables[1],self.l3.variables[0],self.l3.variables[1]]))
Here is how you would train a network like this

How could I use batch normalization in TensorFlow?

I would like to use batch normalization in TensorFlow. I found the related C++ source code in core/ops/nn_ops.cc. However, I did not find it documented on tensorflow.org.
BN has different semantics in MLP and CNN, so I am not sure what exactly this BN does.
I did not find a method called MovingMoments either.

Update July 2016 The easiest way to use batch normalization in TensorFlow is through the higher-level interfaces provided in either contrib/layers, tflearn, or slim.
Previous answer if you want to DIY:
The documentation string for this has improved since the release - see the docs comment in the master branch instead of the one you found. It clarifies, in particular, that it's the output from tf.nn.moments.
You can see a very simple example of its use in the batch_norm test code. For a more real-world use example, I've included below the helper class and use notes that I scribbled up for my own use (no warranty provided!):
"""A helper class for managing batch normalization state.
This class is designed to simplify adding batch normalization
(http://arxiv.org/pdf/1502.03167v3.pdf) to your model by
managing the state variables associated with it.
Important use note: The function get_assigner() returns
an op that must be executed to save the updated state.
A suggested way to do this is to make execution of the
model optimizer force it, e.g., by:
update_assignments = tf.group(bn1.get_assigner(),
bn2.get_assigner())
with tf.control_dependencies([optimizer]):
optimizer = tf.group(update_assignments)
"""
import tensorflow as tf
class ConvolutionalBatchNormalizer(object):
"""Helper class that groups the normalization logic and variables.
Use:
ewma = tf.train.ExponentialMovingAverage(decay=0.99)
bn = ConvolutionalBatchNormalizer(depth, 0.001, ewma, True)
update_assignments = bn.get_assigner()
x = bn.normalize(y, train=training?)
(the output x will be batch-normalized).
"""
def __init__(self, depth, epsilon, ewma_trainer, scale_after_norm):
self.mean = tf.Variable(tf.constant(0.0, shape=[depth]),
trainable=False)
self.variance = tf.Variable(tf.constant(1.0, shape=[depth]),
trainable=False)
self.beta = tf.Variable(tf.constant(0.0, shape=[depth]))
self.gamma = tf.Variable(tf.constant(1.0, shape=[depth]))
self.ewma_trainer = ewma_trainer
self.epsilon = epsilon
self.scale_after_norm = scale_after_norm
def get_assigner(self):
"""Returns an EWMA apply op that must be invoked after optimization."""
return self.ewma_trainer.apply([self.mean, self.variance])
def normalize(self, x, train=True):
"""Returns a batch-normalized version of x."""
if train:
mean, variance = tf.nn.moments(x, [0, 1, 2])
assign_mean = self.mean.assign(mean)
assign_variance = self.variance.assign(variance)
with tf.control_dependencies([assign_mean, assign_variance]):
return tf.nn.batch_norm_with_global_normalization(
x, mean, variance, self.beta, self.gamma,
self.epsilon, self.scale_after_norm)
else:
mean = self.ewma_trainer.average(self.mean)
variance = self.ewma_trainer.average(self.variance)
local_beta = tf.identity(self.beta)
local_gamma = tf.identity(self.gamma)
return tf.nn.batch_norm_with_global_normalization(
x, mean, variance, local_beta, local_gamma,
self.epsilon, self.scale_after_norm)
Note that I called it a ConvolutionalBatchNormalizer because it pins the use of tf.nn.moments to sum across axes 0, 1, and 2, whereas for non-convolutional use you might only want axis 0.
Feedback appreciated if you use it.

As of TensorFlow 1.0 (February 2017) there's also the high-level tf.layers.batch_normalization API included in TensorFlow itself.
It's super simple to use:
# Set this to True for training and False for testing
training = tf.placeholder(tf.bool)
x = tf.layers.dense(input_x, units=100)
x = tf.layers.batch_normalization(x, training=training)
x = tf.nn.relu(x)
...except that it adds extra ops to the graph (for updating its mean and variance variables) in such a way that they won't be dependencies of your training op. You can either just run the ops separately:
extra_update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS)
sess.run([train_op, extra_update_ops], ...)
or add the update ops as dependencies of your training op manually, then just run your training op as normal:
extra_update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS)
with tf.control_dependencies(extra_update_ops):
train_op = optimizer.minimize(loss)
...
sess.run([train_op], ...)

The following works fine for me, it does not require invoking EMA-apply outside.
import numpy as np
import tensorflow as tf
from tensorflow.python import control_flow_ops
def batch_norm(x, n_out, phase_train, scope='bn'):
"""
Batch normalization on convolutional maps.
Args:
x: Tensor, 4D BHWD input maps
n_out: integer, depth of input maps
phase_train: boolean tf.Varialbe, true indicates training phase
scope: string, variable scope
Return:
normed: batch-normalized maps
"""
with tf.variable_scope(scope):
beta = tf.Variable(tf.constant(0.0, shape=[n_out]),
name='beta', trainable=True)
gamma = tf.Variable(tf.constant(1.0, shape=[n_out]),
name='gamma', trainable=True)
batch_mean, batch_var = tf.nn.moments(x, [0,1,2], name='moments')
ema = tf.train.ExponentialMovingAverage(decay=0.5)
def mean_var_with_update():
ema_apply_op = ema.apply([batch_mean, batch_var])
with tf.control_dependencies([ema_apply_op]):
return tf.identity(batch_mean), tf.identity(batch_var)
mean, var = tf.cond(phase_train,
mean_var_with_update,
lambda: (ema.average(batch_mean), ema.average(batch_var)))
normed = tf.nn.batch_normalization(x, mean, var, beta, gamma, 1e-3)
return normed
Example:
import math
n_in, n_out = 3, 16
ksize = 3
stride = 1
phase_train = tf.placeholder(tf.bool, name='phase_train')
input_image = tf.placeholder(tf.float32, name='input_image')
kernel = tf.Variable(tf.truncated_normal([ksize, ksize, n_in, n_out],
stddev=math.sqrt(2.0/(ksize*ksize*n_out))),
name='kernel')
conv = tf.nn.conv2d(input_image, kernel, [1,stride,stride,1], padding='SAME')
conv_bn = batch_norm(conv, n_out, phase_train)
relu = tf.nn.relu(conv_bn)
with tf.Session() as session:
session.run(tf.initialize_all_variables())
for i in range(20):
test_image = np.random.rand(4,32,32,3)
sess_outputs = session.run([relu],
{input_image.name: test_image, phase_train.name: True})

There is also an "official" batch normalization layer coded by the developers. They don't have very good docs on how to use it but here is how to use it (according to me):
from tensorflow.contrib.layers.python.layers import batch_norm as batch_norm
def batch_norm_layer(x,train_phase,scope_bn):
bn_train = batch_norm(x, decay=0.999, center=True, scale=True,
updates_collections=None,
is_training=True,
reuse=None, # is this right?
trainable=True,
scope=scope_bn)
bn_inference = batch_norm(x, decay=0.999, center=True, scale=True,
updates_collections=None,
is_training=False,
reuse=True, # is this right?
trainable=True,
scope=scope_bn)
z = tf.cond(train_phase, lambda: bn_train, lambda: bn_inference)
return z
to actually use it you need to create a placeholder for train_phase that indicates if you are in training or inference phase (as in train_phase = tf.placeholder(tf.bool, name='phase_train')). Its value can be filled during inference or training with a tf.session as in:
test_error = sess.run(fetches=cross_entropy, feed_dict={x: batch_xtest, y_:batch_ytest, train_phase: False})
or during training:
sess.run(fetches=train_step, feed_dict={x: batch_xs, y_:batch_ys, train_phase: True})
I'm pretty sure this is correct according to the discussion in github.
Seems there is another useful link:
http://r2rt.com/implementing-batch-normalization-in-tensorflow.html

You can simply use the build-in batch_norm layer:
batch_norm = tf.cond(is_train,
lambda: tf.contrib.layers.batch_norm(prev, activation_fn=tf.nn.relu, is_training=True, reuse=None),
lambda: tf.contrib.layers.batch_norm(prev, activation_fn =tf.nn.relu, is_training=False, reuse=True))
where prev is the output of your previous layer (can be both fully-connected or a convolutional layer) and is_train is a boolean placeholder. Just use batch_norm as the input to the next layer, then.

Since someone recently edited this, I'd like to clarify that this is no longer an issue.
This answer does not seem correct When phase_train is set to false, it still updates the ema mean and variance. This can be verified with the following code snippet.
x = tf.placeholder(tf.float32, [None, 20, 20, 10], name='input')
phase_train = tf.placeholder(tf.bool, name='phase_train')
# generate random noise to pass into batch norm
x_gen = tf.random_normal([50,20,20,10])
pt_false = tf.Variable(tf.constant(True))
#generate a constant variable to pass into batch norm
y = x_gen.eval()
[bn, bn_vars] = batch_norm(x, 10, phase_train)
tf.initialize_all_variables().run()
train_step = lambda: bn.eval({x:x_gen.eval(), phase_train:True})
test_step = lambda: bn.eval({x:y, phase_train:False})
test_step_c = lambda: bn.eval({x:y, phase_train:True})
# Verify that this is different as expected, two different x's have different norms
print(train_step()[0][0][0])
print(train_step()[0][0][0])
# Verify that this is same as expected, same x's (y) have same norm
print(train_step_c()[0][0][0])
print(train_step_c()[0][0][0])
# THIS IS DIFFERENT but should be they same, should only be reading from the ema.
print(test_step()[0][0][0])
print(test_step()[0][0][0])

Using TensorFlow built-in batch_norm layer, below is the code to load data, build a network with one hidden ReLU layer and L2 normalization and introduce batch normalization for both hidden and out layer. This runs fine and trains fine. Just FYI this example is mostly built upon the data and code from Udacity DeepLearning course.
P.S. Yes, parts of it were discussed one way or another in answers earlier but I decided to gather in one code snippet everything so that you have example of whole network training process with Batch Normalization and its evaluation
# These are all the modules we'll be using later. Make sure you can import them
# before proceeding further.
from __future__ import print_function
import numpy as np
import tensorflow as tf
from six.moves import cPickle as pickle
pickle_file = '/home/maxkhk/Documents/Udacity/DeepLearningCourse/SourceCode/tensorflow/examples/udacity/notMNIST.pickle'
with open(pickle_file, 'rb') as f:
save = pickle.load(f)
train_dataset = save['train_dataset']
train_labels = save['train_labels']
valid_dataset = save['valid_dataset']
valid_labels = save['valid_labels']
test_dataset = save['test_dataset']
test_labels = save['test_labels']
del save # hint to help gc free up memory
print('Training set', train_dataset.shape, train_labels.shape)
print('Validation set', valid_dataset.shape, valid_labels.shape)
print('Test set', test_dataset.shape, test_labels.shape)
image_size = 28
num_labels = 10
def reformat(dataset, labels):
dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)
# Map 2 to [0.0, 1.0, 0.0 ...], 3 to [0.0, 0.0, 1.0 ...]
labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)
return dataset, labels
train_dataset, train_labels = reformat(train_dataset, train_labels)
valid_dataset, valid_labels = reformat(valid_dataset, valid_labels)
test_dataset, test_labels = reformat(test_dataset, test_labels)
print('Training set', train_dataset.shape, train_labels.shape)
print('Validation set', valid_dataset.shape, valid_labels.shape)
print('Test set', test_dataset.shape, test_labels.shape)
def accuracy(predictions, labels):
return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))
/ predictions.shape[0])
#for NeuralNetwork model code is below
#We will use SGD for training to save our time. Code is from Assignment 2
#beta is the new parameter - controls level of regularization.
#Feel free to play with it - the best one I found is 0.001
#notice, we introduce L2 for both biases and weights of all layers
batch_size = 128
beta = 0.001
#building tensorflow graph
graph = tf.Graph()
with graph.as_default():
# Input data. For the training data, we use a placeholder that will be fed
# at run time with a training minibatch.
tf_train_dataset = tf.placeholder(tf.float32,
shape=(batch_size, image_size * image_size))
tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
tf_valid_dataset = tf.constant(valid_dataset)
tf_test_dataset = tf.constant(test_dataset)
#introduce batchnorm
tf_train_dataset_bn = tf.contrib.layers.batch_norm(tf_train_dataset)
#now let's build our new hidden layer
#that's how many hidden neurons we want
num_hidden_neurons = 1024
#its weights
hidden_weights = tf.Variable(
tf.truncated_normal([image_size * image_size, num_hidden_neurons]))
hidden_biases = tf.Variable(tf.zeros([num_hidden_neurons]))
#now the layer itself. It multiplies data by weights, adds biases
#and takes ReLU over result
hidden_layer = tf.nn.relu(tf.matmul(tf_train_dataset_bn, hidden_weights) + hidden_biases)
#adding the batch normalization layerhi()
hidden_layer_bn = tf.contrib.layers.batch_norm(hidden_layer)
#time to go for output linear layer
#out weights connect hidden neurons to output labels
#biases are added to output labels
out_weights = tf.Variable(
tf.truncated_normal([num_hidden_neurons, num_labels]))
out_biases = tf.Variable(tf.zeros([num_labels]))
#compute output
out_layer = tf.matmul(hidden_layer_bn,out_weights) + out_biases
#our real output is a softmax of prior result
#and we also compute its cross-entropy to get our loss
#Notice - we introduce our L2 here
loss = (tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(
out_layer, tf_train_labels) +
beta*tf.nn.l2_loss(hidden_weights) +
beta*tf.nn.l2_loss(hidden_biases) +
beta*tf.nn.l2_loss(out_weights) +
beta*tf.nn.l2_loss(out_biases)))
#now we just minimize this loss to actually train the network
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
#nice, now let's calculate the predictions on each dataset for evaluating the
#performance so far
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(out_layer)
valid_relu = tf.nn.relu( tf.matmul(tf_valid_dataset, hidden_weights) + hidden_biases)
valid_prediction = tf.nn.softmax( tf.matmul(valid_relu, out_weights) + out_biases)
test_relu = tf.nn.relu( tf.matmul( tf_test_dataset, hidden_weights) + hidden_biases)
test_prediction = tf.nn.softmax(tf.matmul(test_relu, out_weights) + out_biases)
#now is the actual training on the ANN we built
#we will run it for some number of steps and evaluate the progress after
#every 500 steps
#number of steps we will train our ANN
num_steps = 3001
#actual training
with tf.Session(graph=graph) as session:
tf.initialize_all_variables().run()
print("Initialized")
for step in range(num_steps):
# Pick an offset within the training data, which has been randomized.
# Note: we could use better randomization across epochs.
offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
# Generate a minibatch.
batch_data = train_dataset[offset:(offset + batch_size), :]
batch_labels = train_labels[offset:(offset + batch_size), :]
# Prepare a dictionary telling the session where to feed the minibatch.
# The key of the dictionary is the placeholder node of the graph to be fed,
# and the value is the numpy array to feed to it.
feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
_, l, predictions = session.run(
[optimizer, loss, train_prediction], feed_dict=feed_dict)
if (step % 500 == 0):
print("Minibatch loss at step %d: %f" % (step, l))
print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
print("Validation accuracy: %.1f%%" % accuracy(
valid_prediction.eval(), valid_labels))
print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))

So a simple example of the use of this batchnorm class:
from bn_class import *
with tf.name_scope('Batch_norm_conv1') as scope:
ewma = tf.train.ExponentialMovingAverage(decay=0.99)
bn_conv1 = ConvolutionalBatchNormalizer(num_filt_1, 0.001, ewma, True)
update_assignments = bn_conv1.get_assigner()
a_conv1 = bn_conv1.normalize(a_conv1, train=bn_train)
h_conv1 = tf.nn.relu(a_conv1)