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Deep learning model stops learning after 30 iterations

I am trying to implement a deep learning model that I made while completing the "Neural Networks and Deep Learning" course on Coursera, using the MNIST dataset for written numbers. During the course, it worked very well identifying cats so I know that the whole model works together, and I have modified all of the input data and the output layer such that the output is an array of size 10 and the array shapes all match what they were during the course.
I have done a little experimentation and come to a very weird problem. My graph of cost over time looks like this:
I would usually expect a more sloping curve that would tend towards a value much closer to zero and the very sharp turn is odd as well. I should also point out that it isn't hundreds, it's tens on the x axis.
The shape of my NN is [784, 200, 50, 10], I'm assuming that this isn't the problem but what I'm really looking for is for someone more experienced in ml to explain why this happens.
My model as it stands goes something like this
# Initialisation of parameters
parameters = initialize_parameters_deep(layers_dims)
for i in range(0, num_iterations):
# Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID.
AL, caches = L_model_forward(train_data, parameters, layers_dims[-1])
# Compute cost.
cost = compute_cost(AL, train_labels)
# Backward propagation.
grads = L_model_backward(AL, train_labels, caches)
# Update parameters.
parameters = update_parameters(parameters, grads, learning_rate)
# Print the cost every 100 training example
if print_cost and i % 100 == 0:
print("Cost after iteration %i: %f" % (i, cost))
if print_cost and i % 10 == 0:
costs.append(cost)
My backward propagation model is as follows
def linear_backward(dZ, cache):
A_prev, W, b = cache
m = A_prev.shape[1]
dW = 1 / m * np.dot(dZ, A_prev.T)
db = 1 / m * np.sum(dZ, axis=1, keepdims=True)
dA_prev = np.dot(W.T, dZ)
assert (dA_prev.shape == A_prev.shape)
assert (dW.shape == W.shape)
assert (db.shape == b.shape)
return dA_prev, dW, db
def linear_activation_backward(dA, cache, activation):
linear_cache, activation_cache = cache
if activation == "relu":
dZ = relu_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
elif activation == "sigmoid":
dZ = sigmoid_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
return dA_prev, dW, db
def L_model_backward(AL, Y, caches):
grads = {}
L = len(caches) # the number of layers
m = AL.shape[1]
Y = Y.reshape(AL.shape) # after this line, Y is the same shape as AL
# Initializing the backpropagation
dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
# Lth layer (SIGMOID -> LINEAR) gradients. Inputs: "dAL, current_cache". Outputs: "grads["dAL-1"], grads["dWL"], grads["dbL"]
current_cache = caches[L - 1]
grads["dA" + str(L - 1)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, activation="sigmoid")
# Loop from l=L-2 to l=0
for l in reversed(range(L - 1)):
# lth layer: (RELU -> LINEAR) gradients.
# Inputs: "grads["dA" + str(l + 1)], current_cache". Outputs: "grads["dA" + str(l)] , grads["dW" + str(l + 1)] , grads["db" + str(l + 1)]
current_cache = caches[l]
dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l + 1)], current_cache, activation="relu")
grads["dA" + str(l)] = dA_prev_temp
grads["dW" + str(l + 1)] = dW_temp
grads["db" + str(l + 1)] = db_temp
return grads
If you need any more code or anything from me specifically then I would be happy to provide it.

Setting custom loss causes RuntimeError: Variable data has to be a tensor, but got Variable in Pytorch

I have custom class for the net definition:
class PyTorchUNet(Model):
....
def set_loss(self):
if self.activation_func == 'softmax': #this is working example
loss_function = partial(mixed_dice_cross_entropy_loss,
dice_loss=multiclass_dice_loss,
cross_entropy_loss=nn.CrossEntropyLoss(),
dice_activation='softmax',
dice_weight=self.architecture_config['model_params']['dice_weight'],
cross_entropy_weight=self.architecture_config['model_params']['bce_weight']
)
elif self.activation_func == 'sigmoid':
loss_function = designed_loss #setting will cause error on validation
else:
raise Exception('Only softmax and sigmoid activations are allowed')
self.loss_function = [('mask', loss_function, 1.0)]
def designed_loss(output, target):
target = target.long() # this should make variable to tensor
return lovasz_hinge(output, target)
# this is just as it from github
def lovasz_hinge(logits, labels, per_image=True, ignore=None):
"""
Binary Lovasz hinge loss
logits: [B, H, W] Variable, logits at each pixel (between -\infty and +\infty)
labels: [B, H, W] Tensor, binary ground truth masks (0 or 1)
per_image: compute the loss per image instead of per batch
ignore: void class id
"""
if per_image:
loss = mean(lovasz_hinge_flat(*flatten_binary_scores(log.unsqueeze(0), lab.unsqueeze(0), ignore))
for log, lab in zip(logits, labels))
else:
loss = lovasz_hinge_flat(*flatten_binary_scores(logits, labels, ignore))
return loss
def lovasz_hinge_flat(logits, labels):
"""
Binary Lovasz hinge loss
logits: [P] Variable, logits at each prediction (between -\infty and +\infty)
labels: [P] Tensor, binary ground truth labels (0 or 1)
ignore: label to ignore
"""
if len(labels) == 0:
# only void pixels, the gradients should be 0
return logits.sum() * 0.
signs = 2. * labels.float() - 1.
errors = (1. - logits * Variable(signs))
errors_sorted, perm = torch.sort(errors, dim=0, descending=True)
perm = perm.data
gt_sorted = labels[perm]
grad = lovasz_grad(gt_sorted)
loss = torch.dot(F.elu(errors_sorted), Variable(grad))
return loss
def mean(l, ignore_nan=False, empty=0):
"""
nanmean compatible with generators.
"""
l = iter(l)
if ignore_nan:
l = ifilterfalse(np.isnan, l)
try:
n = 1
acc = next(l)
except StopIteration:
if empty == 'raise':
raise ValueError('Empty mean')
return empty
for n, v in enumerate(l, 2):
acc += v
if n == 1:
return acc
return acc / n
Working example:
def mixed_dice_cross_entropy_loss(output, target, dice_weight=0.5, dice_loss=None,
cross_entropy_weight=0.5, cross_entropy_loss=None, smooth=0,
dice_activation='softmax'):
num_classes_without_background = output.size(1) - 1
dice_output = output[:, 1:, :, :]
dice_target = target[:, :num_classes_without_background, :, :].long()
cross_entropy_target = torch.zeros_like(target[:, 0, :, :]).long()
for class_nr in range(num_classes_without_background):
cross_entropy_target = where(target[:, class_nr, :, :], class_nr + 1, cross_entropy_target)
if cross_entropy_loss is None:
cross_entropy_loss = nn.CrossEntropyLoss()
if dice_loss is None:
dice_loss = multiclass_dice_loss
return dice_weight * dice_loss(dice_output, dice_target, smooth,
dice_activation) + cross_entropy_weight * cross_entropy_loss(output,
cross_entropy_target)
def multiclass_dice_loss(output, target, smooth=0, activation='softmax'):
"""Calculate Dice Loss for multiple class output.
Args:
output (torch.Tensor): Model output of shape (N x C x H x W).
target (torch.Tensor): Target of shape (N x H x W).
smooth (float, optional): Smoothing factor. Defaults to 0.
activation (string, optional): Name of the activation function, softmax or sigmoid. Defaults to 'softmax'.
Returns:
torch.Tensor: Loss value.
"""
if activation == 'softmax':
activation_nn = torch.nn.Softmax2d()
elif activation == 'sigmoid':
activation_nn = torch.nn.Sigmoid()
else:
raise NotImplementedError('only sigmoid and softmax are implemented')
loss = 0
dice = DiceLoss(smooth=smooth)
output = activation_nn(output)
num_classes = output.size(1)
target.data = target.data.float()
for class_nr in range(num_classes):
loss += dice(output[:, class_nr, :, :], target[:, class_nr, :, :])
return loss / num_classes
As result I keep getting:
RuntimeError: Variable data has to be a tensor, but got Variable
How to fix the problem?

Are you still use pytorch 0.3?
if yes, the following snippet may help
tensor = var.data

What's wrong with my backpropagation?

I'm trying to code a neural network from scratch in python. To check whether everything works I wanted to overfit the network but the loss seems to explode at first and then comes back to the initial value and stops there (Doesn't converge). I've checked my code and could find the reason. I assume my understanding or implementation of backpropagation is incorrect but there might be some other reason. Can anyone help me out or at least point me in the right direction?
# Initialize weights and biases given dimesnsions (For this example the dimensions are set to [12288, 64, 1])
def initialize_parameters(dims):
# Initiate parameters
parameters = {}
L = len(dims) # Number of layers in the network
# Loop over the given dimensions. Initialize random weights and set biases to zero.
for i in range(1, L):
parameters["W" + str(i)] = np.random.randn(dims[i], dims[i-1]) * 0.01
parameters["b" + str(i)] = np.zeros([dims[i], 1])
return parameters
# Activation Functions
def relu(x, deriv=False):
if deriv:
return 1. * (x > 0)
else:
return np.maximum(0,x)
def sigmoid(x, deriv=False):
if deriv:
return x * (1-x)
else:
return 1/(1 + np.exp(-x))
# Forward and backward pass for 2 layer neural network. (1st relu, 2nd sigmoid)
def forward_backward(X, Y, parameters):
# Array for storing gradients
grads = {}
# Get the length of examples
m = Y.shape[1]
# First layer
Z1 = np.dot(parameters["W1"], X) + parameters["b1"]
A1 = relu(Z1)
# Second layer
Z2 = np.dot(parameters["W2"], A1) + parameters["b2"]
AL = sigmoid(Z2)
# Compute cost
cost = (-1 / m) * np.sum(np.multiply(Y, np.log(AL)) + np.multiply(1 - Y, np.log(1 - AL)))
# Backpropagation
# Second Layer
dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
dZ2 = dAL * sigmoid(AL, deriv=True)
grads["dW2"] = np.dot(dZ2, A1.T) / m
grads["db2"] = np.sum(dZ2, axis=1, keepdims=True) / m
# First layer
dA1 = np.dot(parameters["W2"].T, dZ2)
dZ1 = dA1 * relu(A1, deriv=True)
grads["dW1"] = np.dot(dZ1, X.T)
grads["db1"] = np.sum(dZ1, axis=1, keepdims=True) / m
return AL, grads, cost
# Hyperparameters
dims = [12288, 64, 1]
epoches = 2000
learning_rate = 0.1
# Initialize parameters
parameters = initialize_parameters(dims)
log_list = []
# Train the network
for i in range(epoches):
# Get X and Y
x = np.array(train[0:10],ndmin=2).T
y = np.array(labels[0:10], ndmin=2).T
# Perform forward and backward pass
AL, grads, cost = forward_backward(x, y, parameters)
# Compute cost and append to the log_list
log_list.append(cost)
# Update parameters with computed gradients
parameters = update_parameters(grads, parameters, learning_rate)
plt.plot(log_list)
plt.title("Loss of the network")
plt.show()

I am struggling to find the place where you calculate the error gradients and the input training data sample would also help...
I don't know if this will help you, but I'll share my solution for Python neural network to learn XOR problem.
import numpy as np
def sigmoid_function(x, derivative=False):
"""
Sigmoid function
“x” is the input and “y” the output, the nonlinear properties of this function means that
the rate of change is slower at the extremes and faster in the centre. Put plainly,
we want the neuron to “make its mind up” instead of indecisively staying in the middle.
:param x: Float
:param Derivative: Boolean
:return: Float
"""
if (derivative):
return x * (1 - x) # Derivative using the chain rule.
else:
return 1 / (1 + np.exp(-x))
# create dataset for XOR problem
input_data = np.array([[0.0, 0.0], [0.0, 1.0], [1.0, 0.0], [1.0, 1.0]])
ideal_output = np.array([[0.0], [1.0], [1.0], [0.0]])
#initialize variables
learning_rate = 0.1
epoch = 50000 #number or iterations basically - One round of forward and back propagation is called an epoch
# get the second element from the numpy array shape field to detect the count of features for input layer
input_layer_neurons = input_data.shape[1]
hidden_layer_neurons = 3 #number of hidden layer neurons
output_layer_neurons = 1 #number of output layer neurons
#init weight & bias
weights_hidden = np.random.uniform(size=(input_layer_neurons, hidden_layer_neurons))
bias_hidden = np.random.uniform(1, hidden_layer_neurons)
weights_output = np.random.uniform(size=(hidden_layer_neurons, output_layer_neurons))
bias_output = np.random.uniform(1, output_layer_neurons)
for i in range(epoch):
#forward propagation
hidden_layer_input_temp = np.dot(input_data, weights_hidden) #matrix dot product to adjust for weights in the layer
hidden_layer_input = hidden_layer_input_temp + bias_hidden #adjust for bias
hidden_layer_activations = sigmoid_function(hidden_layer_input) #use the activation function
output_layer_input_temp = np.dot(hidden_layer_activations, weights_output)
output_layer_input = output_layer_input_temp + bias_output
output = sigmoid_function(output_layer_input) #final output
#backpropagation (where adjusting of the weights happens)
error = ideal_output - output #error gradient
if (i % 1000 == 0):
print("Error: {}".format(np.mean(abs(error))))
#use derivatives to compute slope of output and hidden layers
slope_output_layer = sigmoid_function(output, derivative=True)
slope_hidden_layer = sigmoid_function(hidden_layer_activations, derivative=True)
#calculate deltas
delta_output = error * slope_output_layer
error_hidden_layer = delta_output.dot(weights_output.T) #calculates the error at hidden layer
delta_hidden = error_hidden_layer * slope_hidden_layer
#change the weights
weights_output += hidden_layer_activations.T.dot(delta_output) * learning_rate
bias_output += np.sum(delta_output, axis=0, keepdims=True) * learning_rate
weights_hidden += input_data.T.dot(delta_hidden) * learning_rate
bias_hidden += np.sum(delta_hidden, axis=0, keepdims=True) * learning_rate

Splitting ndarray gives unexpected results (TensorFlow RNN tutorial)

I am following a tutorial on rnn's in TensorFlow but I have a question concerning the input formats.
They are taking raw_x (one hot vector) and basically first cutting that up in pieces of length 200 (batch_size) to form data_x. That is good.
Then they further cut up data_x in pieces of length 5 (num_step, or graph width) with:
for i in range(epoch_size):
x = data_x[:, i * num_steps:(i + 1) * num_steps]
y = data_y[:, i * num_steps:(i + 1) * num_steps]
yield (x, y)
However, if I look in the data, the slices of x do not match data_x. The first one does, but then they diverge.
Am I misunderstanding the above code? I would like to understand how x is being created or what it is supposed to look like.
I had expected the second item to be 0 1 0 1 0.
Also, I thought an epoch is when you go through the data completely, from this it seems that they split up the data in 1000 parts (epoch size)?
If it helps, this is my full code. I am trying to figure out what is going on in x. at line 48:
import numpy as np
import tensorflow as tf
# %matplotlib inline
import matplotlib.pyplot as plt
# Global config variables
num_steps = 5 # number of truncated backprop steps ('n' in the discussion above)
batch_size = 200
num_classes = 2
state_size = 4
learning_rate = 0.1
def gen_data(size=1000000):
print('generating data');
X = np.array(np.random.choice(2, size=(size,)))
Y = []
for i in range(size):
threshold = 0.5
if X[i-3] == 1:
threshold += 0.5
if X[i-8] == 1:
threshold -= 0.25
if np.random.rand() > threshold:
Y.append(0)
else:
Y.append(1)
return X, np.array(Y)
# adapted from https://github.com/tensorflow/tensorflow/blob/master/tensorflow/models/rnn/ptb/reader.py
def gen_batch(raw_data, batch_size, num_steps):
print('generating batches');
raw_x, raw_y = raw_data
data_length = len(raw_x)
# partition raw data into batches and stack them vertically in a data matrix
batch_partition_length = data_length // batch_size
data_x = np.zeros([batch_size, batch_partition_length], dtype=np.int32)
data_y = np.zeros([batch_size, batch_partition_length], dtype=np.int32)
for i in range(batch_size):
data_x[i] = raw_x[batch_partition_length * i:batch_partition_length * (i + 1)]
data_y[i] = raw_y[batch_partition_length * i:batch_partition_length * (i + 1)]
# further divide batch partitions into num_steps for truncated backprop
epoch_size = batch_partition_length // num_steps
for i in range(epoch_size):
x = data_x[:, i * num_steps:(i + 1) * num_steps]
y = data_y[:, i * num_steps:(i + 1) * num_steps]
yield (x, y)
def gen_epochs(n, num_steps):
for i in range(n):
yield gen_batch(gen_data(), batch_size, num_steps)
"""
Placeholders
"""
x = tf.placeholder(tf.int32, [batch_size, num_steps], name='input_placeholder')
y = tf.placeholder(tf.int32, [batch_size, num_steps], name='labels_placeholder')
init_state = tf.zeros([batch_size, state_size])
"""
RNN Inputs
"""
# Turn our x placeholder into a list of one-hot tensors:
# rnn_inputs is a list of num_steps tensors with shape [batch_size, num_classes]
x_one_hot = tf.one_hot(x, num_classes)
rnn_inputs = tf.unstack(x_one_hot, axis=1)
"""
Definition of rnn_cell
This is very similar to the __call__ method on Tensorflow's BasicRNNCell. See:
https://github.com/tensorflow/tensorflow/blob/master/tensorflow/python/ops/rnn_cell.py
"""
with tf.variable_scope('rnn_cell'):
W = tf.get_variable('W', [num_classes + state_size, state_size])
b = tf.get_variable('b', [state_size], initializer=tf.constant_initializer(0.0))
def rnn_cell(rnn_input, state):
with tf.variable_scope('rnn_cell', reuse=True):
W = tf.get_variable('W', [num_classes + state_size, state_size])
b = tf.get_variable('b', [state_size], initializer=tf.constant_initializer(0.0))
return tf.tanh(tf.matmul(tf.concat(axis=1, values=[rnn_input, state]), W) + b)
"""
Adding rnn_cells to graph
This is a simplified version of the "rnn" function from Tensorflow's api. See:
https://github.com/tensorflow/tensorflow/blob/master/tensorflow/python/ops/rnn.py
"""
state = init_state
rnn_outputs = []
for rnn_input in rnn_inputs:
state = rnn_cell(rnn_input, state)
rnn_outputs.append(state)
final_state = rnn_outputs[-1]
"""
Predictions, loss, training step
Losses and total_loss are simlar to the "sequence_loss_by_example" and "sequence_loss"
functions, respectively, from Tensorflow's api. See:
https://github.com/tensorflow/tensorflow/blob/master/tensorflow/python/ops/seq2seq.py
"""
#logits and predictions
with tf.variable_scope('softmax'):
W = tf.get_variable('W', [state_size, num_classes])
b = tf.get_variable('b', [num_classes], initializer=tf.constant_initializer(0.0))
logits = [tf.matmul(rnn_output, W) + b for rnn_output in rnn_outputs]
predictions = [tf.nn.softmax(logit) for logit in logits]
# Turn our y placeholder into a list labels
y_as_list = [tf.squeeze(i, axis=[1]) for i in tf.split(axis=1, num_or_size_splits=num_steps, value=y)]
#losses and train_step
losses = [tf.nn.sparse_softmax_cross_entropy_with_logits(logits=logit,labels=label) for \
logit, label in zip(logits, y_as_list)]
total_loss = tf.reduce_mean(losses)
train_step = tf.train.AdagradOptimizer(learning_rate).minimize(total_loss)
"""
Function to train the network
"""
def train_network(num_epochs, num_steps, state_size=4, verbose=True):
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
training_losses = []
for idx, epoch in enumerate(gen_epochs(num_epochs, num_steps)):
training_loss = 0
training_state = np.zeros((batch_size, state_size))
if verbose:
print("\nEPOCH", idx)
for step, (X, Y) in enumerate(epoch):
tr_losses, training_loss_, training_state, _ = \
sess.run([losses,
total_loss,
final_state,
train_step],
feed_dict={x:X, y:Y, init_state:training_state})
training_loss += training_loss_
if step % 100 == 0 and step > 0:
if verbose:
print("Average loss at step", step,
"for last 250 steps:", training_loss/100)
training_losses.append(training_loss/100)
training_loss = 0
return training_losses
training_losses = train_network(1,num_steps)
plt.plot(training_losses)

Seems like the batches are actually transposed.
So the first elements of the x-matrix (200 x 5) will fit the first 5 elements of x_raw.
Then only in the next iteration, the next 5-10 elements of x_raw will be in the first elements (again) of x.

What are c_state and m_state in Tensorflow LSTM?

Tensorflow r0.12's documentation for tf.nn.rnn_cell.LSTMCell describes this as the init:
tf.nn.rnn_cell.LSTMCell.__call__(inputs, state, scope=None)
where state is as follows:
state: if state_is_tuple is False, this must be a state Tensor, 2-D, batch x state_size. If state_is_tuple is True, this must be a tuple of state Tensors, both 2-D, with column sizes c_state and m_state.
What aare c_state and m_state and how do they fit into LSTMs? I cannot find reference to them anywhere in the documentation.
Here is a link to that page in the documentation.

I agree that the documentation is unclear. Looking at tf.nn.rnn_cell.LSTMCell.__call__ clarifies (I took the code from TensorFlow 1.0.0):
def __call__(self, inputs, state, scope=None):
"""Run one step of LSTM.
Args:
inputs: input Tensor, 2D, batch x num_units.
state: if `state_is_tuple` is False, this must be a state Tensor,
`2-D, batch x state_size`. If `state_is_tuple` is True, this must be a
tuple of state Tensors, both `2-D`, with column sizes `c_state` and
`m_state`.
scope: VariableScope for the created subgraph; defaults to "lstm_cell".
Returns:
A tuple containing:
- A `2-D, [batch x output_dim]`, Tensor representing the output of the
LSTM after reading `inputs` when previous state was `state`.
Here output_dim is:
num_proj if num_proj was set,
num_units otherwise.
- Tensor(s) representing the new state of LSTM after reading `inputs` when
the previous state was `state`. Same type and shape(s) as `state`.
Raises:
ValueError: If input size cannot be inferred from inputs via
static shape inference.
"""
num_proj = self._num_units if self._num_proj is None else self._num_proj
if self._state_is_tuple:
(c_prev, m_prev) = state
else:
c_prev = array_ops.slice(state, [0, 0], [-1, self._num_units])
m_prev = array_ops.slice(state, [0, self._num_units], [-1, num_proj])
dtype = inputs.dtype
input_size = inputs.get_shape().with_rank(2)[1]
if input_size.value is None:
raise ValueError("Could not infer input size from inputs.get_shape()[-1]")
with vs.variable_scope(scope or "lstm_cell",
initializer=self._initializer) as unit_scope:
if self._num_unit_shards is not None:
unit_scope.set_partitioner(
partitioned_variables.fixed_size_partitioner(
self._num_unit_shards))
# i = input_gate, j = new_input, f = forget_gate, o = output_gate
lstm_matrix = _linear([inputs, m_prev], 4 * self._num_units, bias=True,
scope=scope)
i, j, f, o = array_ops.split(
value=lstm_matrix, num_or_size_splits=4, axis=1)
# Diagonal connections
if self._use_peepholes:
with vs.variable_scope(unit_scope) as projection_scope:
if self._num_unit_shards is not None:
projection_scope.set_partitioner(None)
w_f_diag = vs.get_variable(
"w_f_diag", shape=[self._num_units], dtype=dtype)
w_i_diag = vs.get_variable(
"w_i_diag", shape=[self._num_units], dtype=dtype)
w_o_diag = vs.get_variable(
"w_o_diag", shape=[self._num_units], dtype=dtype)
if self._use_peepholes:
c = (sigmoid(f + self._forget_bias + w_f_diag * c_prev) * c_prev +
sigmoid(i + w_i_diag * c_prev) * self._activation(j))
else:
c = (sigmoid(f + self._forget_bias) * c_prev + sigmoid(i) *
self._activation(j))
if self._cell_clip is not None:
# pylint: disable=invalid-unary-operand-type
c = clip_ops.clip_by_value(c, -self._cell_clip, self._cell_clip)
# pylint: enable=invalid-unary-operand-type
if self._use_peepholes:
m = sigmoid(o + w_o_diag * c) * self._activation(c)
else:
m = sigmoid(o) * self._activation(c)
if self._num_proj is not None:
with vs.variable_scope("projection") as proj_scope:
if self._num_proj_shards is not None:
proj_scope.set_partitioner(
partitioned_variables.fixed_size_partitioner(
self._num_proj_shards))
m = _linear(m, self._num_proj, bias=False, scope=scope)
if self._proj_clip is not None:
# pylint: disable=invalid-unary-operand-type
m = clip_ops.clip_by_value(m, -self._proj_clip, self._proj_clip)
# pylint: enable=invalid-unary-operand-type
new_state = (LSTMStateTuple(c, m) if self._state_is_tuple else
array_ops.concat([c, m], 1))
return m, new_state
The key lines are:
c = (sigmoid(f + self._forget_bias) * c_prev + sigmoid(i) *
self._activation(j))
and
m = sigmoid(o) * self._activation(c)
and
new_state = (LSTMStateTuple(c, m)
If you compare the code to compute c and m with the LSTM equations (see below), you can see it corresponds to the cell state (typically denoted with c) and hidden state (typically denoted with h), respectively:
new_state = (LSTMStateTuple(c, m) indicates that the first element of the returned state tuple is c (cell state a.k.a. c_state), and the second element of the returned state tuple is m (hidden state a.k.a. m_state).

I've stumbled upon same question, here's how I understand it! Minimalistic LSTM example:
import tensorflow as tf
sample_input = tf.constant([[1,2,3]],dtype=tf.float32)
LSTM_CELL_SIZE = 2
lstm_cell = tf.nn.rnn_cell.BasicLSTMCell(LSTM_CELL_SIZE, state_is_tuple=True)
state = (tf.zeros([1,LSTM_CELL_SIZE]),)*2
output, state_new = lstm_cell(sample_input, state)
init_op = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init_op)
print sess.run(output)
Notice that state_is_tuple=True so when passing state to this cell, it needs to be in the tuple form. c_state and m_state are probably "Memory State" and "Cell State", though I honestly am NOT sure, as these terms are only mentioned in the docs. In the code and papers about LSTM - letters h and c are commonly used to denote "output value" and "cell state".
http://colah.github.io/posts/2015-08-Understanding-LSTMs/
Those tensors represent combined internal state of the cell, and should be passed together. Old way to do it was to simply concatenate them, and new way is to use tuples.
OLD WAY:
lstm_cell = tf.nn.rnn_cell.BasicLSTMCell(LSTM_CELL_SIZE, state_is_tuple=False)
state = tf.zeros([1,LSTM_CELL_SIZE*2])
output, state_new = lstm_cell(sample_input, state)
NEW WAY:
lstm_cell = tf.nn.rnn_cell.BasicLSTMCell(LSTM_CELL_SIZE, state_is_tuple=True)
state = (tf.zeros([1,LSTM_CELL_SIZE]),)*2
output, state_new = lstm_cell(sample_input, state)
So, basically all we did, is changed state from being 1 tensor of length 4 into two tensors of length 2. The content remained the same. [0,0,0,0] becomes ([0,0],[0,0]). (This is supposed to make it faster)

Maybe this excerpt from the code will help
def __call__(self, inputs, state, scope=None):
"""Long short-term memory cell (LSTM)."""
with vs.variable_scope(scope or type(self).__name__): # "BasicLSTMCell"
# Parameters of gates are concatenated into one multiply for efficiency.
if self._state_is_tuple:
c, h = state
else:
c, h = array_ops.split(1, 2, state)
concat = _linear([inputs, h], 4 * self._num_units, True)
# i = input_gate, j = new_input, f = forget_gate, o = output_gate
i, j, f, o = array_ops.split(1, 4, concat)
new_c = (c * sigmoid(f + self._forget_bias) + sigmoid(i) *
self._activation(j))
new_h = self._activation(new_c) * sigmoid(o)
if self._state_is_tuple:
new_state = LSTMStateTuple(new_c, new_h)
else:
new_state = array_ops.concat(1, [new_c, new_h])
return new_h, new_state

https://github.com/tensorflow/tensorflow/blob/r1.2/tensorflow/python/ops/rnn_cell_impl.py
Line #308 - 314
class LSTMStateTuple(_LSTMStateTuple):
"""Tuple used by LSTM Cells for state_size, zero_state, and output state.
Stores two elements: (c, h), in that order.
Only used when state_is_tuple=True.
"""