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Deep Learning how to split 5 dimensions timeseries and pass some dimensions through embedding layer

I have an input that is a time series of 5 dimensions:
a = [[8,3],[2] , [4,5],[1], [9,1],[2]...] #total 100 timestamps. For each element, dims 0,1 are numerical data and dim 2 is a numerical encoding of a category. This is per sample, 3200 samples
The category has 3 possible values (0,1,2)
I want to build a NN such that the last dimension (the category) will go through an embedding layer with output size 8, and then will be concatenated back to the first two dims (the numerical data).
So, this will be something like:
input1 = keras.layers.Input(shape=(2,)) #the numerical features
input2 = keras.layers.Input(shape=(1,)) #the encoding of the categories. this part will be embedded to 5 dims
x2 = Embedding(input_dim=1, output_dim = 8)(input2) #apply it to every timestamp and take only dim 3, so [2],[1], [2]
x = concatenate([input1,x2]) #will get 10 dims at each timepoint, still 100 timepoints
x = LSTM(units=24)(x) #the input has 10 dims/features at each timepoint, total 100 timepoints per sample
x = Dense(1, activation='sigmoid')(x)
model = Model(inputs=[input1, input2] , outputs=[x]) #input1 is 1D vec of the width 2 , input2 is 1D vec with the width 1 and it is going through the embedding
model.compile(
loss='binary_crossentropy',
optimizer='adam',
metrics=['acc']
)
How can I do it? (preferably in keras)?
My problem is how to apply the embedding to every time point?
Meaning, if I have 1000 timepoints with 3 dims each, I need to convert it to 1000 timepoints with 8 dims each (The emebedding layer should transform input2 from (1000X1) to (1000X8)

There are a couple of issues you are having here.
First let me give you a working example and explain along the way how to solve your issues.
Imports and Data Generation
import tensorflow as tf
import numpy as np
from tensorflow.keras import layers
from tensorflow.keras.models import Model
num_timesteps = 100
max_features_values = [100, 100, 3]
num_observations = 2
input_list = [[[np.random.randint(0, v) for _ in range(num_timesteps)]
for v in max_features_values]
for _ in range(num_observations)]
input_arr = np.array(input_list) # shape (2, 3, 100)
In order to use an embedding we need to the voc_size as input_dimension, as stated in the LSTM documentation.
Embedding and Concatenation
voc_size = len(np.unique(input_arr[:, 2, :])) + 1 # 4
Now we need to create the inputs. Inputs should be of size [None, 2, num_timesteps] and [None, 1, num_timesteps] where the first dimension is the flexible and will be filled with the number of observations we are passing in. Let's use the embedding right after that using the previously calculated voc_size.
inp1 = layers.Input(shape=(2, num_timesteps)) # TensorShape([None, 2, 100])
inp2 = layers.Input(shape=(1, num_timesteps)) # TensorShape([None, 1, 100])
x2 = layers.Embedding(input_dim=voc_size, output_dim=8)(inp2) # TensorShape([None, 1, 100, 8])
x2_reshaped = tf.transpose(tf.squeeze(x2, axis=1), [0, 2, 1]) # TensorShape([None, 8, 100])
This cannot be easily concatenated since all dimensions must match except for the one along the concatenation axis. But the shapes are not matching unfortunately. Therefore we reshape x2. We do so by removing the first dimension and then transposing.
Now we can concatenate without any issue and everything works in a straight forward fashion:
x = layers.concatenate([inp1, x2_reshaped], axis=1)
x = layers.LSTM(32)(x)
x = layers.Dense(1, activation='sigmoid')(x)
model = Model(inputs=[inp1, inp2], outputs=[x])
Check on Dummy Example
inp1_np = input_arr[:, :2, :]
inp2_np = input_arr[:, 2:, :]
model.predict([inp1_np, inp2_np])
# Output
# array([[0.544262 ],
# [0.6157502]], dtype=float32)
#This outputs values between 0 and 1 just as expected.

In case you are not looking for Embeddings the way it's usually used in Keras (positive integers mapping to dense vectors). You might be looking for some sort of unprojection or basis expansion, in which 3 dimensions get mapped (embedded) to 8 and concatenating the result. This can be done using the kernel trick or other methods, but also happens implicitly in neural networks with non-linear applications.
As such, you can do something like this, following a similar format to pythonic833 because it was good (but with timestamps in the middle per the Keras LSTM documentation asking for [batch, timesteps, feature]):
Input generation
import tensorflow as tf
import numpy as np
from tensorflow.keras import layers
from tensorflow.keras.models import Model
num_timesteps = 100
num_features = 5
num_observations = 2
input_list = [[[np.random.randint(1, 100) for _ in range(num_features)]
for _ in range(num_timesteps)]
for _ in range(num_observations)]
input_arr = np.array(input_list) # shape (2, 100, 5)
Model construction
Then you can process the inputs:
input1 = layers.Input(shape=(num_timesteps, 2,))
input2 = layers.Input(shape=(num_timesteps, 3))
x2 = layers.Dense(8, activation='relu')(input2)
x = layers.concatenate([input1,x2], axis=2) # This produces tensors of shape (None, 100, 10)
x = layers.LSTM(units=24)(x)
x = layers.Dense(1, activation='sigmoid')(x)
model = Model(inputs=[input1, input2] , outputs=[x])
model.compile(
loss='binary_crossentropy',
optimizer='adam',
metrics=['acc']
)
Results
inp1_np = input_arr[:, :, :2]
inp2_np = input_arr[:, :, 2:]
model.predict([inp1_np, inp2_np])
which produces
array([[0.44117224],
[0.23611131]], dtype=float32)
Other explanations about basis expansion to check out:
https://stats.stackexchange.com/questions/527258/embedding-data-into-a-larger-dimension-space
https://www.reddit.com/r/MachineLearning/comments/2ffejw/why_dont_researchers_use_the_kernel_method_in/

Tensorflow Predicting Sequence

So my task is to predict sequence. I have x,y,z values at time t which are float type. I have to predict sequence that has values x,y,z at time (t + 1).
TIME_STEP = 10
N_FEATURES = N_CLASSES = 3
LEARNING_RATE = 0.01
EPOCHS = 50
BATCH_SIZE = 10
x = tf.placeholder(tf.float32, shape = [None, N_FEATURES], name = 'name')
y = tf.placeholder(tf.float32, shape = [N_CLASSES], name = 'labels')
then I have my lstm model, which looks like:
x = tf.transpose(x, [1, 0])
x = tf.reshape(x, [-1, num_features])
hidden = tf.nn.relu(tf.matmul(x, self.h_W) + self.h_biases)
hidden = tf.split(hidden, self.time_step)
lstm_layers = [tf.contrib.rnn.BasicLSTMCell(self.hidden_units, forget_bias=1.0) for _ in range(2)]
lstm_layers = tf.contrib.rnn.MultiRNNCell(lstm_layers)
outputs, _ = tf.contrib.rnn.static_rnn(lstm_layers, hidden, dtype = tf.float32)
lstm_output = outputs[-1]
and finally I define loss function and optimizer
loss = tf.reduce_mean(tf.square(y - y_pred))
opt = tf.train.AdamOptimizer(learning_rate = LEARNING_RATE).minimize(loss)
for now I want to take previous 10 values to predict the 11th one. so I run session like
for time in range(0, len(X)):
sess.run(opt, feed_dict = {x : X[time: time + TIME_STEP ],
y : Y[time + TIME_STEP + 1]})
but when I check loss for this function it has huge value like 99400290.0 and it increases time by time. This is my first experience with predicting sequences so I think I must be missing something huge

Yes, you should normalize your real world input data and it should use the same scaling (same parameters) that you used on your training set.
The reason is, now your model is trained to accept inputs of a certain shape and scale and for it to perform as intended you'll have to scale your test inputs to it.
(sorry for posting this as an answer, not enough rep for commenting)

Have tf.layers.dense connected to different inputs OR have tf.train.optimizer optimize tensors?

I am new to tensorflow and more advanced machine learning, so I tried to get a better grasp of RNNs by implementing one by hand instead of using tf.contrib.rnn.RNNCell. My first problem was that I needed to unroll the net for backpropogation so I looped through my sequence and I needed to keep consistent weights and biases, so I couldn't reinitialize a dense layer with tf.layers.dense each time, but I also needed to have my layer connected to the current timestep of my sequence and I couldn't find a way to change what a dense layer was connected to. To work around this I tried to implement my own version of tf.layers.dense, and this worked fine until I got the error: NotImplementedError("Trying to update a Tensor " ...) when I tried to optimize my custom dense layers.
My code:
import tensorflow as tf
import numpy as np
from tensorflow.contrib import rnn
import random
# -----------------
# WORD PARAMETERS
# -----------------
target_string = ['Hello ','Hello ','World ','World ', '!']
number_input_words = 1
# --------------------------
# TRAINING HYPERPARAMETERS
# --------------------------
training_steps = 4000
batch_size = 9
learning_rate = 0.01
display_step = 150
hidden_cells = 20
# ----------------------
# PREPARE DATA AS DICT
# ----------------------
# TODO AUTOMATICALLY CREATE DICT
dictionary = {'Hello ': 0, 'World ': 1, '!': 2}
reverse_dictionary = dict(zip(dictionary.values(), dictionary.keys()))
vocab_size = len(dictionary)
# ------------
# LSTM MODEL
# ------------
class LSTM:
def __init__(self, sequence_length, number_input_words, hidden_cells, mem_size_x, mem_size_y, learning_rate):
self.sequence = tf.placeholder(tf.float32, (sequence_length, vocab_size), 'sequence')
self.memory = tf.zeros([mem_size_x, mem_size_y])
# sequence_length = self.sequence.shape[0]
units = [vocab_size, 5,4,2,6, vocab_size]
weights = [tf.random_uniform((units[i-1], units[i])) for i in range(len(units))[1:]]
biases = [tf.random_uniform((1, units[i])) for i in range(len(units))[1:]]
self.total_loss = 0
self.outputs = []
for word in range(sequence_length-1):
sequence_w = tf.reshape(self.sequence[word], [1, vocab_size])
layers = []
for i in range(len(weights)):
if i == 0:
layers.append(tf.matmul(sequence_w, weights[0]) + biases[0])
else:
layers.append(tf.matmul(layers[i-1], weights[i]) + biases[i])
percentages = tf.nn.softmax(logits=layers[-1])
self.outputs.append(percentages)
self.total_loss += tf.losses.absolute_difference(tf.reshape(self.sequence[word+1], (1, vocab_size)), tf.reshape(percentages, (1, vocab_size)))
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
self.train_operation = optimizer.minimize(loss=self.total_loss, var_list=weights+biases, global_step=tf.train.get_global_step())
lstm = LSTM(len(target_string), number_input_words, hidden_cells, 10, 5, learning_rate)
# ---------------
# START SESSION
# ---------------
with tf.Session() as sess:
sess.run(tf.local_variables_initializer())
sess.run(tf.global_variables_initializer())
sequence = []
for i in range(len(target_string)):
x = [0]*vocab_size
x[dictionary[target_string[i]]] = 1
sequence.append(x)
print(sequence)
for x in range(1000):
sess.run(lstm.train_operation, feed_dict={lstm.sequence: sequence})
prediction, loss = sess.run((lstm.outputs, lstm.total_loss), feed_dict= {lstm.sequence: sequence})
print(prediction)
print(loss)
Any answers that tell me either how to either connect tf.layers.dense to different variables each time or tell me how to get around my NotImplementedError would be greatly appreciated. I apologize if this question is lengthy or just badly worded, i'm still new to stackoverflow.
EDIT:
I've updated the LSTM class part of my code to:
(Inside def init)
self.sequence = [tf.placeholder(tf.float32, (batch_size, vocab_size), 'sequence') for _ in range(sequence_length-1)]
self.total_loss = 0
self.outputs = []
rnn_cell = rnn.BasicLSTMCell(hidden_cells)
h = tf.zeros((batch_size, hidden_cells))
for i in range(sequence_length-1):
current_sequence = self.sequence[i]
h = rnn_cell(current_sequence, h)
self.outputs.append(h)
But I still get an error on the line: h = rnn_cell(current_sequence, h) about not being able to iterate over tensors. I'm not trying to iterate over any tensors, and if I am I don't mean to.

So there's a standard way of approaching this issue (this is the best approach I know from my knowledge) Instead of trying to create a new list of dense layers. Do the following. Before that lets assume your hidden layer size is h_dim and number of steps to unroll is num_unroll and batch size batch_size
In a for loop, you calculate the output of the RNNCell for each unrolled input
h = tf.zeros(...)
outputs= []
for ui in range(num_unroll):
out, state = rnn_cell(x[ui],state)
outputs.append(out)
Now concat all the outputs to a single tensor of size, [batch_size*num_unroll, h_dim]
Send this through a single dense layer of size [h_dim, num_classes]
logits = tf.matmul(tf.concat(outputs,...), w) + b
predictions = tf.nn.softmax(logits)
You have the logits for all the unrolled inputs now. Now it's just a matter of reshaping the tensor to a [batch_size, num_unroll, num_classes] tensor.
Edited (Feeding in Data): The data will be presented in the form of a list of num_unroll many placeholders. So,
x = [tf.placeholder(shape=[batch_size,3]...) for ui in range(num_unroll)]
Now say you have data like below,
Hello world bye
Bye hello world
Here batch size is 2, sequence length is 3. Once converted to one hot encoding, you're data looks like below (shape [time_steps, batch_size, 3].
data = [ [ [1,0,0], [0,0,1] ], [ [0,1,0], [1,0,0] ], [ [0,0,1], [0,1,0] ] ]
Now feed data in, in the following format.
feed_dict = {}
for ui in range(3):
feed_dict[x[ui]] = data[ui]

Tensorflow: Simple 3D Convnet not learning

I am trying to create a simple 3D U-net for image segmentation, just to learn how to use the layers. Therefore I do a 3D convolution with stride 2 and then a transpose deconvolution to get back the same image size. I am also overfitting to a small set (test set) just to see if my network is learning.
I created the same net in Keras and it works just fine. Now I want to create in tensorflow but I been having trouble with it.
The cost changes slightly but no matter what I do (reduce learning rate, add more epochs, add more layers, change batch size...) the output is always the same. I believe the net is not updating the weights. I am sure I am doing something wrong but I can find what it is. Any help would be greatly appreciate it.
Here is my code:
def forward_propagation(X):
if ( mode == 'train'): print(" --------- Net --------- ")
# Convolutional Layer 1
with tf.variable_scope('CONV1'):
Z1 = tf.layers.conv3d(X, filters = 16, kernel =[3,3,3], strides = [ 2, 2, 2], padding='SAME', name = 'S2/conv3d')
A1 = tf.nn.relu(Z1, name = 'S2/ReLU')
if ( mode == 'train'): print("Convolutional Layer 1 S2 " + str(A1.get_shape()))
# DEConvolutional Layer 1
with tf.variable_scope('DeCONV1'):
output_deconv1 = tf.stack([X.get_shape()[0] , X.get_shape()[1], X.get_shape()[2], X.get_shape()[3], 1])
dZ1 = tf.nn.conv3d_transpose(A1, filters = 1, kernel =[3,3,3], strides = [2, 2, 2], padding='SAME', name = 'S2/conv3d_transpose')
dA1 = tf.nn.relu(dZ1, name = 'S2/ReLU')
if ( mode == 'train'): print("Deconvolutional Layer 1 S1 " + str(dA1.get_shape()))
return dA1
def compute_cost(output, target, method = 'dice_hard_coe'):
with tf.variable_scope('COST'):
if (method == 'sigmoid_cross_entropy') :
# Make them vectors
output = tf.reshape( output, [-1, output.get_shape().as_list()[0]] )
target = tf.reshape( target, [-1, target.get_shape().as_list()[0]] )
loss = tf.nn.sigmoid_cross_entropy_with_logits(logits = output, labels = target)
cost = tf.reduce_mean(loss)
return cost
and the main function for the model:
def model(X_h5, Y_h5, learning_rate = 0.009,
num_epochs = 100, minibatch_size = 64, print_cost = True):
ops.reset_default_graph() # to be able to rerun the model without overwriting tf variables
#tf.set_random_seed(1) # to keep results consistent (tensorflow seed)
#seed = 3 # to keep results consistent (numpy seed)
(m, n_D, n_H, n_W, num_channels) = X_h5["test_data"].shape #TTT
num_labels = Y_h5["test_mask"].shape[4] #TTT
img_size = Y_h5["test_mask"].shape[1] #TTT
costs = [] # To keep track of the cost
accuracies = [] # To keep track of the accuracy
# Create Placeholders of the correct shape
X, Y = create_placeholders(n_H, n_W, n_D, minibatch_size)
# Forward propagation: Build the forward propagation in the tensorflow graph
nn_output = forward_propagation(X)
prediction = tf.nn.sigmoid(nn_output)
# Cost function: Add cost function to tensorflow graph
cost_method = 'sigmoid_cross_entropy'
cost = compute_cost(nn_output, Y, cost_method)
# Backpropagation: Define the tensorflow optimizer. Use an AdamOptimizer that minimizes the cost.
optimizer = tf.train.AdamOptimizer(learning_rate = learning_rate).minimize(cost)
# Initialize all the variables globally
init = tf.global_variables_initializer()
# Start the session to compute the tensorflow graph
with tf.Session() as sess:
print('------ Training ------')
# Run the initialization
tf.local_variables_initializer().run(session=sess)
sess.run(init)
# Do the training loop
for i in range(num_epochs*m):
# ----- TRAIN -------
current_epoch = i//m
patient_start = i-(current_epoch * m)
patient_end = patient_start + minibatch_size
current_X_train = np.zeros((minibatch_size, n_D, n_H, n_W,num_channels))
current_X_train[:,:,:,:,:] = np.array(X_h5["test_data"][patient_start:patient_end,:,:,:,:]) #TTT
current_X_train = np.nan_to_num(current_X_train) # make nan zero
current_Y_train = np.zeros((minibatch_size, n_D, n_H, n_W, num_labels))
current_Y_train[:,:,:,:,:] = np.array(Y_h5["test_mask"][patient_start:patient_end,:,:,:,:]) #TTT
current_Y_train = np.nan_to_num(current_Y_train) # make nan zero
feed_dict = {X: current_X_train, Y: current_Y_train}
_ , temp_cost = sess.run([optimizer, cost], feed_dict=feed_dict)
# ----- TEST -------
# Print the cost every 1/5 epoch
if ((i % (num_epochs*m/5) )== 0):
# Calculate the predictions
test_predictions = np.zeros(Y_h5["test_mask"].shape)
for j in range(0, X_h5["test_data"].shape[0], minibatch_size):
patient_start = j
patient_end = patient_start + minibatch_size
current_X_test = np.zeros((minibatch_size, n_D, n_H, n_W, num_channels))
current_X_test[:,:,:,:,:] = np.array(X_h5["test_data"][patient_start:patient_end,:,:,:,:])
current_X_test = np.nan_to_num(current_X_test) # make nan zero
current_Y_test = np.zeros((minibatch_size, n_D, n_H, n_W, num_labels))
current_Y_test[:,:,:,:,:] = np.array(Y_h5["test_mask"][patient_start:patient_end,:,:,:,:])
current_Y_test = np.nan_to_num(current_Y_test) # make nan zero
feed_dict = {X: current_X_test, Y: current_Y_test}
_, current_prediction = sess.run([cost, prediction], feed_dict=feed_dict)
test_predictions[j:j + minibatch_size,:,:,:,:] = current_prediction
costs.append(temp_cost)
print ("[" + str(current_epoch) + "|" + str(num_epochs) + "] " + "Cost : " + str(costs[-1]))
display_progress(X_h5["test_data"], Y_h5["test_mask"], test_predictions, 5, n_H, n_W)
# plot the cost
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('epochs')
plt.show()
return
I call the model with:
model(hdf5_data_file, hdf5_mask_file, num_epochs = 500, minibatch_size = 1, learning_rate = 1e-3)
These are the results that I am currently getting:
Edit:
I have tried reducing the learning rate and it doesn't help. I also tried using tensorboard debug and the weights are not being updated:
I am not sure why this is happening.
I Created the same simple model in keras and it works fine. I am not sure what I am doing wrong in tensorflow.

Not sure if you are still looking for help, as I am answering this question half a year later your posted date. :) I've listed my observations and also some suggestions for you to try below. It my primary observation is right... then you probably just need a coffee break / a night of good sleep.
primary observation:
tf.reshape( output, [-1, output.get_shape().as_list()[0]] ) seems wrong. If you prefer to flatten the vector, it should be something like tf.reshape(output,[-1,np.prod(image_shape_list)]).
other observations:
With such a shallow network, I doubt the network have enough spatial resolution to differentiate tumor voxels from non-tumor voxels. Can you show the keras implementation and the performance compared to a pure tf implementation? I would probably go with 2+ layers, let's .
say with 3 layers, with a stride of 2 per layer, and an input image width of 256, you will end with a width of 32 at your deepest encoder layer. (If you have a limited GPU memory, downsample the input image.)
if changing the loss computation does not work, as #bremen_matt mentioned, reduce LR to say maybe 1e-5.
after the basic architecture tweaks and you "feel" that the network is sort of learning and not stuck, try augmenting the training data, add dropout, batch norm during training, and then maybe fancy up your loss by adding a discriminator.

How to feed back RNN output to input in tensorflow

In case where suppose I have a trained RNN (e.g. language model), and I want to see what it would generate on its own, how should I feed its output back to its input?
I read the following related questions:
TensorFlow using LSTMs for generating text
TensorFlow LSTM Generative Model
Theoretically it is clear to me, that in tensorflow we use truncated backpropagation, so we have to define the max step which we would like to "trace". Also we reserve a dimension for batches, therefore if I'd like to train a sine wave, I have to feed [None, num_step, 1] inputs.
The following code works:
tf.reset_default_graph()
n_samples=100
state_size=5
lstm_cell = tf.nn.rnn_cell.BasicLSTMCell(state_size, forget_bias=1.)
def_x = np.sin(np.linspace(0, 10, n_samples))[None, :, None]
zero_x = np.zeros(n_samples)[None, :, None]
X = tf.placeholder_with_default(zero_x, [None, n_samples, 1])
output, last_states = tf.nn.dynamic_rnn(inputs=X, cell=lstm_cell, dtype=tf.float64)
pred = tf.contrib.layers.fully_connected(output, 1, activation_fn=tf.tanh)
Y = np.roll(def_x, 1)
loss = tf.reduce_sum(tf.pow(pred-Y, 2))/(2*n_samples)
opt = tf.train.AdamOptimizer().minimize(loss)
sess = tf.InteractiveSession()
tf.global_variables_initializer().run()
# Initial state run
plt.show(plt.plot(output.eval()[0]))
plt.plot(def_x.squeeze())
plt.show(plt.plot(pred.eval().squeeze()))
steps = 1001
for i in range(steps):
p, l, _= sess.run([pred, loss, opt])
The state size of the LSTM can be varied, also I experimented with feeding sine wave into the network and zeros, and in both cases it converged in ~500 iterations. So far I have understood that in this case the graph consists n_samples number of LSTM cells sharing their parameters, and it is only up to me that I feed input to them as a time series. However when generating samples the network is explicitly depending on its previous output - meaning that I cannot feed the unrolled model at once. I tried to compute the state and output at every step:
with tf.variable_scope('sine', reuse=True):
X_test = tf.placeholder(tf.float64)
X_reshaped = tf.reshape(X_test, [1, -1, 1])
output, last_states = tf.nn.dynamic_rnn(lstm_cell, X_reshaped, dtype=tf.float64)
pred = tf.contrib.layers.fully_connected(output, 1, activation_fn=tf.tanh)
test_vals = [0.]
for i in range(1000):
val = pred.eval({X_test:np.array(test_vals)[None, :, None]})
test_vals.append(val)
However in this model it seems that there is no continuity between the LSTM cells. What is going on here?
Do I have to initialize a zero array with i.e. 100 time steps, and assign each run's result into the array? Like feeding the network with this:
run 0: input_feed = [0, 0, 0 ... 0]; res1 = result
run 1: input_feed = [res1, 0, 0 ... 0]; res2 = result
run 1: input_feed = [res1, res2, 0 ... 0]; res3 = result
etc...
What to do if I want to use this trained network to use its own output as its input in the following time step?

If I understood you correctly, you want to find a way to feed the output of time step t as input to time step t+1, right? To do so, there is a relatively easy work around that you can use at test time:
Make sure your input placeholders can accept a dynamic sequence length, i.e. the size of the time dimension is None.
Make sure you are using tf.nn.dynamic_rnn (which you do in the posted example).
Pass the initial state into dynamic_rnn.
Then, at test time, you can loop through your sequence and feed each time step individually (i.e. max sequence length is 1). Additionally, you just have to carry over the internal state of the RNN. See pseudo code below (the variable names refer to your code snippet).
I.e., change the definition of the model to something like this:
lstm_cell = tf.nn.rnn_cell.BasicLSTMCell(state_size, forget_bias=1.)
X = tf.placeholder_with_default(zero_x, [None, None, 1]) # [batch_size, seq_length, dimension of input]
batch_size = tf.shape(self.input_)[0]
initial_state = lstm_cell.zero_state(batch_size, dtype=tf.float32)
def_x = np.sin(np.linspace(0, 10, n_samples))[None, :, None]
zero_x = np.zeros(n_samples)[None, :, None]
output, last_states = tf.nn.dynamic_rnn(inputs=X, cell=lstm_cell, dtype=tf.float64,
initial_state=initial_state)
pred = tf.contrib.layers.fully_connected(output, 1, activation_fn=tf.tanh)
Then you can perform inference like so:
fetches = {'final_state': last_state,
'prediction': pred}
toy_initial_input = np.array([[[1]]]) # put suitable data here
seq_length = 20 # put whatever is reasonable here for you
# get the output for the first time step
feed_dict = {X: toy_initial_input}
eval_out = sess.run(fetches, feed_dict)
outputs = [eval_out['prediction']]
next_state = eval_out['final_state']
for i in range(1, seq_length):
feed_dict = {X: outputs[-1],
initial_state: next_state}
eval_out = sess.run(fetches, feed_dict)
outputs.append(eval_out['prediction'])
next_state = eval_out['final_state']
# outputs now contains the sequence you want
Note that this can also work for batches, however it can be a bit more complicated if you sequences of different lengths in the same batch.
If you want to perform this kind of prediction not only at test time, but also at training time, it is also possible to do, but a bit more complicated to implement.

You can use its own output (last state) as the next-step input (initial state).
One way to do this is to:
use zero-initialized variables as the input state at every time step
each time you completed a truncated sequence and got some output state, update the state variables with this output state you just got.
The second can be done by either:
fetching the states to python and feeding them back next time, as done in the ptb example in tensorflow/models
build an update op in the graph and add a dependency, as done in the ptb example in tensorpack.

I know I'm a bit late to the party but I think this gist could be useful:
https://gist.github.com/CharlieCodex/f494b27698157ec9a802bc231d8dcf31
It lets you autofeed the input through a filter and back into the network as input. To make shapes match up processing can be set as a tf.layers.Dense layer.
Please ask any questions!
Edit:
In your particular case, create a lambda which performs the processing of the dynamic_rnn outputs into your character vector space. Ex:
# if you have:
W = tf.Variable( ... )
B = tf.Variable( ... )
Yo, Ho = tf.nn.dynamic_rnn( cell , inputs , state )
logits = tf.matmul(W, Yo) + B
...
# use self_feeding_rnn as
process_yo = lambda Yo: tf.matmul(W, Yo) + B
Yo, Ho = self_feeding_rnn( cell, seed, initial_state, processing=process_yo)