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In this blog, let us discuss the **concepts** behind the working of Recurrent Neural Networks. Recurrent Neural Networks have **wide applications** in image and video recognition, music composition and machine translation.

We will be checking out the following concepts:

- Why Not Feed-forward Networks?
- What Are Recurrent Neural Networks?
- How To Train Recurrent Neural Networks?
- Vanishing And Exploding Gradients
- Long Short Term Memory (LSTM) Networks
- LSTM Use-Case

Consider an **image classification** use-case where you have **trained** the neural network to **classify images** of various **animals.**

So, let’s say you **feed** in an **image** of a **cat** or a **dog,** the network actually provides an **output** with a **corresponding label** to the image of a cat or a dog **respectively.**

Consider the following diagram:

Here, the **first output** being an **elephant** will have **no influence** of the **previous output** which was a **dog.** This means that output at time **‘t’** is **independent** of output at time **‘t-1’**.

Consider this **scenario** where you will require the **use** of the **previously obtained output:**

The concept is similar to **reading** a **book.** With **every page** you move forward into, you need the **understanding** of the **previous pages** to make **complete** sense of the **information** ahead in most of the **cases.**

With a **feed-forward network** the **new** output at time **‘t+1’** has **no relation** with outputs at either time t, t-1 or t-2.

So, feed-forward networks **cannot be used** when **predicting** a **word** in a sentence as it will have no **absolute relation** with the **previous** set of **words.**

But, with **Recurrent Neural Networks,** this challenge can be **overcome.**

Consider the following diagram:

In the above diagram, we have **certain inputs** at **‘t-1’** which is **fed** into the network. These **inputs** will lead to **corresponding outputs** at time ‘t-1’ as well.

At the **next timestamp,** information from the **previous** input ‘t-1’ is provided **along** with the **input** at ‘t’ to eventually **provide** the **output** at ‘t’ as well.

This process **repeats,** to ensure that the **latest inputs** are **aware** and can use the **information** from the previous **timestamp** is **obtained.**

Next up in this **Recurrent Neural Networks** blog, we need to check out **what** Recurrent Neural Networks (RNNs) **actually are.**

Recurrent Networks are a **type** of **artificial neural network** designed to **recognize patterns** in sequences of data, such as **text,** genomes, handwriting, the spoken word, numerical times **series** data emanating from sensors, **stock markets** and **government agencies.**

For a better clarity, consider the following **analogy:**

You go to the **gym** **regularly** and the **trainer** has given you the following **schedule** for your workout:

Note that all these **exercises** are **repeated** in a proper order **every week.** First, let us use a **feed-forward network** to try and **predict** the type of exercise.

The inputs are **day, month** and the **health status.** A neural network has to be **trained** using these inputs to provide us the with the **prediction** of the **exercises.**

However, this will **not be very accurate** considering the input. To **fix** **this,** we can make use of the concept of **Recurrent Neural Networks** as shown below:

In this case, consider the **inputs** to be the **workout** done on the **previous day.**

So if you did a **shoulder workout** yesterday, you can do a **bicep exercise** today and this **goes on** for the **rest** of the **week** as well.

However, if you happen to **miss** **a ** **day** at the gym, the data from the **previously attended timestamp** can be **considered** as shown below:

If a **model** is trained based on the data it can **obtain** from the **previous exercises,** the output from the model will be **extremely accurate.**

To sum it up, let us **convert** the **data** we have into **vectors.** Well, **what are vectors?**

**Vectors** are **numbers** which are input to the **model** to **denote** if you have **done** the **exercise** or **not.**

So, if you have a **shoulder exercise,** the corresponding **node** will be **‘1’** and the **rest** of the **exercise** nodes will be **mapped** to **‘0’.**

Let us check out the **math** behind the **working** of the **neural network.** Consider the following diagram:

Consider **‘w’** to be the **weight matrix** and **‘b’** being the **bias:**

At time **t=0,** input is **‘x0’** and the task is to figure out what is **‘h0’.** Substituting **t=0** in the **equation** and obtaining the function **h(t) value.** Next, the value of **‘y0’** is found out using the **previously calculated values** when applied to the **new formula.**

This process is **repeated** through **all** of the **timestamps** in the model to **train** a **model.**

So, **how** are Recurrent Neural Networks **trained?**

Recurrent Neural Networks use **backpropagation algorithm** for training, **but** it is **applied** for every **timestamp.** It is commonly known as **Back-propagation Through Time (BTT).**

There are **some issues** with Back-propagation such as:

**Vanishing Gradient****Exploding Gradient**

Let us consider each of these to understand what is going on

When making use of **back-propagation** the **goal** is to **calculate** the **error** which is actually found out by **finding out** the **difference** between the **actual output** and the **model output** and raising that to a power of 2.

Consider the following diagram:

With the **error calculated,** the **changes** in the error with respect to the **change** in the **weight** is **calculated.** But with each **learning** rate, this has to be **multiplied** with the same.

So, the **product** of the **learning rate** with the change **leads** to the value which is the **actual change** in the **weight.**

This change in **weight** is added to the old **set of** **weights** for every training iteration as shown in the **figure.** The issue here is when the **change** **in** **weight** is multiplied, the **value** is **very less.**

Consider you are **predicting** a **sentence** say,**“I am going to** **France”** and you want to predict **“I am going to France, the language spoken there is _____”**

**A lot of iterations** will cause the new weights to be **extremely negligible** and this leads to the **weights not** being **updated.**

The working of the exploding gradient is **similar** but the **weights here** change **drastically** instead of **negligible change.** Notice the **small change** in the diagram below:

We need to **overcome both** of these and it is a **bit** of a **challenge** at first. Consider the following chart:

Continuing this blog on Recurrent Neural Networks, we will be **discussing further on LSTM networks.**

Long Short-Term Memory networks are usually just called **“LSTMs”.**

They are a **special kind** of Recurrent Neural Networks which are **capable** of **learning long-term dependencies.**

**What are long-term dependencies?**

Many times only **recent data** is needed in a model to **perform operations.** But there might be a **requirement** from a **data** which was **obtained** in the **past.**

Let’s look at the following example:

Consider a **language model** trying to predict the **next word** based on the previous ones. If we are trying to **predict** the **last word** in the sentence say **“The clouds are in the sky”**.

The context here was **pretty simple** and the last word ends up being **sky** all the time. In such cases, the gap between the **past information** and the **current requirement** can be **bridged** really easily by using **Recurrent Neural Networks.**

So, problems like **Vanishing** and **Exploding Gradients** do **not exist** and this makes LSTM networks handle **long-term dependencies** easily.

LSTM have **chain-like** neural network layer. In a standard recurrent neural network, the repeating module consists of one **single function **as shown in the below figure:

As shown above, there is a **tanh function** present in the layer. This function is a **squashing function.** So, **what is a squashing function?**

It is a **function** which is basically used in the **range of -1 to +1** and to **manipulate** the **values** based on the **inputs.**

Now, let us consider the **structure** of an LSTM network:

As denoted from the image, each of the functions in the layers has their own structures when it comes to LSTM networks. The cell state is the horizontal line in the figure and it acts like a conveyer belt carrying certain data linearly across the data channel.

Let us consider a step-by-step approach to understand LSTM networks better.

**Step 1:**

The first step in the **LSTM** is to **identify** that information which is **not required** and will be **thrown away** from the **cell state.** This decision is made by a **sigmoid layer** called as **forget gate** **layer.**

The **highlighted layer** in the above is the **sigmoid layer** which is **previously mentioned.**

The **calculation** is **done** by considering the **new input** and the **previous timestamp** which eventually **leads** to the **output** of a number **between 0 and 1** for **each** number in that **cell state.**

As typical binary, **1** represents to **kee**p the cell state while **0** represents to **trash** it.

Consider **gender classification,** it is really important to consider the **latest** and **correct gender** when the network is being **used.**

**Step 2:**

The next step is to **decide,** what **new information** we’re going to **store** in the cell state. This whole process comprises of following steps:

- A
**sigmoid layer**called the “input gate layer” decides**which values**will be**updated.** - The
**tanh layer**creates a**vector**of**new candidate**values, that could be**added**to the state.

The input from the **previous timestamp** and the new input are **passed** through a **sigmoid function** which gives the value **i(t).** This value is then **multiplied by c(t)** and then added to the **cell state.**

In the next step, these **two** are **combined** to **update** the **state.**

**Step 3:**

Now, we will **update** the **old cell state Ct−1,** into the **new** cell state **Ct.**

First, we **multiply** the **old** state **(Ct−1)** by f(t), **forgetting** the things we **decided** to **leave behind** earlier.

Then, we **add i_t* c˜_t.** This is the **new candidate** values, **scaled** by how much we decided to **update each state** value.

In the second step, we decided to do **make use** of the **data** which is only required at that **stage.**

In the third step, we actually **implement** it.

In the language case example which was **previously discussed,** there is where the **old gender** would be **dropped** and the **new gender** would be **considered.**

**Step 4:**

We will run a **sigmoid layer** which decides what **parts** of the **cell state** we’re going to **output.**

Then, we put the **cell state** through **tanh** (push the values to be between −1 and 1)

Later, we **multiply** it by the **output** of the **sigmoid gate,** so that we only output the **parts** we decided to.

The **calculation** in this step is pretty much **straightforward** which **eventually** leads to the **output.**

However, the **output** consists of only the **outputs** there were decided to be **carry forwarded** in the **previous** steps and not all the **outputs** at once.

Summing up all the 4 steps:

In the **first** step, **we found out what was needed to be dropped.**

**The second** step consisted of w**hat new inputs are added to the network.**

**The third** step was to **combine the previously obtained inputs to generate the new cell states.**

**Lastly,** we arrived at the **output as per requirement.**

Next up on this blog about Recurrent Neural Networks, let us consider an** interesting use-case.**

The use case we will be **considering** is to **predict** the **next word** in a sample short story.

We can start by **feeding** an **LSTM** Network with **correct sequences** from the text of 3 **symbols** as **inputs** and 1 labeled symbol.

Eventually, the neural network will **learn** to **predict** the next symbol **correctly!**

**Dataset:**

The LSTM is trained using a **sample short story** which consists of **112 unique symbols. Comma** and **period** are also **considered** as **unique symbols** in this **case.**

*“long ago , the mice had a general council to consider what measures they could take to outwit their common enemy , the cat . some said this , and some said that but at last a young mouse got up and said he had a proposal to make , which he thought would meet the case . you will all agree , said he , that our chief danger consists in the sly and treacherous manner in which the enemy approaches us . now , if we could receive some signal of her approach , we could easily escape from her . **i** venture , therefore , to propose that a small bell be procured , and attached by a ribbon round the neck of the cat . by this means we should always know when she was about , and could easily retire while she was in the neighborhood . this proposal met with general applause , until an old mouse got up and said that is all very well , but who is to bell the cat ? the mice looked at one another and nobody spoke . then the old mouse said it is easy to propose impossible remedies .”*

**Training:**

We already know that **LSTMs** can only **understand real numbers.** So, the first **requirement** is to **convert** the unique symbols into **unique integer** values based on the **frequency** of **occurrence.**

Doing this will create a **customized dictionary** that we can **make use** of later on to **map** the values.

In the above figure, **certain symbols** are mapped to be **integers** as shown.

The network will create a **112-element vector** consisting of the **probability** of **occurrence** of each of these unique integer values.

**Implementation:**

The code is implemented using Tensorflow as shown below:

import numpy as np import tensorflow as tf from tensorflow.contrib import rnn import random import collections import time start_time = time.time() def elapsed(sec): if sec<60: return str(sec) + " sec" elif sec<(60*60): return str(sec/60) + " min" else: return str(sec/(60*60)) + " hr" # Target log path logs_path = '/tmp/tensorflow/rnn_words' writer = tf.summary.FileWriter(logs_path) # Text file containing words for training training_file = 'Story.txt' def read_data(fname): with open(fname) as f: content = f.readlines() content = [x.strip() for x in content] content = [content[i].split() for i in range(len(content))] content = np.array(content) content = np.reshape(content, [-1, ]) return content training_data = read_data(training_file) print("Loaded training data...") def build_dataset(words): count = collections.Counter(words).most_common() dictionary = dict() for word, _ in count: dictionary[word] = len(dictionary) reverse_dictionary = dict(zip(dictionary.values(), dictionary.keys())) return dictionary, reverse_dictionary dictionary, reverse_dictionary = build_dataset(training_data) vocab_size = len(dictionary) # Parameters learning_rate = 0.001 training_iters = 50000 display_step = 1000 n_input = 3 # number of units in RNN cell n_hidden = 512 # tf Graph input x = tf.placeholder("float", [None, n_input, 1]) y = tf.placeholder("float", [None, vocab_size]) # RNN output node weights and biases weights = { 'out': tf.Variable(tf.random_normal([n_hidden, vocab_size])) } biases = { 'out': tf.Variable(tf.random_normal([vocab_size])) } def RNN(x, weights, biases): # reshape to [1, n_input] x = tf.reshape(x, [-1, n_input]) # Generate a n_input-element sequence of inputs # (eg. [had] [a] [general] -> [20] [6] [33]) x = tf.split(x,n_input,1) # 2-layer LSTM, each layer has n_hidden units. # Average Accuracy= 95.20% at 50k iter rnn_cell = rnn.MultiRNNCell([rnn.BasicLSTMCell(n_hidden),rnn.BasicLSTMCell(n_hidden)]) # 1-layer LSTM with n_hidden units but with lower accuracy. # Average Accuracy= 90.60% 50k iter # Uncomment line below to test but comment out the 2-layer rnn.MultiRNNCell above # rnn_cell = rnn.BasicLSTMCell(n_hidden) # generate prediction outputs, states = rnn.static_rnn(rnn_cell, x, dtype=tf.float32) # there are n_input outputs but # we only want the last output return tf.matmul(outputs[-1], weights['out']) + biases['out'] pred = RNN(x, weights, biases) # Loss and optimizer cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=pred, labels=y)) optimizer = tf.train.RMSPropOptimizer(learning_rate=learning_rate).minimize(cost) # Model evaluation correct_pred = tf.equal(tf.argmax(pred,1), tf.argmax(y,1)) accuracy = tf.reduce_mean(tf.cast(correct_pred, tf.float32)) # Initializing the variables init = tf.global_variables_initializer() # Launch the graph with tf.Session() as session: session.run(init) step = 0 offset = random.randint(0,n_input+1) end_offset = n_input + 1 acc_total = 0 loss_total = 0 writer.add_graph(session.graph) while step < training_iters: # Generate a minibatch. Add some randomness on selection process. if offset > (len(training_data)-end_offset): offset = random.randint(0, n_input+1) symbols_in_keys = [ [dictionary[ str(training_data[i])]] for i in range(offset, offset+n_input) ] symbols_in_keys = np.reshape(np.array(symbols_in_keys), [-1, n_input, 1]) symbols_out_onehot = np.zeros([vocab_size], dtype=float) symbols_out_onehot[dictionary[str(training_data[offset+n_input])]] = 1.0 symbols_out_onehot = np.reshape(symbols_out_onehot,[1,-1]) _, acc, loss, onehot_pred = session.run([optimizer, accuracy, cost, pred], feed_dict={x: symbols_in_keys, y: symbols_out_onehot}) loss_total += loss acc_total += acc if (step+1) % display_step == 0: print("Iter= " + str(step+1) + ", Average Loss= " + "{:.6f}".format(loss_total/display_step) + ", Average Accuracy= " + "{:.2f}%".format(100*acc_total/display_step)) acc_total = 0 loss_total = 0 symbols_in = [training_data[i] for i in range(offset, offset + n_input)] symbols_out = training_data[offset + n_input] symbols_out_pred = reverse_dictionary[int(tf.argmax(onehot_pred, 1).eval())] print("%s - [%s] vs [%s]" % (symbols_in,symbols_out,symbols_out_pred)) step += 1 offset += (n_input+1) print("Optimization Finished!") print("Elapsed time: ", elapsed(time.time() - start_time)) print("Run on command line.") print(" tensorboard --logdir=%s" % (logs_path)) print("Point your web browser to: http://localhost:6006/") while True: prompt = "%s words: " % n_input sentence = input(prompt) sentence = sentence.strip() words = sentence.split(' ') if len(words) != n_input: continue try: symbols_in_keys = [dictionary[str(words[i])] for i in range(len(words))] for i in range(32): keys = np.reshape(np.array(symbols_in_keys), [-1, n_input, 1]) onehot_pred = session.run(pred, feed_dict={x: keys}) onehot_pred_index = int(tf.argmax(onehot_pred, 1).eval()) sentence = "%s %s" % (sentence,reverse_dictionary[onehot_pred_index]) symbols_in_keys = symbols_in_keys[1:] symbols_in_keys.append(onehot_pred_index) print(sentence) except: print("Word not in dictionary")

After reading this blog on Convolutional Neural Networks, I am pretty sure you want to know more about Deep Learning and Neural Networks. To know more about Deep Learning and Neural Networks you can refer the following blogs:

**What is Deep Learning?****Deep Learning Tutorial****TensorFlow Tutorial****Neural Network Tutorial****Backpropagation**