The authors tested how NTMs would perform as re-writable tables, similar to N-Gram models. They used all possible 6-Gram distributions over binary sequences: the network first observes the data one bit at a time and then must predict the next bit, requiring it to infer and store the underlying N-Gram statistics in memory.

San Diego State University

Google

NTMs(Neural Turing Machines) are neural network architectures that use external memory. These models are able to infer algorithmic tasks like copying, sorting, associative recall. According to the inventors of this architecture via NTMs they: "extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes"
These models are relatively new compared to LSTMs and RNNs. They were created in 2014. 

Neural Turing Machines (NTM)

An n-gram is a sequence of n tokens, where training models based on this are straightforward and have been used as the building block of statistical language modeling for many years. There are also specific names for small values of n, such as unigram for n - 1, or bigram for n - 2, and trigram for n - 3.

n-grams

Even though, computer programs heavily rely on logical flow control, elementary operations and external memory, the modern machine learning almost never uses two of these fundamental mechanisms: logical flow control and external memory.

Motivation for Creating Neural Turing Machines

NTMs have two basic components, namely, controller and memory bank. Controller uses input and output vectors to interact with outside environment. This is similar to what we have in typical neural network architectures. Additionally, unlike other neural network architectures, it also interacts with the memory bank using read and write operations. 
NTMs can be used with gradient descent and this process would be quite straightforward as each component is differentiable.



NTM Architecture

"The copy task tests whether NTM can store and recall a long sequence of arbitrary information. The network is presented with an input sequence of random binary vectors followed by a delimiter flag. Storage and access of information over long time periods has  always been problematic for RNNs and other dynamic architectures. We were particularly interested to see if an NTM is able to bridge longer time delays than LSTM"

Copy with NTMs

"We test the NTM’s capability for learning an instance of this more interesting class by constructing a list of items so that querying with
one of the items demands that the network return the subsequent item. More specifically, we define an item as a sequence of binary vectors that is bounded on the left and right by delimiter symbols. After several items have been propagated to the network, we query by showing a random item, and we ask the network to produce the next item. In our experiments, each item consisted of three six-bit binary vectors"

Associative Recall with NTMs

N-Grams with NTMs

As it clear from the title, the authors tested how NTMs would perform when it comes to  simple sorting algorithm. The priority is chosen from range [-1, 1]. Input contained binary vectors with their priorities and target contained sorted input. based on their priorities.
 

Priority Sort with NTMs

In terms of training time NTM is not better than LSTM. Furthermore, there are lot's of things going inside NTM which requires more iterations than we would need for LSTM.
In terms of performance, NTM is more likely to beat the LSTM.  Theoretically, NTMs can have an infinite memory across timestamps, thus they are  good when we have large data (**this might not be true in practice**). However, if we have smaller data LSTMs can be a better choice. Therefore depending on the task and the amount of input NTM can be better than LSTM.

https://www.quora.com/Is-the-Neural-Turing-machine-more-efficient-than-the-LSTM?fbclid=IwAR1P-OEKHbp3wCW9FUKzflCSlsJb8S5gcKmIa5wtYezT_dsuC1Ov-fH0sVQ

NTMs vs LSTMs

1. Ability to learn algorithms
2. Ability to generalize
3. Has a good performance even if we have a huge data

Advantages (Neural Turing Machines)

1. Time complexity
2. Difficult to implement
3. Doesn't benefit much from GPU
4. Architecture dependent

Disadvantages (Neural Turing Machines)

The assumption that the probability of a word depends only on the previous word is called a Markov assumption.

Markov used in NLP

Perplexity is a probability-based metric for evaluating language models. It is the weighted average of the number of possible next words that can follow any word, a.k.a. the weighted average branching factor.  

Given a mini-language of 10 words "zero, one ... ten", each word's occurrence probability is 1/10 (unigram), the perplexity is the inverse is 10:

$$
\begin{aligned}
\mathrm{PP}(W) &=P\left(w_{1} w_{2} \ldots w_{N}\right)^{-\frac{1}{N}} \\
&=\left(\frac{1}{10}\right)^{-\frac{1}{N}} \\
&=\frac{1}{10} \\
&=10
\end{aligned}
$$

Perplexity

The general equations of an n-gram model apply the Markov assumption to estimate word probabilities. The conditional probability for the next word is approximated by looking $$N-1$$ words into the past:

$$P(w_n|w_{1:n-1}) \approx P(w_n|w_{n-N+1:n-1})$$

The probability of a complete word sequence is approximated as the product of these conditional probabilities:

$$P(w_{1:n}) \approx \prod^n_{k=1}P(w_k|w_{k-N+1:k-1})$$

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