A long short-term memory (LSTM) network is a type of recurrent neural network (RNN) designed to address the problems of vanishing gradients and exploding gradients using gradient truncation and structures called “constant error carousels” for enforcing constant (as opposed to vanishing or exploding) error flow^[HS97].

LSTM solves such a fundamental problem with traditional RNNs that most of the state-of-the-art results achieved through RNNs can be attributed to LSTM^[YSHZ19].

An LSTM network replaces the traditional neural network layers with LSTM layers, each of which consists of a set of recurrently connected, differentiable memory blocks^[GS05].

Each LSTM block typically contains one recurrently connected memory cell, called an LSTM cell (to be distinguished from a neuron, which is also called a node or unit), but can contain multiple cells.

Fig. 1 illustrates the structure of an LSTM cell, which acts on the current input, $x_t$, and the output of the preceding LSTM cell, $h_{t-1}$.

The forget gate is a later addition^[GSC00] to the original LSTM design; it determines based on $x_t$ and $h_{t-1}$ the amount of information to be discarded from the cell state^[YSHZ19]:

$c_t = f_t \cdot c_{t-1} + i_t \cdot \tilde{c}_t,$

where $f_t = \sigma(W_{fh}h_{t-1} + W_{fx}x_t + b_f)$ and $\tilde{c}_t = g(W_{ch}h_{t-1} + W_{cx}x_t + b_c)$. In the preceding equations,

• $W_{fh}$, $W_{fx}$ and $b_f$ are weights and bias associated with the forget gate;
• $W_{ch}$, $W_{cx}$ and $b_c$ are weights and bias associated with the cell;
• $W_{ih}$, $W_{ix}$ and $b_i$ are weights and bias associated with the input gate.

When the output of the forget gate, $f_t$, is 1, all information in $c_{t-1}$ is retained, and when the output is zero, all information is discarded.

The cell output, $h_t$, is the product:

$h_t = g(c_t) \cdot \sigma(W_{oh}h_{t-1} + W_{ox}x_t + b_o),$

where $W_{oh}$, $W_{ox}$ and $b_o$ are the weights and bias associated with the output gate.

LSTM networks can be classified into two main types^{[YSHZ19, VHMN20]}:

Since the mid 2010s, advances in machine learning (ML) and particularly deep learning (DL), under the banner of artificial intelligence (AI), have been attracting not only media attention but also major capital investments.

The field of ML is decades old, but it was not until 2012, when deep neural networks (DNNs) emerged triumphant in the ImageNet image classification challenge [KSH17], that the field of ML truly took off.

DL is known to have approached or even exceeded human-level performance in many tasks.

DL techniques, especially DNN algorithms, are our main pursuit in this course, but before diving into them, we should get a clear idea about the differences among ML, DL and AI; starting with the subsequent definitions.

AI has the broadest and yet most elusive definition. There are four main schools of thought [RN22, Sec. 1.1; IBM23], namely 1️⃣ systems that think like humans, 2️⃣ systems that act like humans, 3️⃣ systems that think rationally, 4️⃣ systems that act rationally; but a sensible definition boils down to:

Above, a rational agent is one that acts so as to achieve the best outcome or, when there is uncertainty, the best expected outcome [RN22, Sec. 1.1.4].

The definition of AI above is referred to as the standard model of AI [RN22, Sec. 1.1.4].

ML is a subfield of AI:

In the preceding definition, “experience”, “task” and “performance measure” require elaboration. Among the most common ML tasks are:

• Classification: This is usually achieved through supervised learning (see Fig. 1), the aim of which is to learn a mapping $f$ from the input set $\mathcal{X}$ to the output set $\mathcal{Y}$ [ Mur22, Sec. 1.2; GBC16, Sec. 5.1.3; G22, Ch. 1], where

  • every member of $\mathcal{X}$ is a vector of features, attributes, covariates, or predictors;
  • every member of $\mathcal{Y}$ is a label, target, or response;
  • each pair of input $x\in\mathcal{X}$ and associated output $y\in\mathcal{Y}$ is called an example.

  A dataset containing $\mathcal{X}$ and $\mathcal{Y}$ used to “train” a model to predict/infer $y$ given some $x$ is called a training set; and this corresponds to experience $E$ in Definition 2.

  When $\mathcal{Y}$ is a set of unordered and mutually exclusive labels known as classes, the supervised learning task becomes a classification task.

  Classification of only two classes is called binary classification. For example, determining whether an email is spam or not is a binary classification task.

Fig. 1: Supervised learning [ZLLS23, Fig. 1.3.1].

Fig. 2: An example of a regression problem, where given a “new instance”, the target value is to be determined [G22, Figure 1-6].

• Regression: Continuing from classification, if the output set $\mathcal{Y}$ is a continuous set of real values, rather than a discrete set, the classification task becomes a regression task.

  For example, given the features (e.g., mileage, age, brand, model) and associated price for many examples of cars, a plausible regression task is to predict the price of a car given its features; see Fig. 2.

  While the term “label” is more common in the classification context, “target” is more common in the regression context. In the earlier example, the target is the car price.

• Clustering: This is the grouping of similar things together.

  The Euclidean distance between two feature vectors can serve as a similarity measure, but depending on the problem, other similarity measures can be more suitable. In fact, many similarity measures have been proposed in the literature [GMW07, Ch. 6].

  Clustering is a form of unsupervised learning.

  From a probabilistic viewpoint, unsupervised learning is fitting an unconditional model of the form $\Pr\{x\}$, which can generate new data $x$, whereas supervised learning involves fitting a conditional model, $\Pr\{y|x\}$, which specifies (a distribution over) outputs given inputs [Mur22, Sec. 1.3].

• Anomaly detection: This is another form of unsupervised learning, and highly relevant to this course of ours.

  We first encountered anomaly detection in Tutorial 1 on intrusion detection, and we will dive deep into anomaly detection in Tutorial 5 on unsupervised learning.

Common to the aforementioned tasks is the need to measure performance. An example of performance measure is

$\text{accuracy} = \frac{\text{number of correct predictions}}{\text{total number of predictions}}.$

Other performance measures will be investigated as part of Task 1.

DL is in turn a subfield of ML (see Fig. 3):

Definition 3: Deep learning (DL) [RN22, Sec. 1.3.8]

Machine learning using multiple layers of simple, adjustable computing elements.

Simply put, DL is the ever expanding body of ML techniques that leverage deep architectures (algorithmic structures consisting of many levels of nonlinear operations) for learning feature hierarchies, with features from higher levels of the hierarchy formed by composition of lower-level features [Ben09].

Fig. 3: AI → ML → DL [Cop16].

The rest of this tutorial attempts to 1️⃣ shed some light on why DNNs are superior to classical ML algorithms, 2️⃣ provide a brief tutorial on the original/shallow/artificial neural networks (ANNs), and 3️⃣ provide a preview of DNNs.

The good news with the topics of this tutorial is that there is such a vast amount of learning resources in the public domain, that even if the coverage here fails to satisfy your learning needs, there must be some resources out there that can.

This knowledge base entry follows discussion of artificial neural networks and backpropagation.

The backpropagation (“backprop” for short) algorithm calculates gradients to update each weight.

Both problems plague deep neural networks (DNNs) and recurrent neural networks (RNNs) over very long sequences [Mur22, Sec. 13.4.2].

More generally, deep neural networks suffer from unstable gradients, and different layers may learn at widely different speeds.

Watch Prof Ng’s explanation of the problems:

The problems were observed decades ago and were the reasons why DNNs were mostly abandoned in the early 2000s [G22, Ch. 11].

• The causes had been traced to the 1️⃣ usage of sigmoid activation functions, and 2️⃣ initialisation of weights to follow the zero-mean Gaussian distribution with standard deviation 1.
• A sigmoid function saturates at 0 or 1, and when saturated, the derivative is nearly 0.
• As a remedy, current best practices include using 1️⃣ a rectifier activation function, and 2️⃣ the weight initialisation algorithm called He initialisation.
• He initialisation [HZRS15, Sec. 2.2]: at layer $\ell$, weights follow the zero-mean Gaussian distribution with variance $2/n_\ell$, where $n_\ell$ is the fan-in, or equivalently the number of inputs/weights feeding into layer $\ell$.
• He initialisation is implemented by the PyTorch function kaiming_normal_ and the Tensorflow function HeNormal.

Watch Prof Ng’s explanation of weight initialisation: