Swaran Bhagyashree

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The concept of attention is introduced before we talk about the Transformer. There are two main types of care. Soft and hard attention are different within those categories.

It is not necessary to order our inputs and outputs because the transformers are made up of attention modules, which are associations between sets.

Consider a set of symbols.

The $n$-dimensional vector is where each $boldsymbolx_i$ is located. The set has elements that are $t$ and can be represented as a matrix.

The hidden representation $h$ is a linear combination of inputs.

The hidden layer can be written as the matrix product using the matrix representation.

There is a column with components.

This is different from the hidden representation we've seen so far, where the inputs are multiplied by an array of weights.

We can get hard or soft attention depending on the constraints we impose.

The following constraints are placed on the alphas: This means that the one-hot-encoded vector is $vecta$.

The coefficients are equal to zero in the linear combination of inputs and the internal representation reduces to the element that corresponds to the element $alpha_i

We impose that 1$ on soft attention. The internal representation is a linear combination of inputs.

Where did the terms "i$" come from?

We get the $vecta in mathbbRt$ as follows.

Where $\beta$ represents the inverse temperature parameter of $\text{soft(arg)max}(\cdot)$. $\boldsymbol{X}^{\top}\in\mathbb{R}^{t \times n}$ is the matrix transpose representation of the set $\lbrace\boldsymbol{x}_i \rbrace_{i= 1}^t$, and $\boldsymbol{x}$ represents a generic $\boldsymbol{x}_i$ of the set. Note that the $j$-th row of $X^{\top}$ corresponds to an element $\boldsymbol{x}_j\in\mathbb{R}^n$, so the $j$-th row of $\boldsymbol{X}^{\top}\boldsymbol{x}$ is the dot product of $\boldsymbol{x}_j$ with each $\boldsymbol{x}_i$ in $\lbrace \boldsymbol{x} _i \rbrace_{i=1}^t$.

The components of the $vecta$ are called "scores" because they tell us how similar they are. The elements of $vecta$ give information about the similarity of the set as a whole.

The square brackets have an optional argument. If $argmax(cdot)$ is used, we get a one-hot alpha-encoded vector, which results in hard attention. Soft attention is achieved by the $textsoft(arg)max(cdot)$. The sum of the components of the equation is equal to 1.

A set of them, one for each symbol, can be generated in this way. We can stack the alphas in the array if we use the $vecta_i in mathbbRt$.

Since each hidden state is a linear combination of the inputs $\boldsymbol{X}$ and a vector $\vect{a}$, we get a set $t$ of hidden states, which we can stack into an array $\boldsymbol {H}\in \mathbb{R}^{n \times t}$.

A key/value store is a way to store and retrieve data.

Let's suppose that we want to make a dish called lasagna. We searched for the termlasagna in our recipe book, and found it. All possible keys are checked against the data set to make sure that the query is valid.

The highest scoring match is determined by how well the query matches the title. If our output is the argmax function, we extract a recipe with the highest score. If we use the soft argmax function, we can get a list of similar recipes.

The question is what the query is about. We check against each key and get all the content that matches.

Each of the vectors $\vect{q}, \vect{k}, \vect{v}$ can be seen as rotations of the specific input $\vect{x}$, where $\vect{q}$ is simply $\vect{x}$ rotated by $\vect{W_q}$, $\vect{k}$ is $\vect{x}$ rotated by $\vect{W_k}$, and so on for the rest $\vect{v}$. This is the first time that we have presented learning parameters, and we do not include any non- linearities since attention is completely orientation based.

In order to compare the query against all possible keys, $\vect{q}$ and $\vect{k}$ must have the same dimensionality; that is, $\vect{q}, \vect{k} \in \mathbb{R}^{d’}$.

It can be of any size. We need the query to have the same dimensions as the keys, which are the titles of the different recipes we are searching for.

The dimensions of the recipe can be long.

We'll assume that everything has dimensions.

We have a set of values, a set of queries, a set of keys, and a set of $vectx$'s. We can group these sets into matrices, each with their own columns, and each with their own elements.

The array of all keys is compared against a query.

The hidden layer will be the linear combination of the columns of $vectV$ weighted by the coefficients.

We will get their corresponding weights and then a matrix of dimensions of $t times t$.

In matrix notation, we have this.

It's worth mentioning that we typically assign $beta$ as:

It is necessary to divide the square root of the number of dimensions by the temperature to keep it constant. Imagine what the magnitude of the vector is.

For the implementation, we can speed up the calculations by grouping all the $\vect{W}$'s into a vector $\vect{W}$, and then calculate $\vect{q}, \vect{k}, \vect{ v}$ in one go:

The concept of heads is also included. It is possible to have more than one head, but we have seen an example with a single head. Let's say we have heads.

So we have $h$ $\vect{q}$'s, $h$ $\vect{k}$'s, and $h$ $\vect{v}$'s and we end up with a vector in $\mathbb{R} ^{3hd}$:

It is possible to transform multi-head values to the original dimensions using a $vectW_h. The key/value store can be implemented in a number of ways.

We will now understand the fundamental blocks of the transformer in order to expand our knowledge.

We'll walk through a basic transformer from start to finish to see how attention is used in the standard encoder-decoder paradigm and how this compares to sequential architectures of RNNs.

This is a conceptual prerequisite for this part of the course and should be familiar to everyone. The codec imposes a kind of bottleneck on the input, forcing it to be the most important information to pass through.

The information can be used for a variety of unrelated tasks.

The model on the right shows the structure of the auto-encoder. We will see what it looks like inside.

The Add, Norm block is fed directly by the inputs that the module accepts. The output is transmitted through a one-dimensional convolution and another Add block, Norm, to be output later as hidden representations. This set of hidden representations is sent through a number of modules or the decoder.

We will review these blocks in more detail.

The self-care model is not a care model. The query, key and value are generated from the same part of the input. Prior to this step, the data is modeled with the addition of positionalEncodings in tasks that attempt to model sequential data The output of this block is the attention-weighted values, and the self-attention block accepts a set of inputs $1, \cdots , t$ that output $1, \cdots, t$ attention-weighted values, which are the input from the rest of the encoder.

The Add, Norm block has two components. The Add block is a residual connection, followed by the Norm block which is a normalized layer.

A one-dimensional convolution is applied after the previous step. This block has two layers. This block allows you to adjust the dimensions of the output.

The transformer decodes in the same way as the encoder. There is an additional sub- block to consider, in addition to the fact that the inputs of this module are different.

The self-care blocks use the same query preparation, key, and value as Cross-care. The entries are more complex. The data that is passed through the auto-attend and add/norm blocks ends up in the cross-attend blocks. This serves as the query for cross attention, where the key/value pairs are the output $\vect{h}^\text{Enc}$ which is computed using all previous outputs $\vect{x}_1, \ cdots, \vect{x}_{t}$.

The array is fed through the Encoder. An output representation $lbracevecthtextEncrbrace_i=1t$ is obtained, which is fed to the decoder. Cross attention is applied to it after self attention is applied to it. In this block, the query corresponds to a representation of the symbol in the target language $\vect{y}_i$, and the key and values ​​come from the sentence in the source language ($\vect{x}_1$ to $ \vect{x}_{t}$).

We can see that crossed attention determines which values in the input sequence are the most relevant to construct $vecty_t$, being, therefore, deserving of the highest coefficients of attention. The output of this cross-attention is then sent through another one-dimensional convolution sub-block. It's pretty clear to see how to start training for a specific language by comparing the data from the pre-annotated data and the $lbracevecthtextDecrbrace_i=1t$ data.

There are a few important facts that we left out while explaining the most important transformer modules, but we need to discuss them now to understand how transformer can achieve cutting-edge results in language processing tasks.

There is a loss of sequential information when we run operations in parallel and greatly speed up training. Adding a new type of decoding allows us to keep this context.

There are many hidden representations generated during the training of the transformer. The output of the cross attention will give us a representation of the word x_i$, which is similar to the word-based language model example.

It is possible to do more experiments on the output data after that point.

The transformer blocks that were covered previously are in code.

The multi-head attention block is the first module we will look at. It can be used for both self-service and cross-service depending on the values of the query, password and values entered in this module.

The multi-head attention class has been initialized. If a value of d_input is passed, it becomes a topic of discussion. Otherwise, it becomes self-care. A linear transformation of the d_model input is what the query preparation, key, and value are constructed as.

The hidden layer corresponds to the values after being scaled. In order to answer other questions, we return A.

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