# Transformers

## Block Components

The idea is that each Transformer block is made of the **same number** of [`Encoders`](#encoder) and
[`Decoders`](#decoder)

![image](./Images/PNGs/transformer-high-level.png)

> [!NOTE]
> Input and output are vectors of **fixed size** with padding

Before feeding our input, we split and embed each word into a fixed vector size. This size depends on the length of
longest sentence in our training set

### Embedder

While this is not a real component per se, this is the first phase before even coming
to the first `encoder` and `decoder`.

Here we transform each word of the input into an ***embedding*** and add a vector to account for
position. This positional encoding can either be learnt or can follow this formula:


- Even size:
$$
\text{positional\_encoding}_{
    (position, 2\text{size})
} = \sin\left(
        \frac{
            pos
        }{
            10000^{
                \frac{
                    2\text{size}
                }{
                    \text{model\_depth}
                }
            }
        }
    \right)
$$
- Odd size:
$$
\text{positional\_encoding}_{
    (position, 2\text{size} + 1)
} = \cos\left(
        \frac{
            pos
        }{
            10000^{
                \frac{
                    2\text{size}
                }{
                    \text{model\_depth}
                }
            }
        }
    \right)
$$


### Encoder

> [!CAUTION]
> Weights are not shared between `encoders` or `decoders`

Each phase happens for each word. In other words, if our embed size is 512, we have 512 `Self Attentions` and
512 `Feed Forward NN` **per `encoder`**

![Image](./Images/PNGs/encoder.png)

#### Encoder Self Attention

> [!WARNING]
> This step is the most expensive one as it involves many computations

Self Attention is a step in which each ***token*** gets the knowledge of previous ones.

During this step, we produce 3 vectors that are **usually smaller**, for example 64 instead of 512:

- **Queries** $\rightarrow q_{i}$
- **Keys** $\rightarrow k_{i}$
- **Values** $\rightarrow v_{i}$

We use these values to compute a **score** that will tell us **how much to focus on certain parts of the sentence
while encoding a token**

In order to compute the final encoding we do these for each encoding word $i$:

- Compute score for each word $j$ : $\text{score}_{j} = q_{i} \cdot k_{j}$
- Divide each score by the square root of the size of these *helping vectors*:
    $\text{score}_{j} = \frac{\text{score}_{j}}{\sqrt{\text{size}}}$
- Compute softmax of all scores
- Multiply softmax each score per its value: $\text{score}_{j} = \text{score}_{j} \cdot v_{j}$
- Sum them all: $\text{encoding}_{i} = \sum_{j}^{N} \text{score}_{j}$

> [!NOTE]
> These steps will be done with matrices, not in this sequential way

##### Multi-Headed Attention

Instead of doing the Attention operation once, we do it more times, by having differente matrices to produce
our *helping vectors*.

This produces N encodings for each ***token***, or N matrices of encodings.

The trick here is to **concatenate all encoding matrices** and **learn a new weight matrix** that will
**combine them**

#### Residuals

In order no to lose some information along the path, after each `Feed Forward` and `Self-Attention`
we add inputs to each ***sublayer*** `outputs` and we do a `Layer Normalization`

#### Encoder Feed Forward NN

> [!TIP]
> This step is mostly **parallel** as there's no dependency between *neighbour vectors*

### Decoder

> [!NOTE]
> The decoding phase is slower than the encoding one, as it is sequential, producing a token for each iteration.
> However it can be sped up by producing several tokerns at once

After the **last `Encoder`** has produced its `output`, $K$ and $V$ vectors, these are then used by
**all `Decoders`** during their self attention step, meaning they are **shared** among all `Decoders`.

All `Decoders` steps are then **repeated until we get a `<eos>` token** which will tell the decoder to stop.

#### Decoder Self Attention

It's almost the same as in the `encoding` phase, though here, since we have no future `outputs`, we can only take into
account only previous ***tokens***, by setting future ones to `-inf`.
Moreover, here the `Key` and `Values` Mappings come from the `encoder` pase, while the
`Queue` Mapping is learnt here.

#### Final Steps

##### Linear Layer

Produces a vector of ***logits***, one per each ***known words***.

##### Softmax Layer

We then score these ***logits*** over a `SoftMax` to get probabilities. We then take the highest one, usually.

If we implement ***Temperature***, though, we can take some `tokens` that are less probable, but having less predictability and
have some results that feel more natural.

## Training a Transformer

<!-- TODO: See PDF 12 pg. 58 to 65 -->

## Known Transformers

### BERT (Bidirectional Encoder Representations from Transformers)

Differently from other `Transformers`, it uses only `Encoder` blocks.

It can be used as a classifier and can be fine tuned.

The fine tuning happens by **masking** input and **predict** the **masked word**:

- 15% of total words in input are masked
    - 80% will become a `[masked]` token
    - 10% will become random words
    - 10% will remain unchanged

#### Bert tasks

- **Classification**
- **Fine Tuning**
- **2 sentences tasks**
    - **Are they paraphrases?**
    - **Does one sentence follow from this other one?**
- **Feature Extraction**: "Allows us to extract feature to use in our model

### GPT-2

Differently from other `Transformers`, it uses only `Decoder` blocks.

Since it has no `encoders`, `GPT-2` takes `outputs` and append them to the original `input`. This is called **autoregression**.
This, however, limits `GPT-2` on how to learn context on `input` because of `masking`.

During `evaluation`, `GPT-2` does not recompute `V`, `K` and `Q` for previous tokens, but hold on their previosu values.