From 191dc0ff12350f2ebe7600a96828077f6aac289a Mon Sep 17 00:00:00 2001 From: chris-admin Date: Mon, 8 Sep 2025 17:54:01 +0200 Subject: [PATCH] Added Transformers --- Chapters/12-Transformers/INDEX.md | 187 ++ .../Images/Excalidraw/encoder.excalidraw.json | 2055 +++++++++++++++++ .../transformer-high-level.excalidraw.json | 1292 +++++++++++ .../12-Transformers/Images/PNGs/encoder.png | Bin 0 -> 158872 bytes .../Images/PNGs/transformer-high-level.png | Bin 0 -> 115291 bytes 5 files changed, 3534 insertions(+) create mode 100644 Chapters/12-Transformers/Images/Excalidraw/encoder.excalidraw.json create mode 100644 Chapters/12-Transformers/Images/Excalidraw/transformer-high-level.excalidraw.json create mode 100644 Chapters/12-Transformers/Images/PNGs/encoder.png create mode 100644 Chapters/12-Transformers/Images/PNGs/transformer-high-level.png diff --git a/Chapters/12-Transformers/INDEX.md b/Chapters/12-Transformers/INDEX.md index e69de29..c680432 100644 --- a/Chapters/12-Transformers/INDEX.md +++ b/Chapters/12-Transformers/INDEX.md @@ -0,0 +1,187 @@ +# 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 `` 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 + + + +## 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. diff --git a/Chapters/12-Transformers/Images/Excalidraw/encoder.excalidraw.json b/Chapters/12-Transformers/Images/Excalidraw/encoder.excalidraw.json new file mode 100644 index 0000000..04fe38d --- /dev/null +++ b/Chapters/12-Transformers/Images/Excalidraw/encoder.excalidraw.json @@ -0,0 +1,2055 @@ +{ + "type": "excalidraw", + "version": 2, + "source": "https://marketplace.visualstudio.com/items?itemName=pomdtr.excalidraw-editor", + "elements": [ + { + "id": "1kSrI1SjU3TIAyt7I9hO3", + "type": "rectangle", + "x": 293.5, + "y": 52, + "width": 970.5, + "height": 396, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "#b2f2bb", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + 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