From 507da43cd324553d8837c7af7897996199523941 Mon Sep 17 00:00:00 2001 From: Zach Lipp Date: Fri, 6 Dec 2024 18:44:54 -0500 Subject: [PATCH] slides draft --- transformer_review/attention.png | Bin 0 -> 72411 bytes transformer_review/attention_example.png | Bin 0 -> 52267 bytes transformer_review/cnn.png | Bin 0 -> 75919 bytes .../decode-only-transformer.svg | 854 ++++++++++++++++++ transformer_review/generate_slides.sh | 3 + transformer_review/iyyer_slide18.png | Bin 0 -> 32855 bytes transformer_review/iyyer_slide19.png | Bin 0 -> 103987 bytes transformer_review/iyyer_slide20.png | Bin 0 -> 107202 bytes transformer_review/iyyer_slide21.png | Bin 0 -> 126368 bytes transformer_review/iyyer_slide22.png | Bin 0 -> 150129 bytes transformer_review/iyyer_slide23.png | Bin 0 -> 146577 bytes transformer_review/multihead_attention.png | Bin 0 -> 276003 bytes transformer_review/neural_net.svg | 1 + transformer_review/slides.html | 456 ++++++++++ transformer_review/slides.md | 301 ++++++ transformer_review/transformer_arch.webp | Bin 0 -> 48592 bytes 16 files changed, 1615 insertions(+) create mode 100644 transformer_review/attention.png create mode 100644 transformer_review/attention_example.png create mode 100644 transformer_review/cnn.png create mode 100644 transformer_review/decode-only-transformer.svg create mode 100755 transformer_review/generate_slides.sh create mode 100644 transformer_review/iyyer_slide18.png create mode 100644 transformer_review/iyyer_slide19.png create mode 100644 transformer_review/iyyer_slide20.png create mode 100644 transformer_review/iyyer_slide21.png create mode 100644 transformer_review/iyyer_slide22.png create mode 100644 transformer_review/iyyer_slide23.png create mode 100644 transformer_review/multihead_attention.png create mode 100644 transformer_review/neural_net.svg create mode 100644 transformer_review/slides.html create mode 100644 transformer_review/slides.md create mode 100644 transformer_review/transformer_arch.webp diff 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Q8}+!OZJ;M1& literal 0 HcmV?d00001 diff --git a/transformer_review/neural_net.svg b/transformer_review/neural_net.svg new file mode 100644 index 0000000..7f8682d --- /dev/null +++ b/transformer_review/neural_net.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/transformer_review/slides.html b/transformer_review/slides.html new file mode 100644 index 0000000..63cdc3b --- /dev/null +++ b/transformer_review/slides.html @@ -0,0 +1,456 @@ + + + + + + + + Transformers Review + + + + + + +

+
+

Transformers Overview

+
    +
  • “Attention is all you need” (2017)
  • +
  • The go-to architecture for most machine learning problems, +especially language models
  • +
+
+
+

Brief recap of neural nets

+
+“Neural net visualization” +
“Neural net visualization”
+
+
+
+

Brief recap of neural nets (more)

+
    +
  • Individually simple neurons connected via layers
  • +
  • Weights and biases are changed in training +
      +
    • Number of neurons and layer structures do not change in +training
    • +
  • +
  • Theoretically universal +
      +
    • In practice often learns spurious relationships without more +safeguards
    • +
    • Architectures provide these safeguards and are therefore +subtractive not additive
    • +
  • +
  • Calculating with weights and biases can be rewritten as matrix +multiplication and addition +
      +
    • Every layer-to-layer connection of weights can be interpreted as a +matrix of size n x m +
        +
      • n is the size of the previous layer and m is the size of the next +layer
      • +
      • Entries in matrices are connection weights between two neurons
      • +
      • Passing the outputs of one layer as the inputs to the next is +multiplication of those inputs by the matrix
      • +
    • +
    • Every set of biases of a layer of neurons can be interpreted as a +matrix (with a single column) +
        +
      • Each neuron in the layer has one bias entry in the matrix
      • +
    • +
  • +
+
+
+

Transformers Architecture

+
+
+

+
+
+

1. Encoder + decoder

+
+
    +
  1. Attention
  2. +
  3. Multi-Head Attention
  4. +
  5. Positional Encoding
  6. +
  7. Transformer Blocks
  8. +
+
+
+
+
+

1. Encoder + decoder

+
    +
  • Have one neural net (or set of nets) that outputs some abstract +representation of text
  • +
  • Have another neural net (or set of nets) decode that abstract +representation back to natural language
  • +
  • Not new with transformers (e.g. seq2seq 2014)
  • +
+
+
+ +
+
+

+
+
    +
  1. Encoder + decoder
  2. +
+
+

2. Attention

+
+
    +
  1. Multi-Head Attention
  2. +
  3. Positional Encoding
  4. +
  5. Transformer Blocks
  6. +
+
+
+
+
+
+

2a. Attention visualized (Iyyer 2021)

+

+
+
+

2a. Attention visualized (Iyyer 2021)

+

+
+
+

2a. Attention visualized (Iyyer 2021)

+

+
+
+

2a. Attention visualized (Iyyer 2021)

+

+
+
+

2a. Attention visualized (Iyyer 2021)

+

+
+
+

2a. Attention visualized (Iyyer 2021)

+

+
+
+

2b. Attention as a DB query

+
    +
  • I have a database with keys and values. Keys are chosen to play +nicer with queries, values are what I actually return in the data.
  • +
  • [("Alice", "some data about Alice"), ("Bob", "some data about Bob")]
  • +
  • Query “Get me data about keys/names that start with ‘A’”
  • +
  • Match query against key
  • +
+
+
+

2b. Attention as a DB query

+
+
+
    +
  • Abstract steps of DB query
  • +
  • Split data into keys and values
  • +
  • Generate a query
  • +
  • Compare queries with keys
  • +
  • Use comparison to select which values to return
  • +
+
+
    +
  • What about a “fuzzy” DB query?
  • +
  • Split data into keys and values
  • +
  • Generate a query
  • +
  • Instead of binary comparison, yes/no, do a fuzzy match score between +0 and 1
  • +
  • Multiply each value by the fuzzy match and combine them all together +to return a “fuzzy” match
  • +
  • This degenerates to a normal DB query if we just constrain the +fuzziness to either 0 or 1
  • +
+
+
+
+
+

2b. Attention: Equivalents in attention

+
    +
  • Generate a key and value vector from a given word
  • +
  • Generate a query vector from the word
  • +
  • Dot product the query vector against the key vector to generate +weights
  • +
  • Multiply each value vector by the weights
  • +
+
+
+

2b. Attention: Generating the key, value, and query vectors

+
    +
  • We have matrices for each key, value, and query +
      +
    • \(W_k\), \(W_v\), and \(W_q\)
    • +
  • +
  • These matrix values are learned during training
  • +
+
+
+

2b. Attention: Working through a specific example

+
    +
  • “The car was driving too quickly through the field. It +crashed into a tree.”
  • +
  • Look at a single given word “it”, which has some vector form after +embedding
  • +
  • Multiply every word’s embedding by \(W_k\) to generate key vectors for all of +them
  • +
  • Multiply every word’s embedding by \(W_v\) to generate value vectors for all of +them
  • +
  • Multiply “it” embedding by \(W_q\) +to generate a single query vector
  • +
  • Dot product query vector against every key vector to get weights +against every value
  • +
  • Multiply every value by weight and add them altogether to the final +attention result
  • +
  • +Attention weight visualization +
    Attention weight visualization
    +
  • +
+
+
+ +
+
+

+
+
    +
  1. Encoder + decoder
  2. +
  3. Attention
  4. +
+
+

3. Multi-Head Attention

+
+
    +
  1. Positional Encoding
  2. +
  3. Transformer Blocks
  4. +
+
+
+
+
+

3. Multi-Head Attention

+
    +
  • Empirical tuning (like so much of ML!)
  • +
  • The entirety of the reasoning in the original paper: “We found it +beneficial” the original +paper
  • +
+
+
+

3. Attention is relatively unexpressive (Vaswani 2024)

+
    +
  • +
  • +
+
+
+

3. Multi-Head Attention increases expressivity (Vaswani 2024)

+

+
+
+

+
+
+

+
+
    +
  1. Encoder + decoder
  2. +
  3. Attention
  4. +
  5. Multi-Head Attention
  6. +
+
+

4. Positional Encoding

+
+
    +
  1. Transformer Blocks
  2. +
+
+
+
+
+

4. Positional Encoding

+
    +
  • Attention is position invariant, as is almost everything in a +transformer block
  • +
  • It is therefore common to explicitly encode position +information
  • +
  • This is called a positional encoding, where after embedding +a token as a vector of floats, there is another operation that modifies +the vector based on what the index of the token is in the input
  • +
+
+
+

+
+
+

+
+
    +
  1. Encoder + decoder
  2. +
  3. Attention
  4. +
  5. Multi-Head Attention
  6. +
  7. Positional Encoding
  8. +
+
+

5. Transformer Blocks

+
+
+
+
+
+

5. Transformer blocks

+
    +
  • A transformer model consists of all of the components we’ve +discussed, but some of them are repeated in structures called +“blocks”

  • +
  • Remember MLP is just a vanilla neural net.

  • +
+
----------------------------
+|      Output              |
+|        ^                 |
+|        |                 |
+|   Normalization <-----|  |
+|        ^              |  |
+|        |              |  |
+|       MLP             |  |
+|        ^              |  |
+|        | -------------|  |
+|        |                 |
+|   Normalization <-----|  |
+|        ^              |  |
+|        |              |  |
+| Multi-Head Attention  |  |
+|        ^              |  |
+|        |              |  |
+|      Input -----------|  |
+|                          |
+----------------------------
+
+
+

5. Stacking attention on top of attention

+
    +
  • Keep stacking attention matrices on top of rounds of merging +multiple attention streams
  • +
  • Query, key, value intuition kind of falls apart +
      +
    • What is attention “really”?
    • +
    • At the end of the day a particular set of guardrails on neural nets +that seems to make models good at language
    • +
    • Again no reason in theory why a sufficiently large single neural net +couldn’t subsume the idea of attention +
        +
      • It just doesn’t happen in practice
      • +
      • Too many spurious relationships
      • +
      • The guardrails provided by attention cut down on spurious +relationships (i.e. subtractive, not additive new capabilities)
      • +
    • +
  • +
+
+
+

Putting It All Back Together

+
    +
  1. Start with an input text sequence consisting of n +tokens
  2. +
  3. Convert that to n vectors of size d_model +using some pretrained embedding (will use n x +d_model as short-hand for this)
  4. +
  5. Add positional encoding: output is new set of n x +d_model vectors
  6. +
  7. Pass into (multi-head) attention mechanism: output is new set of +n x d_model vectors
  8. +
  9. Normalize the sum of input into attention and its output from the +previous step: output is new set of n x +d_model vectors
  10. +
  11. Pass vectors into MLP: output is new set of n x +d_model vectors
  12. +
  13. Normalize the sum of input into MLP and its output from the previous +step: output is new set of n x d_model +vectors
  14. +
  15. Repeat steps 4-7 for as many transformer blocks as the model has: +output is new set of n x d_model vectors
  16. +
  17. Pass into final linear layer: output is new set of n x +d_vocabulary vectors (d_vocabulary is the +number of possible distinct tokens)
  18. +
  19. Choose the last vector: output is 1 x +d_vocabulary vector
  20. +
  21. Choose index of vector with highest scalar value: output is +1 scalar
  22. +
  23. Lookup that index using vocabulary dictionary back to a text token: +output is a single new token
  24. +
+
+ + diff --git a/transformer_review/slides.md b/transformer_review/slides.md new file mode 100644 index 0000000..d415a8f --- /dev/null +++ b/transformer_review/slides.md @@ -0,0 +1,301 @@ +% Transformers Review + +# Transformers Overview ++ "Attention is all you need" (2017) ++ The go-to architecture for most machine learning problems, especially language models + +# Brief recap of neural nets + +!["Neural net visualization"](./neural_net.svg) + +# Brief recap of neural nets (more) + ++ Individually simple neurons connected via layers ++ Weights and biases are changed in training + * Number of neurons and layer structures do not change in training ++ Theoretically universal + * In practice often learns spurious relationships without more safeguards + * Architectures provide these safeguards and are therefore **subtractive** not + **additive** ++ Calculating with weights and biases can be rewritten as matrix multiplication + and addition + * Every layer-to-layer connection of weights can be interpreted as a matrix of size n x m + - n is the size of the previous layer and m is the size of the next layer + - Entries in matrices are connection weights between two neurons + - Passing the outputs of one layer as the inputs to the next is + multiplication of those inputs by the matrix + * Every set of biases of a layer of neurons can be interpreted as a matrix (with a single column) + - Each neuron in the layer has one bias entry in the matrix + +# Transformers Architecture +::: columns + +:::: column +![](./transformer_arch.webp){ height=800px } +:::: + +:::: column +> **1. Encoder + decoder** + +> 2. Attention +> 3. Multi-Head Attention +> 4. Positional Encoding +> 5. Transformer Blocks + +:::: +::: + +# 1. Encoder + decoder ++ Have one neural net (or set of nets) that outputs some abstract representation + of text ++ Have another neural net (or set of nets) decode that abstract representation + back to natural language ++ Not new with transformers (e.g. seq2seq 2014) + +--- + +::: columns + +:::: column +![](./transformer_arch.webp){ height=800px } +:::: + +:::: column + +> 1. Encoder + decoder + +> **2. Attention** + +> 3. Multi-Head Attention +> 4. Positional Encoding +> 5. Transformer Blocks + +:::: +::: + +# 2. Attention + ++ Inspired by the idea of human attention ++ Allows the model to "attend to" different parts of the input sequence at a given time ++ NLP Professor Raymond Mooney: *"You can’t cram the meaning of a whole %&!$# sentence into a single $&!#* vector!"* + * [...you can use your language model of informal English to fill in the masked portions](https://www.cs.utexas.edu/~mooney/cramming.html) ++ Instead, consider attention as a series of queries, keys, and values ($W_k$, $W_q$, $W_v$) ++ Two ways to explore: + a. [Visual, via Mohit Iyyer, University of Massachusetts Amherst 2021](https://people.cs.umass.edu/~miyyer/cs685_f21/slides/04-attention.pdf) + b. Analogy from Changlin + +# 2a. Attention visualized (Iyyer 2021) +![](iyyer_slide18.png){ height=800px } + +# 2a. Attention visualized (Iyyer 2021) +![](iyyer_slide19.png){ height=800px } + +# 2a. Attention visualized (Iyyer 2021) +![](iyyer_slide20.png){ height=800px } + +# 2a. Attention visualized (Iyyer 2021) +![](iyyer_slide21.png){ height=800px } + +# 2a. Attention visualized (Iyyer 2021) +![](iyyer_slide22.png){ height=800px } + +# 2a. Attention visualized (Iyyer 2021) +![](iyyer_slide23.png){ height=800px } + +# 2b. Attention as a DB query ++ I have a database with keys and values. Keys are chosen to play nicer with + queries, values are what I actually return in the data. ++ `[("Alice", "some data about Alice"), ("Bob", "some data about Bob")]` ++ Query "Get me data about keys/names that start with 'A'" ++ Match query against key + +# 2b. Attention as a DB query +::: columns + +:::: column ++ **Abstract steps of DB query** ++ Split data into keys and values ++ Generate a query ++ Compare queries with keys ++ Use comparison to select which values to return +:::: + +:::: column ++ **What about a "fuzzy" DB query?** ++ Split data into keys and values ++ Generate a query ++ Instead of binary comparison, yes/no, do a fuzzy match score between 0 and 1 ++ Multiply each value by the fuzzy match and combine them all together to return + a "fuzzy" match ++ This degenerates to a normal DB query if we just constrain the fuzziness to + either 0 or 1 +:::: +::: + +# 2b. Attention: Equivalents in attention ++ Generate a key and value vector from a given word ++ Generate a query vector from the word ++ Dot product the query vector against the key vector to generate weights ++ Multiply each value vector by the weights + +# 2b. Attention: Generating the key, value, and query vectors + ++ We have matrices for each key, value, and query + * $W_k$, $W_v$, and $W_q$ ++ These matrix values are learned during training + +# 2b. Attention: Working through a specific example ++ "The car was driving too quickly through the field. *It* crashed into a tree." ++ Look at a single given word "it", which has some vector form after embedding ++ Multiply *every word*'s embedding by $W_k$ to generate key vectors for all of + them ++ Multiply *every word*'s embedding by $W_v$ to generate value vectors for all + of them ++ Multiply "it" embedding by $W_q$ to generate a single query vector ++ Dot product query vector against every key vector to get weights against every + value ++ Multiply every value by weight and add them altogether to the final attention + result ++ ![Attention weight visualization](attention_example.png) + +--- + +::: columns + +:::: column +![](./transformer_arch.webp){ height=800px } +:::: + +:::: column + +> 1. Encoder + decoder +> 2. Attention + +> **3. Multi-Head Attention** + +> 4. Positional Encoding +> 5. Transformer Blocks + +:::: +::: + +# 3. Multi-Head Attention ++ Empirical tuning (like so much of ML!) ++ The entirety of the reasoning in the original paper: "We found it beneficial" + [the original paper](https://arxiv.org/pdf/1706.03762.pdf) + +# 3. Attention is relatively unexpressive (Vaswani 2024) ++ ![](attention.png) ++ ![](cnn.png) + +# 3. Multi-Head Attention increases expressivity (Vaswani 2024) +![](multihead_attention.png) + + +# +::: columns + +:::: column +![](./transformer_arch.webp){ height=800px } +:::: + +:::: column + +> 1. Encoder + decoder +> 2. Attention +> 3. Multi-Head Attention + +> **4. Positional Encoding** + +> 5. Transformer Blocks + +:::: +::: + +# 4. Positional Encoding + ++ Attention is position invariant, as is almost everything in a transformer block ++ It is therefore common to explicitly encode position information ++ This is called a *positional encoding*, where after embedding a token as a vector of floats, there is another operation that modifies the vector based on what the + index of the token is in the input + +# +::: columns + +:::: column +![](./transformer_arch.webp){ height=800px } +:::: + +:::: column + +> 1. Encoder + decoder +> 2. Attention +> 3. Multi-Head Attention +> 4. Positional Encoding + +> **5. Transformer Blocks** + +:::: +::: + +# 5. Transformer blocks ++ A transformer model consists of all of the components we've discussed, but some of them are repeated in structures called "blocks" + ++ Remember MLP is just a vanilla neural net. +``` +---------------------------- +| Output | +| ^ | +| | | +| Normalization <-----| | +| ^ | | +| | | | +| MLP | | +| ^ | | +| | -------------| | +| | | +| Normalization <-----| | +| ^ | | +| | | | +| Multi-Head Attention | | +| ^ | | +| | | | +| Input -----------| | +| | +---------------------------- +``` + + +# 5. Stacking attention on top of attention ++ Keep stacking attention matrices on top of rounds of merging multiple + attention streams ++ Query, key, value intuition kind of falls apart + * What is attention "*really*"? + * At the end of the day a particular set of guardrails on neural nets that + seems to make models good at language + * Again no reason in theory why a sufficiently large single neural net + couldn't subsume the idea of attention + - It just doesn't happen in practice + - Too many spurious relationships + - The guardrails provided by attention cut down on spurious + relationships (i.e. subtractive, not additive new capabilities) + +# Putting It All Together +1. Start with an input text sequence consisting of `n` tokens +2. Convert that to `n` vectors of size `d_model` using some pretrained + embedding (will use `n` x `d_model` as short-hand for this) +3. Add positional encoding: output is new set of `n` x `d_model` vectors +4. Pass into (multi-head) attention mechanism: output is new set of `n` x `d_model` vectors +5. Normalize the sum of input into attention and its output from the previous + step: output is new set of `n` x `d_model` vectors +6. Pass vectors into MLP: output is new set of `n` x `d_model` vectors +7. Normalize the sum of input into MLP and its output from the previous step: + output is new set of `n` x `d_model` vectors +8. Repeat steps 4-7 for as many transformer blocks as the model has: output is + new set of `n` x `d_model` vectors +9. Pass into final linear layer: output is new set of `n` x `d_vocabulary` + vectors (`d_vocabulary` is the number of possible distinct tokens) +10. Choose the last vector: output is `1` x `d_vocabulary` vector +11. Choose index of vector with highest scalar value: output is `1` scalar +12. 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