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The original paper that introduced the Transformer architecture is quite accessible and outlines a lot of the history and rational for the design [1]. [1] http

The original paper that introduced the Transformer architecture is quite accessible and outlines a lot of the history and rational for the design [1]. [1] https://arxiv.org/pdf/1706.03762.pdf https://arxiv.org/pdf/1706.03762.pdf

mrfusion 5y ago
I tried that but it seems to gloss over what an encoder, etc actually are. I think I’d do better with pseudo code or a toy example.
- criticaltinker 5y ago
  Check out The Annotated Transformer, it’s one of my favorite references! It contains straightforward python code side by side with excerpts from the original paper. http://nlp.seas.harvard.edu/2018/04/03/attention.html http://nlp.seas.harvard.edu/2018/04/03/attention.html
- saynay 5y ago
  The encoder is the neural-net that converts the input to the embedding vector. The decoder is the neural-net that converts that vector into output. What that embedding vector "means" is whatever the entire algorithm has learned it means. For more simplified look at embeddings, I would look at Word2Vec (although, it doesn't involve transformers). It encodes single words, instead of entire phrases, and does so by looking at their relative position to other words while being trained. Embeddings are just vectors, and so you can do math or compare them to other embeddings. The famous example is E(king) - E(man) + E(woman) = E(queen)
  - mrfusion 5y ago
    So you’re saying the encoding could be a neural net OR something like word2vec?
    - saynay 5y ago
      Sorry, didn't see this sooner. Word2Vec was just an example of an easier-to-understand embedding (it is actually frequently used as an input to these language models, actually). The process of encoding the input data stream to an embedding is done by a NN. The part that tripped me up when I was first trying to understand it is that the encoding is not like encoding elsewhere in compsci. It isn't trying to convert the input to a well-known encoding format or anything. The "encoder" is just the name of the neural-net that is converting the big, multi-dimensional input into a single-dimension, fixed-length vector. The "decoder" is just the neural-net that converts it to output. That fixed-length vector is entirely meaningless to anything other than the two neural-nets trained to generate/consume it.
      - mrfusion 5y ago
        Thanks. That’s helping the clear it up. So what’s the point of the encoding and decoding steps? Then the transformer is just another neural net in between that does some funny business with attention?
        saynay 5y ago
        The transformer is the neural net in the encode / decode steps. For something like a language model, it takes an input phrase, encodes it to something that has "meaning" to the net, then decodes it into an output phrase. The "attention" mechanism learns how much attention to give to each part of the input, anywhere in it. In languages, the previous common mechanisms (recurrent networks), would only look backwards, with decreasing weight for things further away.
- matt123456789 5y ago
  The attention mechanism, specifically the confusing bits about the Q/K/V layers, are all single linear layers with bias followed by a nonlinearity. Each of Q, K, and V are just square matrices with edge length the same as the “dimension” of the network (which you usually see denoted as “d”). So if you have an input sentence of 10 words, it gets embedded into a 10 x d space by looking up each word’s d-dimensional representation (from a |V| x d matrix). Add in some static position-dependent embedding, which is usually a function of the time index, so that the model can use position information and call the result E_0. Multiply E_0 by your d x d matrix of keys K and set aside as K_0. Do the same for your d x d query matrix Q and call the result Q_0. (The result in both cases is shape 10 x d). Take (Q • K’) which results in a 10 x 10 matrix where entry i,j denotes the amount that vector i attends to vector j. Squash this with a softmax along the time dimension* and set it aside as “attentions”. Create V_0 by running your inputs E_0 through the d x d layer of values V. Finally, calculate the output of the attention layer as (attentions) * V_0. This is just a linear cimbination of the values matrix V_0, where the coefficients are the softmaxed attention values from earlier. This is exactly what’s going on in Eq 1 from the “Attention is all you need” paper. A transformer block is usually the above operation, and then it immediately runs the result through a high-dimensional MLP ending with a layer with dimension d. And it will usually use multi-head attention which splits the input d-dimensional representation into m splits along the d axis (so that you end up with m 10 x m/d vectors) and then does the above calculation on each of the m inputs using layer- and head-specific QKV matrices, and then recombines all the results along the d axis to recover the 10 x d representation. It can be confusing when you read code that does this because it’s all vectorized and the splitting and head-specific matrices are implicit. * after dividing by the square root of d. this reduces absolute value of the inputs to the softmax and mitigates an issue that softmax has with gradients on large inputs becoming 0 on limited precision floating points.
  - mrfusion 5y ago
    Wow thanks. That’s getting clearer. A lot of those steps come off as arbitrary but I guess there’s a good reason behind each step.

mrfusion 5y ago

I tried that but it seems to gloss over what an encoder, etc actually are. I think I’d do better with pseudo code or a toy example.

criticaltinker 5y ago
Check out The Annotated Transformer, it’s one of my favorite references! It contains straightforward python code side by side with excerpts from the original paper. http://nlp.seas.harvard.edu/2018/04/03/attention.html http://nlp.seas.harvard.edu/2018/04/03/attention.html
saynay 5y ago
The encoder is the neural-net that converts the input to the embedding vector. The decoder is the neural-net that converts that vector into output. What that embedding vector "means" is whatever the entire algorithm has learned it means. For more simplified look at embeddings, I would look at Word2Vec (although, it doesn't involve transformers). It encodes single words, instead of entire phrases, and does so by looking at their relative position to other words while being trained. Embeddings are just vectors, and so you can do math or compare them to other embeddings. The famous example is E(king) - E(man) + E(woman) = E(queen)
- mrfusion 5y ago
  So you’re saying the encoding could be a neural net OR something like word2vec?
  - saynay 5y ago
    Sorry, didn't see this sooner. Word2Vec was just an example of an easier-to-understand embedding (it is actually frequently used as an input to these language models, actually). The process of encoding the input data stream to an embedding is done by a NN. The part that tripped me up when I was first trying to understand it is that the encoding is not like encoding elsewhere in compsci. It isn't trying to convert the input to a well-known encoding format or anything. The "encoder" is just the name of the neural-net that is converting the big, multi-dimensional input into a single-dimension, fixed-length vector. The "decoder" is just the neural-net that converts it to output. That fixed-length vector is entirely meaningless to anything other than the two neural-nets trained to generate/consume it.
    - mrfusion 5y ago
      Thanks. That’s helping the clear it up. So what’s the point of the encoding and decoding steps? Then the transformer is just another neural net in between that does some funny business with attention?
      - saynay 5y ago
        The transformer is the neural net in the encode / decode steps. For something like a language model, it takes an input phrase, encodes it to something that has "meaning" to the net, then decodes it into an output phrase. The "attention" mechanism learns how much attention to give to each part of the input, anywhere in it. In languages, the previous common mechanisms (recurrent networks), would only look backwards, with decreasing weight for things further away.
matt123456789 5y ago
The attention mechanism, specifically the confusing bits about the Q/K/V layers, are all single linear layers with bias followed by a nonlinearity. Each of Q, K, and V are just square matrices with edge length the same as the “dimension” of the network (which you usually see denoted as “d”). So if you have an input sentence of 10 words, it gets embedded into a 10 x d space by looking up each word’s d-dimensional representation (from a |V| x d matrix). Add in some static position-dependent embedding, which is usually a function of the time index, so that the model can use position information and call the result E_0. Multiply E_0 by your d x d matrix of keys K and set aside as K_0. Do the same for your d x d query matrix Q and call the result Q_0. (The result in both cases is shape 10 x d). Take (Q • K’) which results in a 10 x 10 matrix where entry i,j denotes the amount that vector i attends to vector j. Squash this with a softmax along the time dimension* and set it aside as “attentions”. Create V_0 by running your inputs E_0 through the d x d layer of values V. Finally, calculate the output of the attention layer as (attentions) * V_0. This is just a linear cimbination of the values matrix V_0, where the coefficients are the softmaxed attention values from earlier. This is exactly what’s going on in Eq 1 from the “Attention is all you need” paper. A transformer block is usually the above operation, and then it immediately runs the result through a high-dimensional MLP ending with a layer with dimension d. And it will usually use multi-head attention which splits the input d-dimensional representation into m splits along the d axis (so that you end up with m 10 x m/d vectors) and then does the above calculation on each of the m inputs using layer- and head-specific QKV matrices, and then recombines all the results along the d axis to recover the 10 x d representation. It can be confusing when you read code that does this because it’s all vectorized and the splitting and head-specific matrices are implicit. * after dividing by the square root of d. this reduces absolute value of the inputs to the softmax and mitigates an issue that softmax has with gradients on large inputs becoming 0 on limited precision floating points.
- mrfusion 5y ago
  Wow thanks. That’s getting clearer. A lot of those steps come off as arbitrary but I guess there’s a good reason behind each step.