How do transformers work? Learn it by hand 👇

𝗪𝗮𝗹𝗸𝘁𝗵𝗿𝗼𝘂𝗴𝗵

[1] Given
↳ Input features from the previous block (5 positions)

[2] Attention
↳ Feed all 5 features to a query-key attention module (QK) to obtain an attention weight matrix (A). I will skip the details of this module. In a follow-up post I will unpack this module.

[3] Attention Weighting
↳ Multiply the input features with the attention weight matrix to obtain attention weighted features (Z). Note that there are still 5 positions.
↳ The effect is to combine features across positions (horizontally), in this case, X1 := X1 + X2, X2 := X2 + X3....etc.

[4] FFN: First Layer
↳ Feed all 5 attention weighted features into the first layer.
↳ Multiply these features with the weights and biases.
↳ The effect is to combine features across feature dimensions (vertically).
↳ The dimensionality of each feature is increased from 3 to 4.
↳ Note that each position is processed by the same weight matrix. This is what the term "position-wise" is referring to.
↳ Note that the FFN is essentially a multi layer perceptron.

[5] ReLU
↳ Negative values are set to zeros by ReLU.

[6] FFN: Second Layer
↳ Feed all 5 features (d=3) into the second layer.
↳ The dimensionality of each feature is decreased from 4 back to 3.
↳ The output is fed to the next block to repeat this process.
↳ Note that the next block would have a completely separate set of parameters.

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[1] 𝗪𝗵𝗮𝘁 𝗠𝗮𝘁𝘁𝗲𝗿𝘀 𝗶𝗻 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿𝘀? 𝗡𝗼𝘁 𝗔𝗹𝗹 𝗔𝘁𝘁𝗲𝗻𝘁𝗶𝗼𝗻 𝗶𝘀 𝗡𝗲𝗲𝗱𝗲𝗱

[2] 𝗣𝗿𝗲𝗱𝗶𝗰𝘁𝗶𝗻𝗴 𝗳𝗿𝗼𝗺 𝗦𝘁𝗿𝗶𝗻𝗴𝘀: 𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲 𝗠𝗼𝗱𝗲𝗹 𝗘𝗺𝗯𝗲𝗱𝗱𝗶𝗻𝗴𝘀 𝗳𝗼𝗿 𝗕𝗮𝘆𝗲𝘀𝗶𝗮𝗻 𝗢𝗽𝘁𝗶𝗺𝗶𝘇𝗮𝘁𝗶𝗼𝗻

[3] 𝗠𝗢𝗗𝗘𝗟 𝗦𝗪𝗔𝗥𝗠𝗦: 𝗖𝗼𝗹𝗹𝗮𝗯𝗼𝗿𝗮𝘁𝗶𝘃𝗲 𝗦𝗲𝗮𝗿𝗰𝗵 𝘁𝗼 𝗔𝗱𝗮𝗽𝘁 𝗟𝗟𝗠 𝗘𝘅𝗽𝗲𝗿𝘁𝘀 𝘃𝗶𝗮 𝗦𝘄𝗮𝗿𝗺 𝗜𝗻𝘁𝗲𝗹𝗹𝗶𝗴𝗲𝗻𝗰𝗲

[4] 𝗧𝗛𝗜𝗡𝗞𝗜𝗡𝗚 𝗟𝗟𝗠𝗦: 𝗚𝗲𝗻𝗲𝗿𝗮𝗹 𝗜𝗻𝘀𝘁𝗿𝘂𝗰𝘁𝗶𝗼𝗻 𝗙𝗼𝗹𝗹𝗼𝘄𝗶𝗻𝗴 𝘄𝗶𝘁𝗵 𝗧𝗵𝗼𝘂𝗴𝗵𝘁 𝗚𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻

[5] 𝗢𝗽𝗲𝗻𝗩𝗟𝗔: 𝗔𝗻 𝗢𝗽𝗲𝗻-𝗦𝗼𝘂𝗿𝗰𝗲 𝗩𝗶𝘀𝗶𝗼𝗻-𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲-𝗔𝗰𝘁𝗶𝗼𝗻 𝗠𝗼𝗱𝗲𝗹

[6] 𝗥𝗧-𝟭: 𝗥𝗼𝗯𝗼𝘁𝗶𝗰𝘀 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿 𝗳𝗼𝗿 𝗥𝗲𝗮𝗹-𝗪𝗼𝗿𝗹𝗱 𝗖𝗼𝗻𝘁𝗿𝗼𝗹 𝗔𝘁 𝗦𝗰𝗮𝗹𝗲

[7] π𝟬: 𝗔 𝗩𝗶𝘀𝗶𝗼𝗻-𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲-𝗔𝗰𝘁𝗶𝗼𝗻 𝗙𝗹𝗼𝘄 𝗠𝗼𝗱𝗲𝗹 𝗳𝗼𝗿 𝗚𝗲𝗻𝗲𝗿𝗮𝗹 𝗥𝗼𝗯𝗼𝘁 𝗖𝗼𝗻𝘁𝗿𝗼𝗹

[8] 𝗥𝗲𝘁𝗿𝗶𝗲𝘃𝗮𝗹𝗔𝘁𝘁𝗲𝗻𝘁𝗶𝗼𝗻: 𝗔𝗰𝗰𝗲𝗹𝗲𝗿𝗮𝘁𝗶𝗻𝗴 𝗟𝗼𝗻𝗴-𝗖𝗼𝗻𝘁𝗲𝘅𝘁 𝗟𝗟𝗠 𝗜𝗻𝗳𝗲𝗿𝗲𝗻𝗰𝗲 𝘃𝗶𝗮 𝗩𝗲𝗰𝘁𝗼𝗿 𝗥𝗲𝘁𝗿𝗶𝗲𝘃𝗮𝗹

[9] 𝗣-𝗥𝗔𝗚: 𝗣𝗿𝗼𝗴𝗿𝗲𝘀𝘀𝗶𝘃𝗲 𝗥𝗲𝘁𝗿𝗶𝗲𝘃𝗮𝗹 𝗔𝘂𝗴𝗺𝗲𝗻𝘁𝗲𝗱 𝗚𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻 𝗙𝗼𝗿 𝗣𝗹𝗮𝗻𝗻𝗶𝗻𝗴 𝗼𝗻 𝗘𝗺𝗯𝗼𝗱𝗶𝗲𝗱 𝗘𝘃𝗲𝗿𝘆𝗱𝗮𝘆 𝗧𝗮𝘀𝗸

[10] 𝗥𝘂𝗔𝗚: 𝗟𝗲𝗮𝗿𝗻𝗲𝗱-𝗥𝘂𝗹𝗲-𝗔𝘂𝗴𝗺𝗲𝗻𝘁𝗲𝗱 𝗚𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻 𝗙𝗼𝗿 𝗟𝗮𝗿𝗴𝗲 𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲 𝗠𝗼𝗱𝗲𝗹𝘀

[11] 𝗢𝗻 𝘁𝗵𝗲 𝗦𝘂𝗿𝗽𝗿𝗶𝘀𝗶𝗻𝗴 𝗘𝗳𝗳𝗲𝗰𝘁𝗶𝘃𝗲𝗻𝗲𝘀𝘀 𝗼𝗳 𝗔𝘁𝘁𝗲𝗻𝘁𝗶𝗼𝗻 𝗧𝗿𝗮𝗻𝘀𝗳𝗲𝗿 𝗳𝗼𝗿 𝗩𝗶𝘀𝗶𝗼𝗻 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿𝘀

[12] 𝗠𝗶𝘅𝘁𝘂𝗿𝗲-𝗼𝗳-𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿𝘀: 𝗔 𝗦𝗽𝗮𝗿𝘀𝗲 𝗮𝗻𝗱 𝗦𝗰𝗮𝗹𝗮𝗯𝗹𝗲 𝗔𝗿𝗰𝗵𝗶𝘁𝗲𝗰𝘁𝘂𝗿𝗲 𝗳𝗼𝗿 𝗠𝘂𝗹𝘁𝗶-𝗠𝗼𝗱𝗮𝗹 𝗙𝗼𝘂𝗻𝗱𝗮𝘁𝗶𝗼𝗻 𝗠𝗼𝗱𝗲𝗹𝘀

[13]-[14] 𝗘𝗱𝗶𝗳𝘆 𝟯𝗗: 𝗦𝗰𝗮𝗹𝗮𝗯𝗹𝗲 𝗛𝗶𝗴𝗵-𝗤𝘂𝗮𝗹𝗶𝘁𝘆 𝟯𝗗 𝗔𝘀𝘀𝗲𝘁 𝗚𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻

[15] 𝗕𝘆𝘁𝗲 𝗟𝗮𝘁𝗲𝗻𝘁 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿: 𝗣𝗮𝘁𝗰𝗵𝗲𝘀 𝗦𝗰𝗮𝗹𝗲 𝗕𝗲𝘁𝘁𝗲𝗿 𝗧𝗵𝗮𝗻 𝗧𝗼𝗸𝗲𝗻𝘀

[16]-[18] 𝗗𝗲𝗲𝗽𝗦𝗲𝗲𝗸-𝗩𝟯 (𝗣𝗮𝗿𝘁 𝟭-𝟯)

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