{"componentChunkName":"component---src-templates-blog-post-js","path":"/transformer/","result":{"data":{"site":{"siteMetadata":{"title":"Nicolae Vartolomei"}},"mdx":{"id":"39678122-d193-524f-b5ad-ed660eb3149a","body":"function _extends(){_extends=Object.assign||function(target){for(var i=1;i=0)continue;if(!Object.prototype.propertyIsEnumerable.call(source,key))continue;target[key]=source[key];}}return target;}function _objectWithoutPropertiesLoose(source,excluded){if(source==null)return{};var target={};var sourceKeys=Object.keys(source);var key,i;for(i=0;i=0)continue;target[key]=source[key];}return target;}/* @jsx mdx */var _frontmatter={\"title\":\"Transformer: A Top-Down Explanation\",\"date\":\"2026-10-11T00:00:00Z\",\"darkImages\":\"invert\",\"importance\":4.5};var layoutProps={_frontmatter:_frontmatter};var MDXLayout=\"wrapper\";return function MDXContent(_ref){var components=_ref.components,props=_objectWithoutProperties(_ref,[\"components\"]);return mdx(MDXLayout,_extends({},layoutProps,props,{components:components,mdxType:\"MDXLayout\"}),mdx(\"p\",null,mdx(\"em\",{parentName:\"p\"},mdx(\"strong\",{parentName:\"em\"},\"Work in progress\"))),mdx(\"p\",null,\"Alternative titles: \",mdx(\"em\",{parentName:\"p\"},\"Applying the Feynman Technique to Understanding the\\nTransformer Architecture\"),\", or \",mdx(\"em\",{parentName:\"p\"},\"The Life of a Token Inside a Transformer\"),\",\\nor \",mdx(\"em\",{parentName:\"p\"},\"The Transformer for the Impatient\"),\".\"),mdx(\"div\",{className:\"table-of-contents\"},mdx(\"ul\",null,mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#intro\"}),\"Intro\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#high-level-overview\"}),\"High-level Overview\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#gpt\"}),\"GPT\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#auto-regressive-generation\"}),\"Auto-regressive Generation\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#from-text-to-numbers\"}),\"From Text to Numbers\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#through-the-encoder\"}),\"Through the Encoder\"),mdx(\"ul\",{parentName:\"li\"},mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#inside-an-encoder-layer\"}),\"Inside an Encoder Layer\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#two-eight-heads-are-better-than-one\"}),mdx(\"em\",{parentName:\"a\"},mdx(\"del\",{parentName:\"em\"},\"Two\"),\" Eight Heads Are Better Than One\"))),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#inside-an-encoder-attention-head\"}),\"Inside an Encoder Attention Head\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#putting-the-heads-together\"}),\"Putting the Heads Together\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#first-residual-connection\"}),\"First Residual Connection\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#encoder-feed-forward-network\"}),\"Encoder Feed-Forward Network\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#six-layers-later\"}),\"Six Layers Later\")),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#encoder-only-models\"}),\"Encoder-Only Models\")))),mdx(\"li\",{parentName:\"ul\"},mdx(\"a\",_extends({parentName:\"li\"},{\"href\":\"#through-the-decoder\"}),\"Through the Decoder\")))),mdx(\"h2\",{\"id\":\"intro\",\"style\":{\"position\":\"relative\"}},\"Intro\",mdx(\"a\",_extends({parentName:\"h2\"},{\"href\":\"#intro\",\"aria-label\":\"intro permalink\",\"className\":\"anchor after\"}),mdx(\"svg\",_extends({parentName:\"a\"},{\"aria-hidden\":\"true\",\"focusable\":\"false\",\"height\":\"16\",\"version\":\"1.1\",\"viewBox\":\"0 0 16 16\",\"width\":\"16\"}),mdx(\"path\",_extends({parentName:\"svg\"},{\"fillRule\":\"evenodd\",\"d\":\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"}))))),mdx(\"p\",null,\"In 2017, researchers at Google publish the\\n\",mdx(\"a\",_extends({parentName:\"p\"},{\"href\":\"https://arxiv.org/abs/1706.03762\"}),mdx(\"em\",{parentName:\"a\"},\"Attention Is All You Need\")),\" paper, in which they introduce\\nthe \",mdx(\"strong\",{parentName:\"p\"},\"Transformer architecture\"),\". The world runs with it.\"),mdx(\"p\",null,\"Soon after, researchers at OpenAI develop a belief that this architecture scales\\nbetter than anything they\\u2019ve seen. In 2020, they publish the\\n\",mdx(\"a\",_extends({parentName:\"p\"},{\"href\":\"https://arxiv.org/abs/2001.08361\"}),mdx(\"em\",{parentName:\"a\"},\"Scaling Laws for Neural Language Models\")),\" paper and keep feeding\\ndata and compute to a variant of the Transformer, which they then teach to\\nfollow instructions. In November 2022, \",mdx(\"strong\",{parentName:\"p\"},\"ChatGPT\"),\" is born.\"),mdx(\"p\",null,\"The field has moved fast since, but today\\u2019s \",mdx(\"strong\",{parentName:\"p\"},\"large language models\"),\" (LLMs)\\nare still Transformers. Understanding the original gives you a point of\\nreference for everything that came after. At least that\\u2019s my bet.\"),mdx(\"p\",null,\"So let\\u2019s travel back to 2017 and figure out how the \",mdx(\"del\",{parentName:\"p\"},\"sausage\"),\" token is made.\"),mdx(\"p\",null,\"My focus here is on the arithmetic, not intelligence.\"),mdx(\"h2\",{\"id\":\"high-level-overview\",\"style\":{\"position\":\"relative\"}},\"High-level Overview\",mdx(\"a\",_extends({parentName:\"h2\"},{\"href\":\"#high-level-overview\",\"aria-label\":\"high level overview permalink\",\"className\":\"anchor after\"}),mdx(\"svg\",_extends({parentName:\"a\"},{\"aria-hidden\":\"true\",\"focusable\":\"false\",\"height\":\"16\",\"version\":\"1.1\",\"viewBox\":\"0 0 16 16\",\"width\":\"16\"}),mdx(\"path\",_extends({parentName:\"svg\"},{\"fillRule\":\"evenodd\",\"d\":\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"}))))),mdx(\"figure\",{style:{maxWidth:\"400px\",marginLeft:\"auto\",marginRight:\"auto\"}},mdx(\"p\",null,mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"gatsby-resp-image-wrapper\",\"style\":{\"position\":\"relative\",\"display\":\"block\",\"marginLeft\":\"auto\",\"marginRight\":\"auto\",\"maxWidth\":\"590px\"}}),\"\\n \",mdx(\"a\",_extends({parentName:\"span\"},{\"className\":\"gatsby-resp-image-link\",\"href\":\"/static/fac942f68181c809efc96cc4ce340e86/891d5/transformer.png\",\"style\":{\"display\":\"block\"},\"target\":\"_blank\",\"rel\":\"noopener\"}),\"\\n \",mdx(\"span\",_extends({parentName:\"a\"},{\"className\":\"gatsby-resp-image-background-image\",\"style\":{\"paddingBottom\":\"147.2972972972973%\",\"position\":\"relative\",\"bottom\":\"0\",\"left\":\"0\",\"display\":\"block\"}})),\"\\n \",mdx(\"img\",_extends({parentName:\"a\"},{\"className\":\"gatsby-resp-image-image\",\"alt\":\"Transformer architecture diagram\",\"title\":\"Transformer architecture diagram\",\"src\":\"/static/fac942f68181c809efc96cc4ce340e86/fcda8/transformer.png\",\"srcSet\":[\"/static/fac942f68181c809efc96cc4ce340e86/12f09/transformer.png 148w\",\"/static/fac942f68181c809efc96cc4ce340e86/e4a3f/transformer.png 295w\",\"/static/fac942f68181c809efc96cc4ce340e86/fcda8/transformer.png 590w\",\"/static/fac942f68181c809efc96cc4ce340e86/efc66/transformer.png 885w\",\"/static/fac942f68181c809efc96cc4ce340e86/c83ae/transformer.png 1180w\",\"/static/fac942f68181c809efc96cc4ce340e86/891d5/transformer.png 1520w\"],\"sizes\":\"(max-width: 590px) 100vw, 590px\",\"style\":{\"width\":\"100%\",\"height\":\"100%\",\"margin\":\"0\",\"verticalAlign\":\"middle\",\"position\":\"absolute\",\"top\":\"0\",\"left\":\"0\"},\"loading\":\"eager\"})),\"\\n \"),\"\\n \")),mdx(\"figcaption\",null,\"The Transformer - model architecture.\",mdx(\"br\",null),\"Figure 1 from \",mdx(\"a\",{href:\"https://arxiv.org/abs/1706.03762\"},mdx(\"em\",null,\"Attention Is All You Need\")),\" (Vaswani et al., 2017).\")),mdx(\"p\",null,\"The Transformer is introduced as a transduction model, mainly in the context\\nof machine translation. That is, the model takes a phrase in one language\\nand \",mdx(\"strong\",{parentName:\"p\"},\"transforms\"),\" (transduces) it into another.\"),mdx(\"p\",null,\"Let\\u2019s pick an example we\\u2019ll follow through the rest of the 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op-limits\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"vlist-t vlist-t2\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"vlist-r\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"vlist\",\"style\":{\"height\":\"0.6944em\"}}),mdx(\"span\",_extends({parentName:\"span\"},{\"style\":{\"top\":\"-2.1535em\",\"marginLeft\":\"0em\"}}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"pstrut\",\"style\":{\"height\":\"3em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-sizing reset-size6 size3 mtight\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mtight\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord text mtight\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord 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an input sequence of symbol representations\\n\",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\"(\"),mdx(\"msub\",{parentName:\"mrow\"},mdx(\"mi\",{parentName:\"msub\"},\"x\"),mdx(\"mn\",{parentName:\"msub\"},\"1\")),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"separator\":\"true\"}),\",\"),mdx(\"mo\",{parentName:\"mrow\"},\"\\u2026\"),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"separator\":\"true\"}),\",\"),mdx(\"msub\",{parentName:\"mrow\"},mdx(\"mi\",{parentName:\"msub\"},\"x\"),mdx(\"mi\",{parentName:\"msub\"},\"n\")),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\")\")),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"(x_1, 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We\\u2019ll solve that after a short\\ndetour.\"),mdx(\"h2\",{\"id\":\"gpt\",\"style\":{\"position\":\"relative\"}},\"GPT\",mdx(\"a\",_extends({parentName:\"h2\"},{\"href\":\"#gpt\",\"aria-label\":\"gpt permalink\",\"className\":\"anchor after\"}),mdx(\"svg\",_extends({parentName:\"a\"},{\"aria-hidden\":\"true\",\"focusable\":\"false\",\"height\":\"16\",\"version\":\"1.1\",\"viewBox\":\"0 0 16 16\",\"width\":\"16\"}),mdx(\"path\",_extends({parentName:\"svg\"},{\"fillRule\":\"evenodd\",\"d\":\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"}))))),mdx(\"p\",null,\"In the intro, I drew a timeline from the Transformer to ChatGPT-like LLMs.\\nBefore it becomes confusing, I need to draw a line from machine translation\\nmodels to chat and agentic models.\"),mdx(\"p\",null,\"In chat and agentic models, we don\\u2019t want our input to be transformed. We want\\nthe model to \",mdx(\"em\",{parentName:\"p\"},\"respond to it\"),\". To make this happen, we figured we could ignore the\\nencoder side, pass the input as if the decoder wrote it, and let it \",mdx(\"em\",{parentName:\"p\"},\"continue\\nit\"),\". We take that newly written output as the model response.\"),mdx(\"p\",null,\"The original ChatGPT and pretty much all LLMs today are built only on the\\ndecoder stack of the Transformer, the right side of the diagram above (minus the\\nmiddle attention block that connects the encoder). Such models are called\\n\",mdx(\"strong\",{parentName:\"p\"},\"decoder-only Transformers\"),\". The decoder is the half that \",mdx(\"em\",{parentName:\"p\"},\"generates\"),\", which\\ngives us the \",mdx(\"em\",{parentName:\"p\"},\"G\"),\" and the \",mdx(\"em\",{parentName:\"p\"},\"T\"),\" in GPT.\"),mdx(\"figure\",{style:{maxWidth:\"400px\",marginLeft:\"auto\",marginRight:\"auto\"}},mdx(\"p\",null,mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"gatsby-resp-image-wrapper\",\"style\":{\"position\":\"relative\",\"display\":\"block\",\"marginLeft\":\"auto\",\"marginRight\":\"auto\",\"maxWidth\":\"590px\"}}),\"\\n \",mdx(\"a\",_extends({parentName:\"span\"},{\"className\":\"gatsby-resp-image-link\",\"href\":\"/static/330e4892f98e82514b41b85635768203/891d5/transformer-decoder-only.png\",\"style\":{\"display\":\"block\"},\"target\":\"_blank\",\"rel\":\"noopener\"}),\"\\n \",mdx(\"span\",_extends({parentName:\"a\"},{\"className\":\"gatsby-resp-image-background-image\",\"style\":{\"paddingBottom\":\"147.2972972972973%\",\"position\":\"relative\",\"bottom\":\"0\",\"left\":\"0\",\"display\":\"block\"}})),\"\\n \",mdx(\"img\",_extends({parentName:\"a\"},{\"className\":\"gatsby-resp-image-image\",\"alt\":\"From Transformer to Decoder-only Transformer\",\"title\":\"From Transformer to Decoder-only Transformer\",\"src\":\"/static/330e4892f98e82514b41b85635768203/fcda8/transformer-decoder-only.png\",\"srcSet\":[\"/static/330e4892f98e82514b41b85635768203/12f09/transformer-decoder-only.png 148w\",\"/static/330e4892f98e82514b41b85635768203/e4a3f/transformer-decoder-only.png 295w\",\"/static/330e4892f98e82514b41b85635768203/fcda8/transformer-decoder-only.png 590w\",\"/static/330e4892f98e82514b41b85635768203/efc66/transformer-decoder-only.png 885w\",\"/static/330e4892f98e82514b41b85635768203/c83ae/transformer-decoder-only.png 1180w\",\"/static/330e4892f98e82514b41b85635768203/891d5/transformer-decoder-only.png 1520w\"],\"sizes\":\"(max-width: 590px) 100vw, 590px\",\"style\":{\"width\":\"100%\",\"height\":\"100%\",\"margin\":\"0\",\"verticalAlign\":\"middle\",\"position\":\"absolute\",\"top\":\"0\",\"left\":\"0\"},\"loading\":\"eager\"})),\"\\n \"),\"\\n \"))),mdx(\"p\",null,\"There\\u2019s more though, \",mdx(\"strong\",{parentName:\"p\"},\"encoder-only Transformer\"),\" variants also exist and are\\nactively used for tasks such as classification, semantic similarity, etc. It is\\nimpressive how many problems have been influenced by this paper. We are getting\\na taste of why it is such a big deal.\"),mdx(\"h2\",{\"id\":\"auto-regressive-generation\",\"style\":{\"position\":\"relative\"}},\"Auto-regressive Generation\",mdx(\"a\",_extends({parentName:\"h2\"},{\"href\":\"#auto-regressive-generation\",\"aria-label\":\"auto regressive generation permalink\",\"className\":\"anchor after\"}),mdx(\"svg\",_extends({parentName:\"a\"},{\"aria-hidden\":\"true\",\"focusable\":\"false\",\"height\":\"16\",\"version\":\"1.1\",\"viewBox\":\"0 0 16 16\",\"width\":\"16\"}),mdx(\"path\",_extends({parentName:\"svg\"},{\"fillRule\":\"evenodd\",\"d\":\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"}))))),mdx(\"p\",null,\"Why do Output arrows go \",mdx(\"em\",{parentName:\"p\"},\"into\"),\" the Transformer? It makes more sense if we\\nrewind the translation a couple of steps:\"),mdx(\"figure\",{style:{maxWidth:\"400px\",marginLeft:\"auto\",marginRight:\"auto\"}},mdx(\"p\",null,mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"gatsby-resp-image-wrapper\",\"style\":{\"position\":\"relative\",\"display\":\"block\",\"marginLeft\":\"auto\",\"marginRight\":\"auto\",\"maxWidth\":\"590px\"}}),\"\\n \",mdx(\"a\",_extends({parentName:\"span\"},{\"className\":\"gatsby-resp-image-link\",\"href\":\"/static/f111a919099f686aadc0aaf054301061/891d5/transformer-inputs-outputs-t-1.png\",\"style\":{\"display\":\"block\"},\"target\":\"_blank\",\"rel\":\"noopener\"}),\"\\n \",mdx(\"span\",_extends({parentName:\"a\"},{\"className\":\"gatsby-resp-image-background-image\",\"style\":{\"paddingBottom\":\"161.48648648648648%\",\"position\":\"relative\",\"bottom\":\"0\",\"left\":\"0\",\"display\":\"block\"}})),\"\\n \",mdx(\"img\",_extends({parentName:\"a\"},{\"className\":\"gatsby-resp-image-image\",\"alt\":\"Transformer inputs outputs\",\"title\":\"Transformer inputs outputs\",\"src\":\"/static/f111a919099f686aadc0aaf054301061/fcda8/transformer-inputs-outputs-t-1.png\",\"srcSet\":[\"/static/f111a919099f686aadc0aaf054301061/12f09/transformer-inputs-outputs-t-1.png 148w\",\"/static/f111a919099f686aadc0aaf054301061/e4a3f/transformer-inputs-outputs-t-1.png 295w\",\"/static/f111a919099f686aadc0aaf054301061/fcda8/transformer-inputs-outputs-t-1.png 590w\",\"/static/f111a919099f686aadc0aaf054301061/efc66/transformer-inputs-outputs-t-1.png 885w\",\"/static/f111a919099f686aadc0aaf054301061/c83ae/transformer-inputs-outputs-t-1.png 1180w\",\"/static/f111a919099f686aadc0aaf054301061/891d5/transformer-inputs-outputs-t-1.png 1520w\"],\"sizes\":\"(max-width: 590px) 100vw, 590px\",\"style\":{\"width\":\"100%\",\"height\":\"100%\",\"margin\":\"0\",\"verticalAlign\":\"middle\",\"position\":\"absolute\",\"top\":\"0\",\"left\":\"0\"},\"loading\":\"eager\"})),\"\\n \"),\"\\n \"))),mdx(\"p\",null,\"Remember the last sentence of the opening paragraph of the \",mdx(\"em\",{parentName:\"p\"},\"Model Architecture\"),\" section:\"),mdx(\"blockquote\",null,mdx(\"p\",{parentName:\"blockquote\"},\"At each step the model is auto-regressive, consuming the previously generated\\nsymbols as additional input when generating the next.\")),mdx(\"p\",null,\"So before the word \",mdx(\"code\",_extends({parentName:\"p\"},{\"className\":\"language-text\"}),\"apples\"),\" is predicted, we pass the previously generated output \",mdx(\"code\",_extends({parentName:\"p\"},{\"className\":\"language-text\"}),\"Ana has\"),\"\\ninto the model and the model predicts \",mdx(\"em\",{parentName:\"p\"},\"the next word\"),\". In this case \",mdx(\"code\",_extends({parentName:\"p\"},{\"className\":\"language-text\"}),\"apples\"),\" by giving it\\na probability of \",mdx(\"code\",_extends({parentName:\"p\"},{\"className\":\"language-text\"}),\"0.92\"),\".\"),mdx(\"p\",null,\"There are three missing details from the diagram to make it complete at this\\nlevel of abstraction. One of them is probably already on your mind: \",mdx(\"em\",{parentName:\"p\"},\"How do we know\\nwhen to stop generating new words?\"),\" For this, we use a special word: \",mdx(\"code\",_extends({parentName:\"p\"},{\"className\":\"language-text\"}),\"EOS\"),\" (\",mdx(\"em\",{parentName:\"p\"},\"End of\\nSequence\"),\"). When the model picks it as the next word, we stop.\"),mdx(\"p\",null,\"The second is that the decoder doesn\\u2019t output just one probability distribution\\nfor the next word. It outputs one for every position in the\\noutput sequence \",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"mi\",_extends({parentName:\"mrow\"},{\"mathvariant\":\"bold\"}),\"y\")),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"\\\\mathbf{y}\")))),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-html\",\"aria-hidden\":\"true\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-base\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-strut\",\"style\":{\"height\":\"0.6389em\",\"verticalAlign\":\"-0.1944em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mathbf\",\"style\":{\"marginRight\":\"0.016em\"}}),\"y\")))),\", predicting the word that follows that\\nposition.\"),mdx(\"p\",null,\"This creates a chicken-and-egg problem: if every word is predicted from the\\nposition before it, where does the first word come from? To solve this, we\\nintroduce another special word, the third missing detail:\\n\",mdx(\"code\",_extends({parentName:\"p\"},{\"className\":\"language-text\"}),\"BOS\"),\" (\",mdx(\"em\",{parentName:\"p\"},\"Beginning of Sequence\"),\") and put it in the first position.\\nThe distribution at that position gives us the first word.\"),mdx(\"p\",null,\"At this conceptual level, the complete diagram of the last step looks like this:\"),mdx(\"figure\",{style:{maxWidth:\"400px\",marginLeft:\"auto\",marginRight:\"auto\"}},mdx(\"p\",null,mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"gatsby-resp-image-wrapper\",\"style\":{\"position\":\"relative\",\"display\":\"block\",\"marginLeft\":\"auto\",\"marginRight\":\"auto\",\"maxWidth\":\"590px\"}}),\"\\n \",mdx(\"a\",_extends({parentName:\"span\"},{\"className\":\"gatsby-resp-image-link\",\"href\":\"/static/d7e6d3b0ac7886fd07ffe96953709526/1e1c3/transformer-inputs-outputs-full.png\",\"style\":{\"display\":\"block\"},\"target\":\"_blank\",\"rel\":\"noopener\"}),\"\\n \",mdx(\"span\",_extends({parentName:\"a\"},{\"className\":\"gatsby-resp-image-background-image\",\"style\":{\"paddingBottom\":\"161.48648648648648%\",\"position\":\"relative\",\"bottom\":\"0\",\"left\":\"0\",\"display\":\"block\"}})),\"\\n \",mdx(\"img\",_extends({parentName:\"a\"},{\"className\":\"gatsby-resp-image-image\",\"alt\":\"Transformer inputs outputs full fidelity\",\"title\":\"Transformer inputs outputs full fidelity\",\"src\":\"/static/d7e6d3b0ac7886fd07ffe96953709526/fcda8/transformer-inputs-outputs-full.png\",\"srcSet\":[\"/static/d7e6d3b0ac7886fd07ffe96953709526/12f09/transformer-inputs-outputs-full.png 148w\",\"/static/d7e6d3b0ac7886fd07ffe96953709526/e4a3f/transformer-inputs-outputs-full.png 295w\",\"/static/d7e6d3b0ac7886fd07ffe96953709526/fcda8/transformer-inputs-outputs-full.png 590w\",\"/static/d7e6d3b0ac7886fd07ffe96953709526/efc66/transformer-inputs-outputs-full.png 885w\",\"/static/d7e6d3b0ac7886fd07ffe96953709526/c83ae/transformer-inputs-outputs-full.png 1180w\",\"/static/d7e6d3b0ac7886fd07ffe96953709526/1e1c3/transformer-inputs-outputs-full.png 1670w\"],\"sizes\":\"(max-width: 590px) 100vw, 590px\",\"style\":{\"width\":\"100%\",\"height\":\"100%\",\"margin\":\"0\",\"verticalAlign\":\"middle\",\"position\":\"absolute\",\"top\":\"0\",\"left\":\"0\"},\"loading\":\"eager\"})),\"\\n \"),\"\\n \"))),mdx(\"p\",null,\"Each term \",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"mi\",{parentName:\"mrow\"},\"P\"),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\"(\"),mdx(\"msub\",{parentName:\"mrow\"},mdx(\"mi\",{parentName:\"msub\"},\"y\"),mdx(\"mi\",{parentName:\"msub\"},\"i\")),mdx(\"mo\",{parentName:\"mrow\"},\"\\u2223\"),mdx(\"msub\",{parentName:\"mrow\"},mdx(\"mi\",{parentName:\"msub\"},\"y\"),mdx(\"mrow\",{parentName:\"msub\"},mdx(\"mo\",{parentName:\"mrow\"},\"<\"),mdx(\"mi\",{parentName:\"mrow\"},\"i\"))),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"separator\":\"true\"}),\",\"),mdx(\"mi\",{parentName:\"mrow\"},\"x\"),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\")\")),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"P(y_i \\\\mid y_{ \"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"token interpolation\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"token punctuation\"}),\"{\"),\"ids\",mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"token punctuation\"}),\"}\")),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"token string\"}),\"\\\"\")),mdx(\"span\",_extends({parentName:\"code\"},{\"className\":\"token punctuation\"}),\")\")))),mdx(\"div\",{\"className\":\"gatsby-highlight\",\"data-language\":\"bash\"},mdx(\"pre\",_extends({parentName:\"div\"},{\"className\":\"language-bash\"}),mdx(\"code\",_extends({parentName:\"pre\"},{\"className\":\"language-bash\"}),\"uv run --with tiktoken python tokens.py\"))),mdx(\"div\",{\"className\":\"gatsby-highlight\",\"data-language\":\"text\"},mdx(\"pre\",_extends({parentName:\"div\"},{\"className\":\"language-text\"}),mdx(\"code\",_extends({parentName:\"pre\"},{\"className\":\"language-text\"}),\"'Ana are mere.': ['An', 'a', ' are', ' mere', '.'] -> [2025, 64, 389, 5019, 13]\")))),mdx(\"p\",null,\"For the output, we will go the other way: pick a token ID from each probability\\ndistribution, then turn the IDs back into text.\"),mdx(\"p\",null,\"Note: \",mdx(\"code\",_extends({parentName:\"p\"},{\"className\":\"language-text\"}),\"r50k_base\"),\" has no separate \",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\"\\u27E8\"),mdx(\"mtext\",{parentName:\"mrow\"},\"BOS\"),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\"\\u27E9\")),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"\\\\langle\\\\text{BOS}\\\\rangle\")))),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-html\",\"aria-hidden\":\"true\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-base\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-strut\",\"style\":{\"height\":\"1em\",\"verticalAlign\":\"-0.25em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mopen\"}),\"\\u27E8\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord text\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord\"}),\"BOS\")),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mclose\"}),\"\\u27E9\")))),\" and\\n\",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\"\\u27E8\"),mdx(\"mtext\",{parentName:\"mrow\"},\"EOS\"),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\"\\u27E9\")),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"\\\\langle\\\\text{EOS}\\\\rangle\")))),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-html\",\"aria-hidden\":\"true\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-base\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-strut\",\"style\":{\"height\":\"1em\",\"verticalAlign\":\"-0.25em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mopen\"}),\"\\u27E8\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord 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We add the attention output back to the input, a \",mdx(\"em\",{parentName:\"p\"},\"residual connection\"),\",\\nand normalize the sum (\",mdx(\"strong\",{parentName:\"p\"},\"Add & Norm\"),\"). Normalizing rescales each token\\u2019s\\nnumbers into the same range, so they don\\u2019t grow as every layer adds to them.\\nWe\\u2019ll name the normalized sum 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In the\\ncase of the encoder, all three inputs of the middle sub-figure carry the same\\nmatrix: \",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"msup\",{parentName:\"mrow\"},mdx(\"mi\",_extends({parentName:\"msup\"},{\"mathvariant\":\"bold\"}),\"z\"),mdx(\"mrow\",{parentName:\"msup\"},mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\"(\"),mdx(\"mi\",_extends({parentName:\"mrow\"},{\"mathvariant\":\"normal\"}),\"\\u2113\"),mdx(\"mo\",{parentName:\"mrow\"},\"\\u2212\"),mdx(\"mn\",{parentName:\"mrow\"},\"1\"),mdx(\"mo\",_extends({parentName:\"mrow\"},{\"stretchy\":\"false\"}),\")\")))),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"\\\\mathbf{z}^{(\\\\ell-1)}\")))),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-html\",\"aria-hidden\":\"true\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-base\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-strut\",\"style\":{\"height\":\"0.888em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mathbf\"}),\"z\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"msupsub\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"vlist-t\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"vlist-r\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"vlist\",\"style\":{\"height\":\"0.888em\"}}),mdx(\"span\",_extends({parentName:\"span\"},{\"style\":{\"top\":\"-3.063em\",\"marginRight\":\"0.05em\"}}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"pstrut\",\"style\":{\"height\":\"2.7em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-sizing reset-size6 size3 mtight\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mtight\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mopen mtight\"}),\"(\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mtight\"}),\"\\u2113\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mbin mtight\"}),\"\\u2212\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mtight\"}),\"1\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mclose mtight\"}),\")\")))))))))))),\"! This is the trident we\\nsaw earlier\\u2014\",mdx(\"em\",{parentName:\"p\"},\"binding\"),\" the input to parameter names.\"),mdx(\"p\",null,\"You can see that each of the V, K, Q lines on the diagram forks further into \",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"mi\",{parentName:\"mrow\"},\"h\")),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"h\")))),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-html\",\"aria-hidden\":\"true\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-base\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-strut\",\"style\":{\"height\":\"0.6944em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mathnormal\"}),\"h\")))),\"\\nseparate branches, the heads, matching its \",mdx(\"strong\",{parentName:\"p\"},\"Multi-Head\"),\" name. Think of each\\n\",mdx(\"em\",{parentName:\"p\"},\"head\"),\" as an independent computation process. Each has the same structure and\\nits own parameters, so each can focus on different \",mdx(\"em\",{parentName:\"p\"},\"features\"),\" of the input.\"),mdx(\"p\",null,\"In the paper, the authors use \",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"mi\",{parentName:\"mrow\"},\"h\"),mdx(\"mo\",{parentName:\"mrow\"},\"=\"),mdx(\"mn\",{parentName:\"mrow\"},\"8\")),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"h = 8\")))),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-html\",\"aria-hidden\":\"true\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-base\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-strut\",\"style\":{\"height\":\"0.6944em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mathnormal\"}),\"h\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mspace\",\"style\":{\"marginRight\":\"0.2778em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mrel\"}),\"=\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mspace\",\"style\":{\"marginRight\":\"0.2778em\"}}))),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-base\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-strut\",\"style\":{\"height\":\"0.6444em\"}})),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord\"}),\"8\")))),\" heads. So the layer 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mtight\"}),\"\\u2212\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mord mtight\"}),\"1\"),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"mclose mtight\"}),\")\")))))))))))),\" inside Multi-Head Attention is really referenced\\n\",mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"katex\"}),mdx(\"span\",_extends({parentName:\"span\"},{\"className\":\"katex-mathml\"}),mdx(\"math\",_extends({parentName:\"span\"},{\"xmlns\":\"http://www.w3.org/1998/Math/MathML\"}),mdx(\"semantics\",{parentName:\"math\"},mdx(\"mrow\",{parentName:\"semantics\"},mdx(\"mn\",{parentName:\"mrow\"},\"3\"),mdx(\"mo\",{parentName:\"mrow\"},\"\\xD7\"),mdx(\"mn\",{parentName:\"mrow\"},\"8\"),mdx(\"mo\",{parentName:\"mrow\"},\"=\"),mdx(\"mn\",{parentName:\"mrow\"},\"24\")),mdx(\"annotation\",_extends({parentName:\"semantics\"},{\"encoding\":\"application/x-tex\"}),\"3 \\\\times 8 = 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times: V, K, Q once for each head.\"),mdx(\"h3\",{\"id\":\"inside-an-encoder-attention-head\",\"style\":{\"position\":\"relative\"}},\"Inside an Encoder Attention Head\",mdx(\"a\",_extends({parentName:\"h3\"},{\"href\":\"#inside-an-encoder-attention-head\",\"aria-label\":\"inside an encoder attention head permalink\",\"className\":\"anchor after\"}),mdx(\"svg\",_extends({parentName:\"a\"},{\"aria-hidden\":\"true\",\"focusable\":\"false\",\"height\":\"16\",\"version\":\"1.1\",\"viewBox\":\"0 0 16 16\",\"width\":\"16\"}),mdx(\"path\",_extends({parentName:\"svg\"},{\"fillRule\":\"evenodd\",\"d\":\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"}))))),mdx(\"p\",null,\"Let\\u2019s bring our attention (pun!) to a single \",mdx(\"strong\",{parentName:\"p\"},\"attention head\"),\". I\\u2019ll zoom in\\non the diagram and make it more concrete. For this one, I dropped the paper\\u2019s\\n\",mdx(\"strong\",{parentName:\"p\"},\"Mask (opt.)\"),\" box between Scale and SoftMax because only the decoder uses it;\\nwe\\u2019ll get to it there.\"),mdx(\"figure\",{style:{maxWidth:\"400px\",marginLeft:\"auto\",marginRight:\"auto\"}},mdx(\"p\",null,mdx(\"span\",_extends({parentName:\"p\"},{\"className\":\"gatsby-resp-image-wrapper\",\"style\":{\"position\":\"relative\",\"display\":\"block\",\"marginLeft\":\"auto\",\"marginRight\":\"auto\",\"maxWidth\":\"590px\"}}),\"\\n \",mdx(\"a\",_extends({parentName:\"span\"},{\"className\":\"gatsby-resp-image-link\",\"href\":\"/static/8941622c182ba06eceb8aad238f6e4b8/5a190/transformer-encoder-attention-head.png\",\"style\":{\"display\":\"block\"},\"target\":\"_blank\",\"rel\":\"noopener\"}),\"\\n 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