For a sequence of T tokens, each already embedded as a vector of dimension d_model, the attention computation begins by projecting every token into three spaces via learned weight matrices W_Q, W_K, W_V:

Q = X · W_Q    K = X · W_K    V = X · W_V

Q and K are each T × d_k matrices (one row per token) — they must share the same dimension so that QK^T is defined. V is T × d_v, where d_v can differ from d_k in principle, though in practice the original transformer sets d_v = d_k for each head. The attention output is:

Attention(Q, K, V) = softmax( QK^T / √d_k ) · V

QK^T is a T×T matrix of all pairwise query-key dot products. Dividing by √d_k prevents the values from growing large enough to push softmax into near-zero-gradient regions. Softmax is applied row-wise, producing a probability distribution per token. Multiplying by V yields T output vectors — one updated representation per token, incorporating context from across the sequence.

One important property: this computation is permutation-invariant. If you shuffled all tokens randomly, you would get the same outputs (just rearranged). The model has no intrinsic sense of word order. Positional information is added separately — as a "positional encoding" vector added to each token's embedding before any attention computation — making word-order sensitivity a separable, engineered addition to an otherwise orderless mechanism.

A useful (if imperfect) gloss on the Q/K/V decomposition: queries and keys tend to track syntactic relationships — which tokens need to consult which other tokens, based on grammatical structure. Values tend to carry semantic content — what information actually flows when a relationship is established.

This isn't designed in — it emerges from training. But it makes intuitive sense: the question "does this adjective modify this noun?" is structurally determined, while the information that flows from noun to adjective (or vice versa) is semantic.

The decomposition is imperfect in practice. Some heads appear to do primarily syntactic work; others primarily semantic work; others something less interpretable. The query-key similarity determines whether information flows; the value determines what information flows. But these aren't orthogonal — a token's value may encode information about its syntactic role, and its key may encode semantic properties that determine relevance.

BERT (Bidirectional Encoder Representations from Transformers, Devlin et al. 2018) and GPT (Generative Pre-trained Transformer, Radford et al. 2018)⁴ represent two distinct uses of the transformer architecture, developed almost simultaneously.

BERT is a bidirectional encoder: it processes the entire sequence at once, allowing every token to attend to every other token in both directions. This produces rich contextual representations well-suited for tasks that require understanding complete sentences — classification, named entity recognition, reading comprehension. BERT cannot generate text autoregressively because it has no mechanism for producing one token at a time without "seeing" future tokens.

GPT is an autoregressive decoder: it processes tokens left-to-right, with each token only able to attend to previous tokens (future tokens are masked during training). This constraint is what enables text generation — the model predicts each next token based only on what came before. In principle, a bidirectional model could generate text by jointly predicting all tokens in a fixed-length window simultaneously, but this is computationally unwieldy and not used in practice.

The models you interact with (Claude, ChatGPT, Gemini) use GPT-style autoregressive architectures. BERT-style encoders are more common in specialized NLP applications where generation isn't required.

The sentences chosen for this artifact reflect a particular set of linguistic phenomena — pronoun resolution, adjective-noun modification, subject-verb agreement — that are well-studied in the English-language NLP literature. These are real and important phenomena, but they're not the only phenomena worth understanding, and they reflect assumptions about what "interesting" linguistic structure looks like.

Languages with different syntactic structures — verb-final languages like Japanese or Turkish, languages with grammatical gender agreement like French or Arabic, languages with complex evidentiality systems like many indigenous American languages — would present different attention patterns and different challenges. A pronoun disambiguation example presupposes a pronominal system like English's; many languages handle reference tracking very differently.

BERT itself was trained primarily on English Wikipedia and BookCorpus. Its attention patterns reflect the statistical structure of that corpus. Multilingual BERT (mBERT) extends this to 104 languages but with much less training data per language. The attention phenomena visualized here are real; whether they generalize to other languages and linguistic structures is an empirical question, not an assumption.

The field of mechanistic interpretability attempts to understand what neural networks are actually computing — not just what outputs they produce, but what internal mechanisms produce them. Attention weight visualization is one tool in this effort, but it has known limitations: Jain and Wallace (2019)⁵ showed that attention weights do not always correspond to which tokens are most influential for the final output, complicating simple "the model attended to X therefore X mattered" interpretations.

More recent work has identified specific circuits — small subgraphs of attention heads and feedforward layers — that implement recognizable computations: indirect object identification, factual retrieval, in-context learning. Anthropic's interpretability team has published work on "superposition" (how models pack more features than they have dimensions by using overlapping representations) and "circuits" (how specific capabilities are implemented across layers and heads).⁶

The honest state of the field: we can identify some things some heads do in some models under some conditions. We cannot reliably read off what a model knows or believes from its internal representations. The model works; its workings remain substantially opaque. This is both a scientific challenge and a governance challenge — systems with capabilities we can't fully audit are harder to verify and harder to trust.

Multi-head attention learns to track linguistic relationships from training data. The relationships it learns best are those most consistently represented in that data. For a model trained predominantly on English text, this means English syntactic structures — subject-verb-object order, English pronoun systems, English patterns of modification — are well-represented, while structures specific to other languages may be learned poorly or not at all.

This has practical consequences. A model that has learned robust attention patterns for English pronoun resolution may perform that task reliably. The same model handling a language with different pronoun systems, or a language where reference is tracked through verb morphology rather than pronouns, may produce attention patterns that don't map onto the relevant structure. The problem isn't that attention can't represent these structures — it can — but that learning them requires training data in those languages, and that data is systematically scarcer for most of the world's languages.

The result is models that are, in a precise technical sense, better at some languages than others — not because of architectural limitations but because of data distribution choices. This is a version of the tokenization equity problem discussed in the tokenization explainer, operating at a deeper level of the architecture.

The multi-head structure makes this more precise. A multilingual model needs to develop attention heads that track syntactic relationships across all its training languages simultaneously. Some heads may specialize effectively for one language's structural patterns while being less useful for another's. A head that reliably tracks subject-verb agreement in English — where subjects typically precede verbs — may be less useful for verb-final languages like Japanese or Turkish, where the structural cues appear in different positions. The total number of heads is fixed; the specialization that emerges reflects what the training data rewarded. Languages with more training data get more specialized, more reliable head behavior. The architecture is flexible enough to represent any language's structure in principle; the training distribution determines which structures actually get learned.