Do these 3 things before closing this tab:
1Repair Windows errors before they cause bigger problems2Scan for outdated or missing drivers - takes under a minute3Clear out junk files and repair common Windows errorsSelf-attention is a Transformer operation that lets each position in a sequence combine information from other positions in that same sequence. It computes how relevant other positions are to each position, then uses those scores to mix their content into updated representations. In a Transformer, this makes it possible to relate distant tokens without processing them one at a time.
How self-attention works
For each input position, the model creates three learned vectors: a query, a key, and a value. A query represents what the position is looking for; keys let positions be compared with that query; values hold the information that can be combined into the result. These are computational roles, not conscious questions or fixed meanings.
Let X represent the sequence of input vectors. Learned linear projections of X produce queries Q, keys K, and values V. The scaled dot-product attention calculation is:
Attention(Q, K, V) = softmax(QKᵀ / √dₖ)V
Here, QKᵀ gives query-key compatibility scores. Dividing by the square root of the key dimension dₖ scales those scores; softmax turns each row into normalized weights; and multiplying by V forms a weighted mixture of value vectors. The result is a new representation for each position. In self-attention, all three inputs—queries, keys, and values—come from the same sequence representation. An attention mask can restrict which positions are available to a query. Vaswani et al. introduced this formulation in the 2017 Transformer paper.
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Why Transformers use multiple heads and positional information
Multiple heads
Multi-head attention uses several separate learned sets of projections to calculate attention in parallel. Their outputs are concatenated and projected to form the layer’s result. This gives the model multiple learned ways to combine information, but it does not mean that a particular head always represents a fixed concept such as a specific grammatical relationship.
Positional information
Attention alone does not encode token order: the operation compares and combines representations, but does not inherently distinguish a sequence from a reordering of the same positions. The original Transformer therefore adds positional encodings to input embeddings. Position-wise feed-forward networks, residual connections, and layer normalization also contribute to a Transformer block; self-attention is one operation within the architecture, not the whole model.
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Self-attention, causal attention, and cross-attention
| Mechanism | Where queries, keys, and values come from | What it permits |
|---|---|---|
| Encoder self-attention | Queries, keys, and values come from the encoder’s input sequence. | Each position can incorporate information from other positions in that input, subject to any mask. |
| Decoder causal self-attention | Queries, keys, and values come from the decoder’s sequence representation. | A causal mask blocks access to subsequent output positions, so a prediction cannot use future target tokens. |
| Encoder-decoder cross-attention | Queries come from decoder representations; keys and values come from encoder outputs. | The decoder can use information from the encoder sequence. Because the two sides use different representations, this is not self-attention. |
The distinction matters most in generation. A decoder can build each next-token prediction from earlier output positions while using cross-attention to consult the encoded input, without seeing the future target sequence.
Why full self-attention becomes expensive
In full self-attention, each sequence position can interact with every other position. The attention-score matrix therefore has a number of entries that grows quadratically with sequence length: doubling the number of positions produces roughly four times as many pairwise interactions. This can make memory use and computation substantial for long sequences.
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The direct interactions also have benefits: distant positions can connect in one attention operation, and the operation can be parallelized across positions during training. Alternatives change the formulation or restrict or approximate interactions, so their costs and quality depend on the method, task, and implementation.
Linear attention as one alternative
Katharopoulos et al. describe a linear-attention formulation that uses kernel feature maps and matrix associativity to reduce sequence-length complexity from O(N²) to O(N). In their 2020 experiments, the authors reported up to 4000× faster autoregressive prediction on very long sequences. That is a result for their experiments, not a general speed guarantee for every model or workload. Read the paper and its experimental context.
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What attention weights do—and do not—explain
Attention weights show how a particular attention operation distributes weight across available value vectors. They are useful for understanding the calculation, but they are not a complete explanation of a model’s reasoning: the output also depends on learned projections, other heads and layers, feed-forward networks, residual connections, and the rest of the model.
A related theoretical result has a narrow scope. Dong, Cordonnier, and Loukas analyze pure self-attention without skip connections or MLPs and find that, with depth, it converges toward rank one. Their analysis also finds that skip connections and MLPs prevent the described degeneration. This result concerns the stated pure-attention setup; it does not establish that ordinary Transformers collapse in practice. See the assumptions and analysis in the paper.
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The original Transformer’s reported translation scores
As context for the architecture’s original evaluation, Vaswani et al. reported 28.4 BLEU on WMT 2014 English-to-German and 41.8 BLEU on WMT 2014 English-to-French in the original paper. These are reported results from that paper, not general measures of what self-attention achieves on other models or tasks. The Google Research record displays 41.0 for English-to-French, whereas the paper’s arXiv abstract states 41.8; the figures should not be silently combined. Original paper · Google Research record.
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