Scaled dot-product attention

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Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these stages with maximum subtraction for numerical stability. Compatible nonempty query/key widths and matching key/value counts are needed for the standard interpretation.

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Original context

template<size_t SEQ_LEN, size_t DIM>
struct Attention {
    // Attention weights after softmax
    float weights[SEQ_LEN][SEQ_LEN];

    // Compute attention
    // Attention(Q,K,V) = softmax(QK^T/√d_k)V
    void compute(const float Q[][DIM], const float K[][DIM], const float V[][DIM],
                 float output[][DIM]) {
        float scale = 1.0f / std::sqrt(static_cast<float>(DIM));

        // Compute QK^T
        for (size_t i = 0; i < SEQ_LEN; ++i) {
            for (size_t j = 0; j < SEQ_LEN; ++j) {
                float dot = 0.0f;
                for (size_t k = 0; k < DIM; ++k) {
                    dot += Q[i][k] * K[j][k];

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

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