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9 results for “transform”

Formulae (8)

\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\, e^{-2\pi i x \xi}\, dx

Decomposes a function or signal into the frequencies that make it up — converting between the time (or space) domain and the frequency domain.

E_{total} = \text{const}

Energy cannot be created or destroyed, only transformed.

E_{total} = \text{constant}

Energy cannot be created or destroyed, only transformed.

\frac{V_p}{V_s} = \frac{N_p}{N_s}

Voltage ratio equals turns ratio.

\frac{V_p}{V_s} = \frac{N_p}{N_s}

Voltage ratio equals the turns ratio.

\text{Attn}(Q,K,V)=\text{softmax}\!\left(\dfrac{QK^\top}{\sqrt{d_k}}\right)V

Lets each token weigh and aggregate information from all others — the heart of Transformers.

PE_{(pos,2i)}=\sin\!\left(\dfrac{pos}{10000^{2i/d}}\right)

Injects word-order information into a Transformer that otherwise ignores position.

\hat{x}=\dfrac{x-\mu}{\sqrt{\sigma^2+\epsilon}}\,\gamma+\beta

Normalizes across features within a single sample; standard in Transformers.

Transform numbers with large digits (6-9) into "vinculum" form using complements from 10, making calculations easier.