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15 results for “formation”

Formulae (15)

H = -\sum_{i=1}^{n} p_i \log_2 p_i

Measures the uncertainty or information content of a distribution.

\varepsilon = \frac{\Delta L}{L_0}

Relative deformation of a material.

\varepsilon = \frac{\Delta L}{L_0}

Fractional deformation under load.

H = -\sum_i p_i \log_2 p_i

Average information content of a random source (bits).

b = \lceil \log_2(n) \rceil

Minimum number of bits to represent n distinct values.

H(S) = -\sum_i p_i \log_2 p_i

Measures impurity/uncertainty of a set; used to split decision trees.

IG = H(S) - \sum_k \dfrac{|S_k|}{|S|}H(S_k)

Reduction in entropy achieved by splitting a node on a feature.

\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.

D_{KL}(P\Vert Q)=\sum_i P(i)\log\dfrac{P(i)}{Q(i)}

Measures how one probability distribution differs from a reference distribution.

H = -\sum_i p_i \log_2 p_i

Average information content — and the theoretical strength of a random source.

VPI = EV_{info} - EV_{no\,info}

How much better decisions become with full information.

MW = \frac{P_{pore}}{0.052 \times TVD}

Mud weight needed to just balance formation pore pressure.

P_f = G_f \times TVD

Pore pressure of a formation from its gradient and depth.

S(\rho) = -\text{tr}(\rho \log_2 \rho)

Quantum analogue of Shannon entropy — measures the uncertainty in a quantum state.