Alternative Equation Formats

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MathML

\begin{aligned} g_{k} & = \nabla f_{k} (w_{k}) \\ m_{k + 1} & = β_{1} m_{k} + (1 - β_{1}) g_{k + 1} \\ v_{k + 1} & = β_{2} v_{k} + (1 - β_{2}) g_{k + 1}^{2} \\ {\hat{m}}_{k} & = \frac{m_{k}}{1 - β_{1}^{k}} \\ {\hat{v}}_{k} & = \frac{v_{k}}{1 - β_{2}^{k}} \\ w_{k + 1} & = w_{k} - \frac{η}{\sqrt{{\hat{v}}_{k}} + 10^{- 8}} {\hat{m}}_{k} \end{aligned}

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Math as LaTeX Source

\begin{align*} g_ k& = \nabla f_ k(w_ k) \\ m_{k+1}& = \beta _1 m_ k + \left(1-\beta _1\right)g_{k+1} \\ v_{k+1}& = \beta _2 v_ k + \left(1-\beta _2\right)g_{k+1}^2 \\ \hat{m}_ k& = \frac{m_ k}{1-\beta _1^ k} \\ \hat{v}_ k& = \frac{v_ k}{1-\beta _2^ k} \\ w_{k+1}& = w_ k - \frac{\eta }{\sqrt{\hat{v}_ k} + 10^{-8}}\hat{m}_ k \end{align*}