brr
-\log(1-\sigma(0.15+\mathbf{w}^\intercal\mathbf{x}))=0.274 \\
-\log\sigma(0.15+\mathbf{w}^\intercal(2\mathbf{x})) =\space?
1-\sigma(0.15+\mathbf{w}^\intercal\mathbf{x})=e^{-0.274} \\
\sigma(0.15+\mathbf{w}^\intercal\mathbf{x})=1-e^{-0.274} \\
\mathbf{w}^\intercal\mathbf{x}=\log(-\frac{1-e^{-0.274}}{1-e^{-0.274}-1})-0.15 \\
=\log(\frac{1-e^{-0.274}}{e^{-0.274}})-0.15 \\
=\log(e^{0.274}-1)-0.15
-\log\sigma(0.15+\mathbf{w}^\intercal(2\mathbf{x})) = -\log\sigma(0.15+2\mathbf{w}^\intercal\mathbf{x}) \\
=-\log\sigma(0.15+2(\log(e^{0.274}-1)-0.15)) \\
=-\log\sigma(0.15+2(\log(e^{0.274}-1)-0.15)) \\
=-\log\sigma(2\log(e^{0.274}-1)-0.15) \\
\approx 2.54
