What is the relationship between "square loss" and "Mean squared error"?
$$V(f(x), y) = (1-yf(x))^2$$

In the context of classification where $y_i$ is $1$ or $-1$:

\begin{align} 
MSE &amp;= \frac1m \sum_{i=1}^m (y_i-f(x_i))^2 \\
&amp;= \frac1m \sum_{i=1}^m y_i^2 (1-y_if(x_i))^2\\
&amp;= \frac1m \sum_{i=1}^m (1-y_if(x_i))^2\\
&amp;= \frac1m \sum_{i=1}^m V(f(x_i), y_i)
\end{align}