math-modemath-operators
Writing the code
The weight decay was set to $1 \times {10^{−4}}$ for Model 8 and $5\times 10^{−4}$.
the negative sign is missing.
And these are the packages I'm using
\usepackage{jmlr2e}
\usepackage{indentfirst}
% Definitions of handy macros can go here
\usepackage{float}
\usepackage{underscore}
\restylefloat{table}
\newcommand{\dataset}{{\cal D}}
\newcommand{\fracpartial}[2]{\frac{\partial #1}{\partial #2}}
These adjustments have to be done manually, of course, because they depend on the actual interrelation between formulas.
With \hphantom{...} you can leave the space that would be occupied by the argument:
\begin{equation}
\left\lbrace
\begin{aligned}
a_x &= - \sin \alpha \cos \beta \\
a_y &= \hphantom{-}\cos \alpha \cos \beta
\end{aligned}
\right.
\end{equation}
A subtle point is that \hphantom always creates an object that behaves like normal letters with respect to surrounding spaces, so sometimes one has to help TeX by telling the type of the object, putting it as the argument of \mathbin or \mathrel (if it must match an operation symbol or a relation, respectively). In this case the "minus sign" is treated as an ordinary symbol, so no adjustment is necessary.
I wouldn't use cases in this particular formula, but it doesn't harm either (it just adds an unnecessary level).
Here's an alternative that uses TikZ. With the amsmath and tikz packages loaded, put the following in your preamble
\newcommand\constructosum[3]{%
\begin{tikzpicture}[baseline=(char.base), inner sep=0, outer sep=0]
\draw (#1,0) circle (#2);
\node (char) at (0,0) {$#3\sum$}; % Want to define a second symbol for inline...
\end{tikzpicture}%
}
\newcommand{\modtwosum}{\mathop{\mathchoice
{\constructosum{-0.3ex}{0.1}{\displaystyle}}
{\constructosum{-0.3ex}{0.06}{\textstyle}}
{\constructosum{-0.2ex}{0.04}{\scriptstyle}}
{\constructosum{-0.15ex}{0.03}{\scriptscriptstyle}}
}\displaylimits
}
This defines four operators corresponding to display style math environments, inline math, script size math and script script size math in that order. Each has a coordinate for the loop which may be adjusted, and a size for the loop. For example the display style version has
\constructosum{-0.3ex}{0.1}{\displaystyle}
which places the loop at -0.3ex (moves it horizontally backwards a bit) with a radius of 0.1cm. To use it, simply use the new operator \modtwosum inside any math environment. e.g.
\[
G=\modtwosum_a^b H
\]
A demo of this operator in each of the four situations that may occur:
Thanks goes to egreg for pointing out that I could reduce the original version of this with a helper \newcommand to contain the TikZ code.
Best Answer
The problem occurs because the symbol
−that's used in both exponents is not a "normal" dash symbol,-. Instead, it is the Unicode symbolU+2212, the "math minus" symbol. (Did you maybe copy and paste the input from some other source?)Here are three remedies:
Switch to either XeLaTeX or LuaLaTeX and load either the
fontspecpackage or theunicode-mathpackage (which loadsfontspecautomatically).If you need to use pdfLaTeX, add the following instructions to your preamble:
Finally, consider simply replacing all instances of
−with-. (That's what's done in the code below.)