我最终发现它是$items->classes 因此，使用描述助行器检查是否存在空$items->classes[0].

! empty( $item->classes[0] )
    and $attributes .= \' class="\'   . esc_attr( $item->classes[0]        ) .\'"\';

class description_walker extends Walker_Nav_Menu
{
/**
 * Start the element output.
 *
 * @param  string $output Passed by reference. Used to append additional content.
 * @param  object $item   Menu item data object.
 * @param  int $depth     Depth of menu item. May be used for padding.
 * @param  array|object $args    Additional strings. Actually always an 
                                 instance of stdClass. But this is WordPress.
 * @return void
 */
function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 )
{
    $classes     = empty ( $item->classes ) ? array () : (array) $item->classes;

    $class_names = join(
        \' \'
    ,   apply_filters(
            \'nav_menu_css_class\'
        ,   array_filter( $classes ), $item
        )
    );

    ! empty ( $class_names )
        and $class_names = \' class="\'. esc_attr( $class_names ) . \'"\';

    $output .= "<li id=\'menu-item-$item->ID\' $class_names>";

    $attributes  = \'\';

    ! empty( $item->attr_title )
        and $attributes .= \' title="\'  . esc_attr( $item->attr_title ) .\'"\';
    ! empty( $item->target )
        and $attributes .= \' target="\' . esc_attr( $item->target     ) .\'"\';
    ! empty( $item->xfn )
        and $attributes .= \' rel="\'    . esc_attr( $item->xfn        ) .\'"\';
    ! empty( $item->url )
        and $attributes .= \' href="\'   . esc_attr( $item->url        ) .\'"\';

//if the custom classes field is NOT empty dump it into the link attributes. 
    ! empty( $item->classes[0] )
        and $attributes .= \' class="\'   . esc_attr( $item->classes[0]        ) .\'"\';

    // insert description for top level elements only
    // you may change this
    $description = ( ! empty ( $item->description ) and 0 == $depth )
        ? \'<small class="nav_desc">\' . esc_attr( $item->description ) . \'</small>\' : \'\';

    $title = apply_filters( \'the_title\', $item->title, $item->ID );

    $item_output = $args->before
        . "<a $attributes>"
        . $args->link_before
        . $title
        . \'</a> \'
        . $args->link_after
        . $description
        . $args->after;

    // Since $output is called by reference we don\'t need to return anything.
    $output .= apply_filters(
        \'walker_nav_menu_start_el\'
    ,   $item_output
    ,   $item
    ,   $depth
    ,   $args
    );
}
}