foreach $thing ( keys %INPUT ) 
{
    if( ref( $INPUT{$thing} ) eq "ARRAY" ) 
    { 
        $INPUT{$thing} = join '^', @{$INPUT{$thing}}
    }
}

# You can also write the above like this:
$INPUT{$_} = join '^', @{$INPUT{$_}} for grep {"ARRAY" eq ref $INPUT{$_}} keys %INPUT