For the code below, after a submission, the radio with value '0' will not be re-selected (it will not be rendered with 'selected' clause).
{{Form::open()}}
{{Form::radio('someInput', '0')}}
{{Form::radio('someInput', '1')}}
{{Form::radio('someInput', '2')}}
{{Form::radio('someInput', '3')}}
{{Form::close()}}