<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def as_flat_dict(self):
 """ Returns the parameters of a flat dictionary from keys to values. Nested structure is collapsed with periods. """

        flat_params = {}
        def recurse(parameters, path):
            for key, value in parameters.items():
                newpath = path + [key]
                if isinstance(value, dict):
                    recurse(value, newpath)
                else:
                    flat_params['.'.join(newpath)] = value

        recurse(self.params, [])
        return flat_params