If there is an accident during training, who is responsible?

That would depend if you are flying solo or with the instructor. In solo flight, you are the PIC and an accident or incident is your fault. If the instructor is with you on a dual training flight, the instructor is the PIC and the fault rests with the instructor. Otherwise, if you are both qualified in the aircraft, the fault will usually come down to the pilot who is PIC for the flight.