Write a module with two pieces of state:

• scale, a learnable scalar parameter initialised to scale_init
• running_offset, a registered buffer holding offset_init

whose forward pass returns x * scale + running_offset.

Return the tuple (parameter_names, buffer_names, state_dict_keys, output), each name list taken in the order PyTorch yields it and state_dict_keys sorted.

A buffer is state that moves with the model, is saved in state_dict and follows .to(device), but is not a parameter and takes no gradient. Running statistics are the usual example; registering them as parameters instead would have the optimiser trying to train them.

Input

x = tensor([1., 2.])
scale_init = 3.0
offset_init = 0.5

Output

(['scale'],
 ['running_offset'],
 ['running_offset', 'scale'],
 tensor([3.5000, 6.5000]))