Allow for different sizes in input units for symbolic/unfolded representations

[adrianjav]

If we try to create a symbolic circuit containing a Kronecker layer whose input units have different dimensionality, the current implementation throws an exception after checking that these sizes are different.

The problem is the code below, which seems to be a stub remaining from when there was no distinction between symbolic and compiled circuits.

cirkit/cirkit/symbolic/circuit.py

Lines 265 to 269 in dee8f1d

	if any(sl.num_input_units != num_units for num_units in sl_ins_units):
	raise ValueError(
	f"{sl}: expected number of input units {sl.num_input_units}, "
	f"but found input layers {sl_ins}"
	)

The symbolic Circuit should construct the circuit without issues. The check should therefore be done at compilation time as it is a limitation of the current torch backend and the way folding is handled at the moment.

[adrianjav]

After checking the source code, it seems that the solution is not as simple as moving the check to the torch backend.

In short, the constructor of ProductLayer (and that of KroneckerLayer) in the symbolic representation expect the number of inputs and the arity, hence equal number of inputs per input layer. See below:

cirkit/cirkit/symbolic/layers.py

Lines 619 to 635 in dee8f1d

	class ProductLayer(Layer, ABC):
	"""The abstract base class for symbolic product layers."""
	def __init__(self, num_input_units: int, num_output_units: int, arity: int = 2):
	"""Initializes a product layer.
	Args:
	num_input_units: The number of units in each input layer.
	num_output_units: The number of product units in the product layer.
	arity: The arity of the layer, i.e., the number of input layers to the product layer.
	Raises:
	ValueError: If the arity is less than two.
	"""
	if arity < 2:
	raise ValueError("The arity should be at least 2")
	super().__init__(num_input_units, num_output_units, arity)

The simplest solution I can think of would be to change the constructors to request a list of num inputs units, from which the arity would be its length, but this would require a somewhat deeper refactorization.