Introduce Symbolic circuit

[IrwinChay]

Basically following what we discussed in week 8,

specifically, using re-param for placeholder (uninitialized) parameters

Also stored all the information (layer_cls and efamily_cls) so the tensorized circuit could be directly converted into tensorized form, no additional input needed

CP layers and sum layer (previously called mixing layer) not implemented yet

"Building symbolic circuit from RG" will be implemented in another file, writing now

[IrwinChay]

Alternative: use a "sum product node" class to store the CP and Tucker placeholder parameters? instead of storing everything in the sum node class?

[lkct]

As just discussed: (to keep a note here)

"Building symbolic circuit from RG" will be implemented in another file, writing now

Better include it in this PR, which also requires some changes to the __init__ interface.

Alternative: use a "sum product layer" class to store the CP and Tucker placeholder parameters? instead of storing everything in the sum layer class?

It's better to split sum and prod in symbolic layers. Fusing them into SumProductLayer with einsum is just a computational trick but not the semantics of circuit.

Also some nomenclature renamings mentioned in discussion.

[IrwinChay]

Update:

renamed from node to layer, num_input_units into num_units, product layer type

Added CP parameter construction

Added symbolic circuit class, construction from Region Graph, compatibility test,

re-arranged folder structure to /new/symbolic

[lkct]

For linting, just ignore for the moment. Will be looked after during future refactoring.

Regarding SymbolicCircuit:

1. from_region_graph should directly become __init__ because SC can only be constructed from RG. We don't need add_layer and add_edge publicly.
2. Just save a copy of RG, and the structural properties can be directly retrieved from the RG. NO need to repeat code and recalculate.

[IrwinChay]

For linting, just ignore for the moment. Will be looked after during future refactoring.

Regarding SymbolicCircuit:

1. from_region_graph should directly become __init__ because SC can only be constructed from RG. We don't need add_layer and add_edge publicly.
2. Just save a copy of RG, and the structural properties can be directly retrieved from the RG. NO need to repeat code and recalculate.

Update:

moved from_region_graph to __init__

removed smooth and decomposability tests, which are copies of that in RG

retained is_compatible, will move it to new/RG

[lkct]

I still have questions about the motivation of some code.
But I think it's OK to merge and I'll fix those along with linting.

[lkct]

let's mark self.region_graph public.
and where are the properties? I expect something like self.is_smooth=region_graph.is_smooth

[IrwinChay]

added, will require new/RG

[lkct]

why using this function but not merging into __init__?
also do we really need __func instead of _func?

[IrwinChay]

legacy issues, fixed

[lkct]

Thanks!