Compressed subgraph layers

Compressed layers are particularly useful for higher order GNNs with large subgraphs. The construction of the layers is particularly straightforward because there is a natural choice of compression basis, consisting of the leading (lowest eigenvalue) eigenvectors of the Laplacian of the subgraph. Ptens provides two specialized classes for compressed sugraph layers: csubgraphlayer1 and csubgraphlayer2. Their usage is almost exactly the same as of regular subgraph layers, with the exception that their constructors also require specifying the number of basis vectors .

As usual such as objects can be initialized using the zeros, randn, etc., constructors or from a data tensor:

>> G=ptens.ggraph.random(8,0.5)
>> S=ptens.subgraph.triangle()
>> A=ptens.csubgraphlayer1.randn(G,S,nvecs,3)
>> print(A)

csubgraphlayer1:
  CPtensor1[0,5,6]:
    [ 0.493525 -0.342878 1.44645 ]
    [ -0.982564 -0.097045 -1.00078 ]
    [ -0.123699 0.282664 0.444347 ]
  CPtensor1[4,7,6]:
    [ -0.191068 -1.37902 0.478407 ]
    [ 1.22947 -0.338276 1.01485 ]
    [ 0.754955 -1.30173 -1.71202 ]
  CPtensor1[4,6,5]:
    [ -0.34454 0.92664 0.145421 ]
    [ -0.734754 -0.457473 -0.733602 ]
    [ 0.722986 -0.308857 0.765271 ]

Note that unlike for the cptensorlayer classes, the bases and atomspacks do not need to be explicitly specified, since they are computed automatically from the Laplacian of the subgraph S. This makes the syntax much simpler.

The linmaps and gather operations work much the same way between compressed subgraphlayers and other compressed or non-compressed layers of any order as before:

>> B=ptens.csubgraphlayer1.linmaps(A)
>> A2=ptens.csubgraphlayer2.randn(G,S,nvecs,3)
>> B2=ptens.csubgraphlayer1.gather(S,A2)

The compressed subgraph layers have their own caching mechanism to facilitate fast computation.