Optimized tensor network contraction using einexpr when specifying output indices

[bartdv123]

Hi there!

I'm been using Tenet the past year during my master's thesis and I stumbled upon a problem when trying to optimize a partial tensor network contraction, instead of a full contraction. The documentation states in einexpr.jl to specify the open indices in the path. But even when specifying the open indices in the einexpr with the outptus = inds(....) - keyword Tenet.contract(network, path=cpath) contracts the whole network?

Example:

output_inds =[Symbol("7"), :v2, Symbol("12"), Symbol("9"), :v3, :v1, Symbol("8"), :v5, Symbol("14"), :v4, Symbol("15")]

cpath = einexpr(transformed_2_mps_network, outputs = output_inds)
mps_network = Tenet.contract(mps_network, path=cpath)
println(typeof(mps_network)) --> return not a tensor network but a single tensor, so contracts all indices and doesn't leave the specified indices open?

See this image for definition of what the indices mean:

[bartdv123]

Found a work around for my specific use case

[jofrevalles]

Hi, @bartdv123! Thanks for noticing this potential issue.

I managed to find a reproducing example of this behavior:

julia> using Tenet

julia> using EinExprs

julia> tn = TensorNetwork([
           Tensor(rand(2, 2, 2), [:i, :j, :k]),
           Tensor(rand(2, 2), [:j, :l]),
           Tensor(rand(2, 2, 2, 2), [:l, :k, :m, :n]),
           Tensor(rand(2, 2, 2), [:n, :o, :p])])
TensorNetwork (#tensors=4, #inds=8)

julia> output_inds = inds(tn, :open)
4-element Vector{Symbol}:
 :m
 :o
 :p
 :i

julia> contract_all = einexpr(tn)
SizedEinExpr{Symbol}(EinExpr{Symbol}([:i, :m, :o, :p], EinExpr{Symbol}[EinExpr{Symbol}([:n, :o, :p], EinExpr{Symbol}[]), EinExpr{Symbol}([:i, :m, :n], EinExpr{Symbol}[EinExpr{Symbol}([:i, :k, :l], EinExpr{Symbol}[EinExpr{Symbol}([:i, :j, :k], EinExpr{Symbol}[]), EinExpr{Symbol}([:j, :l], EinExpr{Symbol}[])]), EinExpr{Symbol}([:l, :k, :m, :n], EinExpr{Symbol}[])])]), Dict(:l => 2, :m => 2, :o => 2, :p => 2, :n => 2, :j => 2, :k => 2, :i => 2))

julia> t1 = contract(tn, path=cpath) |> inds
4-element Vector{Symbol}:
 :o
 :p
 :i
 :m

julia> cpath = einexpr(tn, outputs=[:i, :p])
SizedEinExpr{Symbol}(EinExpr{Symbol}([:i, :m, :o, :p], EinExpr{Symbol}[EinExpr{Symbol}([:n, :o, :p], EinExpr{Symbol}[]), EinExpr{Symbol}([:i, :m, :n], EinExpr{Symbol}[EinExpr{Symbol}([:i, :k, :l], EinExpr{Symbol}[EinExpr{Symbol}([:i, :j, :k], EinExpr{Symbol}[]), EinExpr{Symbol}([:j, :l], EinExpr{Symbol}[])]), EinExpr{Symbol}([:l, :k, :m, :n], EinExpr{Symbol}[])])]), Dict(:l => 2, :m => 2, :o => 2, :p => 2, :n => 2, :j => 2, :k => 2, :i => 2))

julia> t2 = contract(tn, path=cpath) |> inds
4-element Vector{Symbol}:
 :o
 :p
 :i
 :m

@mofeing It seems that Tenet.einexpr is not finding the proper EinExpr that has the correct outputs indices.

[mofeing]

hi @bartdv123
nice to see a new user!

The documentation states in einexpr.jl to specify the open indices in the path. But even when specifying the open indices in the einexpr with the outptus = inds(....) - keyword Tenet.contract(network, path=cpath) contracts the whole network?

mmm nope. what it does is it's just selecting and contracting the tensors involved in the EinExpr. the resulting tensor is the result of contracting the sub-Tensor Network.

It seems that Tenet.einexpr is not finding the proper EinExpr that has the correct outputs indices.

@jofrevalles Well, the EinExpr is mostly correct: It just needs to modify the head in the top EinExpr.

I'm moving the issue to EinExprs.jl because that is where the issue has its origin.