My thinking on derivative(f::AbstractFormNetwork, state_vertices::Vector) is that for a form, you can only take the derivative with respect to the state vertices, so a separate function derivative_state wouldn't be necessary.

@mtfishman In terms of derivative(f::AbstractFormNetwork, state_vertices::Vector) instead of derivative_state(f::AbstractFormNetwork, state_vertices::Vector), the issue is that it conflicts with derivative(itn::AbstractITensorNetwork, vertices::Vector) in src/derivative.jl which I want derivative_state to forward to. We have the hierarchy FormNetwork <: AbstractITensorNetwork and so currently that would just create a circular loop.

I was originally defining derivative(itn::AbstractITensorNetwork, vertices::Vector) and having derivative(f::AbstractFormNetwork, state_vertices::Vector) pass to that by calling derivative(itensornetwork(f), vertices(f, state_vertices)) but the logic for building the bp_cache (if it is not defined) is in derivative(itn::AbstractITensorNetwork, vertices::Vector) and I want the default cache (default partitioning) to be different for an AbstractFormNetwork vs an AbstractITensorNetwork`. I.e I have:

default_partitioning(ψ::AbstractITensorNetwork) = group(v -> v, vertices(ψ))
default_partitioning(f::AbstractFormNetwork) = group(v -> state_vertex(f,v), vertices(f))

at the moment so a standard ψ::AbstractITensorNetwork just has simple BP done on it with no partitioning but a f::AbstractFormNetwork will partition itself by the state_vertices by default.

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Can't you specify a different default partitioning in derivative(f::AbstractFormNetwork, state_vertices::Vector)? That issue seems like something we can circumvent without having to define a new function derivative_state.

Yeah good point: I can make the choice partitioning a kwarg of derivative(Alg::"BP", ...) and have derivative(f::AbstractForm, ...) define that and pass it on

Looks good, thanks! One more step towards BP-based DMRG/TDVP...