Derivatives and environments about tensornetwork HOT 11 CLOSED

By the way, I suspect (although I have not checked) that using the proposed environments() has the same asymptotic computational time scaling as using tf.gradients(). Hence it might only be advantageous for backends without autodiff functionality. On the other hand, environments() might be easier to fit into any upcoming automatic multi-device support?

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I think remove_node() is a great idea. It would reduce the length of MERA code (and also others) a lot. It would be good to also have the automated optimal contractor then. @Thenerdstation what is the status on that? I saw the stochastic contractor. Is someone working on a deterministic optimal cotractors?

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Adam is working on it, but he is a 20%er. I've asked him to add a branch of his work so far, so hopefully that'll be added soon.

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Remove node should be easy enough to add. Though I think we'll use disconnect to break the edges rather than modify the edges in place. This is consistent with the rest of the code base.

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@Thenerdstation The only trouble I see with replacing the connected edges is that it makes it tricky to keep track of them across the remove_node(). In particular, I would want to know which of the new dangling edges was connected to which axis of the removed node. Ideally, I would not have to remember the axis ordering of the removed node for this to work - the axis names would be enough.

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Could you give a tiny example of what your ideal workflow would look like? I still don't quite see how modifying the edges in place is more beneficial than just replacing them.

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Something like:

net = TensorNetwork()
n1 = net.add_node(t1, axis_names=['a', 'b', 'c'])
n2 = net.add_node(t2, ...)
...
# (connect edges so that there are no danglings)
...
output_edges = [n1['a'], n1['b'], n1['c']]
net.remove_node(n1)

net.contract_all_naively()  # or whatever :)

env = net.get_final_node()
env.reorder_edges(output_edges)  # want my output_edges to still be part of the network

# I might also want to contract the environment with another node.
# The following replaces the removed node to reproduce the result
# of contracting the original network.
n1 = net.add_node(t1, axis_names=['a', 'b', 'c'])
net.connect(n1['a'], output_edge[0])
net.connect(n1['b'], output_edge[1])
net.connect(n1['c'], output_edge[2])
net.contract_between(n1, env)

If the edges are replaced, one could alternatively have something like
output_edges = net.remove_node(n1, output_edge_axes=['a', 'b', 'c']), I suppose.

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Oh I see what you mean now. You will need the broken edges for reshaping and to possibly connect it to a different node.

Let me think about this some more. I wanna keep the API as clean and intuitive as possible.

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Alright this is my compromise. remove_node() will return a Dict[Union[int, Text], Edge] which maps the index/axis name to the newly broken edge. That way, we can use disconnect and keep our current edge pattern consistent and you can continue to use the edge mapping that node had before.

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@amilsted Please comment on the PR if you have any concerns about the design choice.

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@mganahl You too.

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