quimb.experimental.belief_propagation.hd1bp

Hyper dense belief propagation for arbitrary quimb tensor networks. This is the classic 1-norm version of belief propagation, which treats the tensor network directly as a factor graph. Messages are processed one at a time.

TODO:

  • [ ] implement ‘touching’, so that only necessary messages are updated

  • [ ] implement sequential update

Classes

BeliefPropagationCommon

Common interfaces for belief propagation algorithms.

HD1BP

Object interface for hyper, dense, 1-norm belief propagation. This is

Functions

compute_all_index_marginals_from_messages(tn, messages)

Compute all index marginals from belief propagation messages.

contract_hyper_messages(tn, messages[, ...])

Estimate the contraction of tn given messages, via the

initialize_hyper_messages(tn[, fill_fn, smudge_factor])

Initialize messages for belief propagation, this is equivalent to doing

prod(xs)

Product of all elements in xs.

compute_all_hyperind_messages_prod(ms[, smudge_factor])

Given set of messages ms incident to a single index, compute the

compute_all_hyperind_messages_tree(ms)

Given set of messages ms incident to a single index, compute the

compute_all_tensor_messages_shortcuts(x, ms, ndim)

compute_all_tensor_messages_prod(x, ms[, backend, ...])

Given set of messages ms incident to tensor with data x, compute

compute_all_tensor_messages_tree(x, ms[, backend])

Given set of messages ms incident to tensor with data x, compute

iterate_belief_propagation_basic(tn, messages[, ...])

Run a single iteration of belief propagation. This is the basic version

contract_hd1bp(tn[, messages, max_iterations, tol, ...])

Estimate the contraction of tn with hyper, vectorized, 1-norm

run_belief_propagation_hd1bp(tn[, messages, ...])

Run belief propagation on a tensor network until it converges. This

sample_hd1bp(tn[, messages, output_inds, ...])

Sample all indices of a tensor network using repeated belief propagation

Module Contents

class quimb.experimental.belief_propagation.hd1bp.BeliefPropagationCommon

Common interfaces for belief propagation algorithms.

Parameters:
  • max_iterations (int, optional) – The maximum number of iterations to perform.

  • tol (float, optional) – The convergence tolerance for messages.

  • progbar (bool, optional) – Whether to show a progress bar.

run(max_iterations=1000, tol=5e-06, info=None, progbar=False)
quimb.experimental.belief_propagation.hd1bp.compute_all_index_marginals_from_messages(tn, messages)

Compute all index marginals from belief propagation messages.

Parameters:
  • tn (TensorNetwork) – The tensor network to compute marginals for.

  • messages (dict) – The belief propagation messages.

Returns:

marginals – The marginals for each index.

Return type:

dict

quimb.experimental.belief_propagation.hd1bp.contract_hyper_messages(tn, messages, strip_exponent=False, backend=None)

Estimate the contraction of tn given messages, via the exponential of the Bethe free entropy.

quimb.experimental.belief_propagation.hd1bp.initialize_hyper_messages(tn, fill_fn=None, smudge_factor=1e-12)

Initialize messages for belief propagation, this is equivalent to doing a single round of belief propagation with uniform messages.

Parameters:
  • tn (TensorNetwork) – The tensor network to initialize messages for.

  • fill_fn (callable, optional) – A function to fill the messages with, of signature fill_fn(shape).

  • smudge_factor (float, optional) – A small number to add to the messages to avoid numerical issues.

Returns:

messages – The initial messages. For every index and tensor id pair, there will be a message to and from with keys (ix, tid) and (tid, ix).

Return type:

dict

quimb.experimental.belief_propagation.hd1bp.prod(xs)

Product of all elements in xs.

quimb.experimental.belief_propagation.hd1bp.compute_all_hyperind_messages_prod(ms, smudge_factor=1e-12)

Given set of messages ms incident to a single index, compute the corresponding next output messages, using the ‘product’ implementation.

quimb.experimental.belief_propagation.hd1bp.compute_all_hyperind_messages_tree(ms)

Given set of messages ms incident to a single index, compute the corresponding next output messages, using the ‘tree’ implementation.

quimb.experimental.belief_propagation.hd1bp.compute_all_tensor_messages_shortcuts(x, ms, ndim)
quimb.experimental.belief_propagation.hd1bp.compute_all_tensor_messages_prod(x, ms, backend=None, smudge_factor=1e-12)

Given set of messages ms incident to tensor with data x, compute the corresponding next output messages, using the ‘prod’ implementation.

quimb.experimental.belief_propagation.hd1bp.compute_all_tensor_messages_tree(x, ms, backend=None)

Given set of messages ms incident to tensor with data x, compute the corresponding next output messages, using the ‘tree’ implementation.

quimb.experimental.belief_propagation.hd1bp.iterate_belief_propagation_basic(tn, messages, damping=None, smudge_factor=1e-12, tol=None)

Run a single iteration of belief propagation. This is the basic version that does not vectorize contractions.

Parameters:
  • tn (TensorNetwork) – The tensor network to run BP on.

  • messages (dict) – The current messages. For every index and tensor id pair, there should be a message to and from with keys (ix, tid) and (tid, ix).

  • smudge_factor (float, optional) – A small number to add to the denominator of messages to avoid division by zero. Note when this happens the numerator will also be zero.

Returns:

new_messages – The new messages.

Return type:

dict

class quimb.experimental.belief_propagation.hd1bp.HD1BP(tn, messages=None, damping=None, smudge_factor=1e-12)

Bases: quimb.experimental.belief_propagation.bp_common.BeliefPropagationCommon

Object interface for hyper, dense, 1-norm belief propagation. This is standard belief propagation in tensor network form.

Parameters:
  • tn (TensorNetwork) – The tensor network to run BP on.

  • messages (dict, optional) – Initial messages to use, if not given then uniform messages are used.

  • smudge_factor (float, optional) – A small number to add to the denominator of messages to avoid division by zero. Note when this happens the numerator will also be zero.

iterate(**kwargs)
get_gauged_tn()

Assuming the supplied tensor network has no hyper or dangling indices, gauge it by inserting the BP-approximated transfer matrix eigenvectors, which may be complex. The BP-contraction of this gauged network is then simply the product of zeroth entries of each tensor.

contract(strip_exponent=False)

Estimate the total contraction, i.e. the exponential of the ‘Bethe free entropy’.

quimb.experimental.belief_propagation.hd1bp.contract_hd1bp(tn, messages=None, max_iterations=1000, tol=5e-06, damping=0.0, smudge_factor=1e-12, strip_exponent=False, info=None, progbar=False)

Estimate the contraction of tn with hyper, vectorized, 1-norm belief propagation, via the exponential of the Bethe free entropy.

Parameters:
  • tn (TensorNetwork) – The tensor network to run BP on, can have hyper indices.

  • messages (dict, optional) – Initial messages to use, if not given then uniform messages are used.

  • max_iterations (int, optional) – The maximum number of iterations to perform.

  • tol (float, optional) – The convergence tolerance for messages.

  • damping (float, optional) – The damping factor to use, 0.0 means no damping.

  • smudge_factor (float, optional) – A small number to add to the denominator of messages to avoid division by zero. Note when this happens the numerator will also be zero.

  • strip_exponent (bool, optional) – Whether to strip the exponent from the final result. If True then the returned result is (mantissa, exponent).

  • info (dict, optional) – If specified, update this dictionary with information about the belief propagation run.

  • progbar (bool, optional) – Whether to show a progress bar.

Return type:

scalar or (scalar, float)

quimb.experimental.belief_propagation.hd1bp.run_belief_propagation_hd1bp(tn, messages=None, max_iterations=1000, tol=5e-06, damping=0.0, smudge_factor=1e-12, info=None, progbar=False)

Run belief propagation on a tensor network until it converges. This is the basic version that does not vectorize contractions.

Parameters:
  • tn (TensorNetwork) – The tensor network to run BP on.

  • messages (dict, optional) – The current messages. For every index and tensor id pair, there should be a message to and from with keys (ix, tid) and (tid, ix). If not given, then messages are initialized as uniform.

  • max_iterations (int, optional) – The maximum number of iterations to run for.

  • tol (float, optional) – The convergence tolerance.

  • smudge_factor (float, optional) – A small number to add to the denominator of messages to avoid division by zero. Note when this happens the numerator will also be zero.

  • info (dict, optional) – If specified, update this dictionary with information about the belief propagation run.

  • progbar (bool, optional) – Whether to show a progress bar.

Returns:

  • messages (dict) – The final messages.

  • converged (bool) – Whether the algorithm converged.

quimb.experimental.belief_propagation.hd1bp.sample_hd1bp(tn, messages=None, output_inds=None, max_iterations=1000, tol=0.01, damping=0.0, smudge_factor=1e-12, bias=False, seed=None, progbar=False)

Sample all indices of a tensor network using repeated belief propagation runs and decimation.

Parameters:
  • tn (TensorNetwork) – The tensor network to sample.

  • messages (dict, optional) – The current messages. For every index and tensor id pair, there should be a message to and from with keys (ix, tid) and (tid, ix). If not given, then messages are initialized as uniform.

  • output_inds (sequence of str, optional) – The indices to sample. If not given, then all indices are sampled.

  • max_iterations (int, optional) – The maximum number of iterations for each message passing run.

  • tol (float, optional) – The convergence tolerance for each message passing run.

  • smudge_factor (float, optional) – A small number to add to each message to avoid zeros. Making this large is similar to adding a temperature, which can aid convergence but likely produces less accurate marginals.

  • bias (bool or float, optional) – Whether to bias the sampling towards the largest marginal. If False (the default), then indices are sampled proportional to their marginals. If True, then each index is ‘sampled’ to be its largest weight value always. If a float, then the local probability distribution is raised to this power before sampling.

  • thread_pool (bool, int or ThreadPoolExecutor, optional) – Whether to use a thread pool for parallelization. If an integer, then this is the number of threads to use. If True, then the number of threads is set to the number of cores. If a ThreadPoolExecutor, then this is used directly.

  • seed (int, optional) – A random seed to use for the sampling.

  • progbar (bool, optional) – Whether to show a progress bar.

Returns:

  • config (dict[str, int]) – The sample configuration, mapping indices to values.

  • tn_config (TensorNetwork) – The tensor network with all index values (or just those in output_inds if supllied) selected. Contracting this tensor network (which will just be a sequence of scalars if all index values have been sampled) gives the weight of the sample, e.g. should be 1 for a SAT problem and valid assignment.

  • omega (float) – The probability of choosing this sample (i.e. product of marginal values). Useful possibly for importance sampling.