code: from toposort import toposort
  import contextlib
  import numpy as np
  import tensorflow as tf
  import tensorflow.contrib.graph_editor as ge
  import time
  import sys
  sys.setrecursionlimit(10000)
  # refers back to current module if we decide to split helpers out
  util = sys.modules[__name__]
  
  # getting rid of "WARNING:tensorflow:VARIABLES collection name is deprecated"
  setattr(tf.GraphKeys, "VARIABLES", "variables")
  
  # save original gradients since tf.gradient could be monkey-patched to point
  # to our version
  from tensorflow.python.ops import gradients as tf_gradients_lib
  tf_gradients = tf_gradients_lib.gradients
  
  MIN_CHECKPOINT_NODE_SIZE=1024    # use lower value during testing
  
  # specific versions we can use to do process-wide replacement of tf.gradients
  def gradients_speed(ys, xs, grad_ys=None, **kwargs):
      return gradients(ys, xs, grad_ys, checkpoints='speed', **kwargs)
  
  def gradients_memory(ys, xs, grad_ys=None, **kwargs):
      return gradients(ys, xs, grad_ys, checkpoints='memory', **kwargs)
          
  def gradients_collection(ys, xs, grad_ys=None, **kwargs):
      return gradients(ys, xs, grad_ys, checkpoints='collection', **kwargs)
  
  def gradients(ys, xs, grad_ys=None, checkpoints='collection', **kwargs):
      '''
      Authors: Tim Salimans & Yaroslav Bulatov
  
      memory efficient gradient implementation inspired by "Training Deep Nets with Sublinear Memory Cost"
      by Chen et al. 2016 (https://arxiv.org/abs/1604.06174)
  
      ys,xs,grad_ys,kwargs are the arguments to standard tensorflow tf.gradients
      (https://www.tensorflow.org/versions/r0.12/api_docs/python/train.html#gradients)
  
      'checkpoints' can either be
          - a list consisting of tensors from the forward pass of the neural net
            that we should re-use when calculating the gradients in the backward pass
            all other tensors that do not appear in this list will be re-computed
          - a string specifying how this list should be determined. currently we support
              - 'speed':  checkpoint all outputs of convolutions and matmuls. these ops are usually the most expensive,
                          so checkpointing them maximizes the running speed
                          (this is a good option if nonlinearities, concats, batchnorms, etc are taking up a lot of memory)
              - 'memory': try to minimize the memory usage
                          (currently using a very simple strategy that identifies a number of bottleneck tensors in the graph to checkpoint)
              - 'collection': look for a tensorflow collection named 'checkpoints', which holds the tensors to checkpoint
      '''
  
      #    print("Calling memsaving gradients with", checkpoints)
      if not isinstance(ys,list):
          ys = [ys]
      if not isinstance(xs,list):
          xs = [xs]
  
      bwd_ops = ge.get_backward_walk_ops([y.op for y in ys],
                                         inclusive=True)
  
      debug_print("bwd_ops: %s", bwd_ops)
      
      # forward ops are all ops that are candidates for recomputation
      fwd_ops = ge.get_forward_walk_ops([x.op for x in xs],
                                        inclusive=True,
                                        within_ops=bwd_ops)
      debug_print("fwd_ops: %s", fwd_ops)
      
      # exclude ops with no inputs
      fwd_ops = [op for op in fwd_ops if op.inputs]
  
      # don't recompute xs, remove variables
      xs_ops = _to_ops(xs)
      fwd_ops = [op for op in fwd_ops if not op in xs_ops]
      fwd_ops = [op for op in fwd_ops if not '/assign' in op.name]
      fwd_ops = [op for op in fwd_ops if not '/Assign' in op.name]
      fwd_ops = [op for op in fwd_ops if not '/read' in op.name]
      ts_all = ge.filter_ts(fwd_ops, True) # get the tensors
      ts_all = [t for t in ts_all if '/read' not in t.name]
      ts_all = set(ts_all) - set(xs) - set(ys)
  
      # construct list of tensors to checkpoint during forward pass, if not
      # given as input
      if type(checkpoints) is not list:
          if checkpoints == 'collection':
              checkpoints = tf.get_collection('checkpoints')
              
          elif checkpoints == 'speed':
              # checkpoint all expensive ops to maximize running speed
              checkpoints = ge.filter_ts_from_regex(fwd_ops, 'conv2d|Conv|MatMul')
              
          elif checkpoints == 'memory':
  
              # remove very small tensors and some weird ops
              def fixdims(t): # tf.Dimension values are not compatible with int, convert manually
                  try:
                      return [int(e if e.value is not None else 64) for e in t]
                  except:
                      return [0]  # unknown shape
              ts_all = [t for t in ts_all if np.prod(fixdims(t.shape)) > MIN_CHECKPOINT_NODE_SIZE]
              ts_all = [t for t in ts_all if 'L2Loss' not in t.name]
              ts_all = [t for t in ts_all if 'entropy' not in t.name]
              ts_all = [t for t in ts_all if 'FusedBatchNorm' not in t.name]
              ts_all = [t for t in ts_all if 'Switch' not in t.name]
              ts_all = [t for t in ts_all if 'dropout' not in t.name]
              # DV: FP16_FIX - need to add 'Cast' layer here to make it work for FP16
              ts_all = [t for t in ts_all if 'Cast' not in t.name]
  
              # filter out all tensors that are inputs of the backward graph
              with util.capture_ops() as bwd_ops:
                  tf_gradients(ys, xs, grad_ys, **kwargs)
  
              bwd_inputs = [t for op in bwd_ops for t in op.inputs]
              # list of tensors in forward graph that is in input to bwd graph
              ts_filtered = list(set(bwd_inputs).intersection(ts_all))
              debug_print("Using tensors %s", ts_filtered)
  
              # try two slightly different ways of getting bottlenecks tensors
              # to checkpoint
              for ts in [ts_filtered, ts_all]:
  
                  # get all bottlenecks in the graph
                  bottleneck_ts = []
                  for t in ts:
                      b = set(ge.get_backward_walk_ops(t.op, inclusive=True, within_ops=fwd_ops))
                      f = set(ge.get_forward_walk_ops(t.op, inclusive=False, within_ops=fwd_ops))
                      # check that there are not shortcuts
                      b_inp = set([inp for op in b for inp in op.inputs]).intersection(ts_all)
                      f_inp = set([inp for op in f for inp in op.inputs]).intersection(ts_all)
                      if not set(b_inp).intersection(f_inp) and len(b_inp)+len(f_inp) >= len(ts_all):
                          bottleneck_ts.append(t)  # we have a bottleneck!
                      else:
                          debug_print("Rejected bottleneck candidate and ops %s", [t] + list(set(ts_all) - set(b_inp) - set(f_inp)))
  
                  # success? or try again without filtering?
                  if len(bottleneck_ts) >= np.sqrt(len(ts_filtered)): # yes, enough bottlenecks found!
                      break
  
              if not bottleneck_ts:
                  raise Exception('unable to find bottleneck tensors! please provide checkpoint nodes manually, or use checkpoints="speed".')
  
              # sort the bottlenecks
              bottlenecks_sorted_lists = tf_toposort(bottleneck_ts, within_ops=fwd_ops)
              sorted_bottlenecks = [t for ts in bottlenecks_sorted_lists for t in ts]
  
              # save an approximately optimal number ~ sqrt(N)
              N = len(ts_filtered)
              if len(bottleneck_ts) <= np.ceil(np.sqrt(N)):
                  checkpoints = sorted_bottlenecks
              else:
                  step = int(np.ceil(len(bottleneck_ts) / np.sqrt(N)))
                  checkpoints = sorted_bottlenecks[step::step]
              
          else:
              raise Exception('%s is unsupported input for "checkpoints"' % (checkpoints,))
  
      checkpoints = list(set(checkpoints).intersection(ts_all))
  
      # at this point automatic selection happened and checkpoints is list of nodes
      assert isinstance(checkpoints, list)
  
      debug_print("Checkpoint nodes used: %s", checkpoints)
      # better error handling of special cases
      # xs are already handled as checkpoint nodes, so no need to include them
      xs_intersect_checkpoints = set(xs).intersection(set(checkpoints))
      if xs_intersect_checkpoints:
          debug_print("Warning, some input nodes are also checkpoint nodes: %s",
                      xs_intersect_checkpoints)
      ys_intersect_checkpoints = set(ys).intersection(set(checkpoints))
      debug_print("ys: %s, checkpoints: %s, intersect: %s", ys, checkpoints,
                  ys_intersect_checkpoints)
      # saving an output node (ys) gives no benefit in memory while creating
      # new edge cases, exclude them
      if ys_intersect_checkpoints:
          debug_print("Warning, some output nodes are also checkpoints nodes: %s",
                format_ops(ys_intersect_checkpoints))
  
      # remove initial and terminal nodes from checkpoints list if present
      checkpoints = list(set(checkpoints) - set(ys) - set(xs))
      
      # check that we have some nodes to checkpoint
      if not checkpoints:
          raise Exception('no checkpoints nodes found or given as input! ')
  
      # disconnect dependencies between checkpointed tensors
      checkpoints_disconnected = {}
      for x in checkpoints:
          if x.op and x.op.name is not None:
              grad_node = tf.stop_gradient(x, name=x.op.name+"_sg")
          else:
              grad_node = tf.stop_gradient(x)
          checkpoints_disconnected[x] = grad_node
  
      # partial derivatives to the checkpointed tensors and xs
      ops_to_copy = fast_backward_ops(seed_ops=[y.op for y in ys],
                                      stop_at_ts=checkpoints, within_ops=fwd_ops)
      debug_print("Found %s ops to copy within fwd_ops %s, seed %s, stop_at %s",
                      len(ops_to_copy), fwd_ops, [r.op for r in ys], checkpoints)
      debug_print("ops_to_copy = %s", ops_to_copy)
      debug_print("Processing list %s", ys)
      copied_sgv, info = ge.copy_with_input_replacements(ge.sgv(ops_to_copy), {})
      for origin_op, op in info._transformed_ops.items():
          op._set_device(origin_op.node_def.device)
      copied_ops = info._transformed_ops.values()
      debug_print("Copied %s to %s", ops_to_copy, copied_ops)
      ge.reroute_ts(checkpoints_disconnected.values(), checkpoints_disconnected.keys(), can_modify=copied_ops)
      debug_print("Rewired %s in place of %s restricted to %s",
                  checkpoints_disconnected.values(), checkpoints_disconnected.keys(), copied_ops)
  
      # get gradients with respect to current boundary + original x's
      copied_ys = [info._transformed_ops[y.op]._outputs[0] for y in ys]
      boundary = list(checkpoints_disconnected.values())
      dv = tf_gradients(ys=copied_ys, xs=boundary+xs, grad_ys=grad_ys, **kwargs)
      debug_print("Got gradients %s", dv)
      debug_print("for %s", copied_ys)
      debug_print("with respect to %s", boundary+xs)
  
      inputs_to_do_before = [y.op for y in ys]
      if grad_ys is not None:
          inputs_to_do_before += grad_ys
      wait_to_do_ops = list(copied_ops) + [g.op for g in dv if g is not None]
      my_add_control_inputs(wait_to_do_ops, inputs_to_do_before)
  
      # partial derivatives to the checkpointed nodes
      # dictionary of "node: backprop" for nodes in the boundary
      d_checkpoints = {r: dr for r,dr in zip(checkpoints_disconnected.keys(),
                                          dv[:len(checkpoints_disconnected)])}
      # partial derivatives to xs (usually the params of the neural net)
      d_xs = dv[len(checkpoints_disconnected):]
  
      # incorporate derivatives flowing through the checkpointed nodes
      checkpoints_sorted_lists = tf_toposort(checkpoints, within_ops=fwd_ops)
      for ts in checkpoints_sorted_lists[::-1]:
          debug_print("Processing list %s", ts)
          checkpoints_other = [r for r in checkpoints if r not in ts]
          checkpoints_disconnected_other = [checkpoints_disconnected[r] for r in checkpoints_other]
  
          # copy part of the graph below current checkpoint node, stopping at
          # other checkpoints nodes
          ops_to_copy = fast_backward_ops(within_ops=fwd_ops, seed_ops=[r.op for r in ts], stop_at_ts=checkpoints_other)
          debug_print("Found %s ops to copy within %s, seed %s, stop_at %s",
                      len(ops_to_copy), fwd_ops, [r.op for r in ts],
                      checkpoints_other)
          debug_print("ops_to_copy = %s", ops_to_copy)
          if not ops_to_copy: # we're done!
              break
          copied_sgv, info = ge.copy_with_input_replacements(ge.sgv(ops_to_copy), {})
          for origin_op, op in info._transformed_ops.items():
              op._set_device(origin_op.node_def.device)
          copied_ops = info._transformed_ops.values()
          debug_print("Copied %s to %s", ops_to_copy, copied_ops)
          ge.reroute_ts(checkpoints_disconnected_other, checkpoints_other, can_modify=copied_ops)
          debug_print("Rewired %s in place of %s restricted to %s",
                      checkpoints_disconnected_other, checkpoints_other, copied_ops)
  
          # gradient flowing through the checkpointed node
          boundary = [info._transformed_ops[r.op]._outputs[0] for r in ts]
          substitute_backprops = [d_checkpoints[r] for r in ts]
          dv = tf_gradients(boundary,
                            checkpoints_disconnected_other+xs,
                            grad_ys=substitute_backprops, **kwargs)
          debug_print("Got gradients %s", dv)
          debug_print("for %s", boundary)
          debug_print("with respect to %s", checkpoints_disconnected_other+xs)
          debug_print("with boundary backprop substitutions %s", substitute_backprops)
  
          inputs_to_do_before = [d_checkpoints[r].op for r in ts]
          wait_to_do_ops = list(copied_ops) + [g.op for g in dv if g is not None]
          my_add_control_inputs(wait_to_do_ops, inputs_to_do_before)
  
          # partial derivatives to the checkpointed nodes
          for r, dr in zip(checkpoints_other, dv[:len(checkpoints_other)]):
              if dr is not None:
                  if d_checkpoints[r] is None:
                      d_checkpoints[r] = dr
                  else:
                      d_checkpoints[r] += dr
          def _unsparsify(x):
              if not isinstance(x, tf.IndexedSlices):
                  return x
              assert x.dense_shape is not None, "memory_saving_gradients encountered sparse gradients of unknown shape"
              indices = x.indices
              while indices.shape.ndims < x.values.shape.ndims:
                  indices = tf.expand_dims(indices, -1)
              return tf.scatter_nd(indices, x.values, x.dense_shape)
  
          # partial derivatives to xs (usually the params of the neural net)
          d_xs_new = dv[len(checkpoints_other):]
          for j in range(len(xs)):
              if d_xs_new[j] is not None:
                  if d_xs[j] is None:
                      d_xs[j] = _unsparsify(d_xs_new[j])
                  else:
                      d_xs[j] += _unsparsify(d_xs_new[j])
  
  
      return d_xs
  
  def tf_toposort(ts, within_ops=None):
      all_ops = ge.get_forward_walk_ops([x.op for x in ts], within_ops=within_ops)
  
      deps = {}
      for op in all_ops:
          for o in op.outputs:
              deps[o] = set(op.inputs)
      sorted_ts = toposort(deps)
  
      # only keep the tensors from our original list
      ts_sorted_lists = []
      for l in sorted_ts:
          keep = list(set(l).intersection(ts))
          if keep:
              ts_sorted_lists.append(keep)
  
      return ts_sorted_lists
  
  def fast_backward_ops(within_ops, seed_ops, stop_at_ts):
      bwd_ops = set(ge.get_backward_walk_ops(seed_ops, stop_at_ts=stop_at_ts))
      ops = bwd_ops.intersection(within_ops).difference([t.op for t in stop_at_ts])
      return list(ops)
  
  @contextlib.contextmanager
  def capture_ops():
    """Decorator to capture ops created in the block.
    with capture_ops() as ops:
      # create some ops
    print(ops) # => prints ops created.
    """
  
    micros = int(time.time()*10**6)
    scope_name = str(micros)
    op_list = []
    with tf.name_scope(scope_name):
      yield op_list
  
    g = tf.get_default_graph()
    op_list.extend(ge.select_ops(scope_name+"/.*", graph=g))
  
  def _to_op(tensor_or_op):
    if hasattr(tensor_or_op, "op"):
      return tensor_or_op.op
    return tensor_or_op
  
  def _to_ops(iterable):
    if not _is_iterable(iterable):
      return iterable
    return [_to_op(i) for i in iterable]
  
  def _is_iterable(o):
    try:
      _ = iter(o)
    except Exception:
      return False
    return True
  
  DEBUG_LOGGING=False
  def debug_print(s, *args):
    """Like logger.log, but also replaces all TensorFlow ops/tensors with their
    names. Sensitive to value of DEBUG_LOGGING, see enable_debug/disable_debug
  
    Usage:
      debug_print("see tensors %s for %s", tensorlist, [1,2,3])
    """
  
    if DEBUG_LOGGING:
      formatted_args = [format_ops(arg) for arg in args]
      print("DEBUG "+s % tuple(formatted_args))
  
  def format_ops(ops, sort_outputs=True):
    """Helper method for printing ops. Converts Tensor/Operation op to op.name,
    rest to str(op)."""
      
    if hasattr(ops, '__iter__') and not isinstance(ops, str):
      l = [(op.name if hasattr(op, "name") else str(op)) for op in ops]
      if sort_outputs:
        return sorted(l)
      return l
    else:
      return ops.name if hasattr(ops, "name") else str(ops)
  
  def my_add_control_inputs(wait_to_do_ops, inputs_to_do_before):
      for op in wait_to_do_ops:
          ci = [i for i in inputs_to_do_before if op.control_inputs is None or i not in op.control_inputs]
          ge.add_control_inputs(op, ci)
  
apis: numpy.sqrt tensorflow.contrib.graph_editor.sgv tensorflow.scatter_nd tensorflow.contrib.graph_editor.filter_ts tensorflow.get_collection tensorflow.contrib.graph_editor.get_forward_walk_ops tensorflow.contrib.graph_editor.reroute_ts tensorflow.expand_dims tensorflow.stop_gradient tensorflow.contrib.graph_editor.filter_ts_from_regex tensorflow.contrib.graph_editor.get_backward_walk_ops tensorflow.name_scope tensorflow.get_default_graph tensorflow.contrib.graph_editor.add_control_inputs tensorflow.contrib.graph_editor.select_ops