问题
In usual backprop, we forward-prop once, compute gradients, then apply them to update weights. But suppose we wish to forward-prop twice, and backprop through both, and apply gradients only then (skip on first).
Suppose the following:
x = tf.Variable([2.])
w = tf.Variable([4.])
with tf.GradientTape(persistent=True) as tape:
w.assign(w * x)
y = w * w # w^2 * x
print(tape.gradient(y, x)) # >>None
From docs, a tf.Variable is a stateful object, which blocks gradients, and weights are tf.Variables.
Examples are differentiable hard attention (as opposed to RL), or simply passing a hidden state between layers in subsequent forward passes, as in diagram below. Neither TF nor Keras have an API-level support for stateful gradients, including RNNs, which only keep a stateful state tensor; gradient does not flow beyond one batch.
How can this be accomplished?
回答1:
We'll need to elaborately apply tf.while_loop; from help(TensorArray):
This class is meant to be used with dynamic iteration primitives such as
while_loopandmap_fn. It supports gradient back-propagation via special "flow" control flow dependencies.
We thus seek to write a loop such that all outputs we are to backpropagate through are written to a TensorArray. Code accomplishing this, and its high-level description, below. At bottom is a validating example.
Description:
- Code borrows from K.rnn, rewritten for simplicity and relevance
- For better understanding, I suggest inspecting
K.rnn, SimpleRNNCell.call, and RNN.call. model_rnnhas a few needless checks for sake of case 3; will link cleaner version- The idea's as follows: we traverse the network first bottom-to-top, then left-to-right, and write the entire forwar pass to a single
TensorArrayunder a singletf.while_loop; this ensures TF caches tensor ops throughout for backpropagation.
from tensorflow.python.util import nest
from tensorflow.python.ops import array_ops, tensor_array_ops
from tensorflow.python.framework import ops
def model_rnn(model, inputs, states=None, swap_batch_timestep=True):
def step_function(inputs, states):
out = model([inputs, *states], training=True)
output, new_states = (out if isinstance(out, (tuple, list)) else
(out, states))
return output, new_states
def _swap_batch_timestep(input_t):
# (samples, timesteps, channels) -> (timesteps, samples, channels)
# iterating dim0 to feed (samples, channels) slices expected by RNN
axes = list(range(len(input_t.shape)))
axes[0], axes[1] = 1, 0
return array_ops.transpose(input_t, axes)
if swap_batch_timestep:
inputs = nest.map_structure(_swap_batch_timestep, inputs)
if states is None:
states = (tf.zeros(model.inputs[0].shape, dtype='float32'),)
initial_states = states
input_ta, output_ta, time, time_steps_t = _process_args(model, inputs)
def _step(time, output_ta_t, *states):
current_input = input_ta.read(time)
output, new_states = step_function(current_input, tuple(states))
flat_state = nest.flatten(states)
flat_new_state = nest.flatten(new_states)
for state, new_state in zip(flat_state, flat_new_state):
if isinstance(new_state, ops.Tensor):
new_state.set_shape(state.shape)
output_ta_t = output_ta_t.write(time, output)
new_states = nest.pack_sequence_as(initial_states, flat_new_state)
return (time + 1, output_ta_t) + tuple(new_states)
final_outputs = tf.while_loop(
body=_step,
loop_vars=(time, output_ta) + tuple(initial_states),
cond=lambda time, *_: tf.math.less(time, time_steps_t))
new_states = final_outputs[2:]
output_ta = final_outputs[1]
outputs = output_ta.stack()
return outputs, new_states
def _process_args(model, inputs):
time_steps_t = tf.constant(inputs.shape[0], dtype='int32')
# assume single-input network (excluding states)
input_ta = tensor_array_ops.TensorArray(
dtype=inputs.dtype,
size=time_steps_t,
tensor_array_name='input_ta_0').unstack(inputs)
# assume single-input network (excluding states)
# if having states, infer info from non-state nodes
output_ta = tensor_array_ops.TensorArray(
dtype=model.outputs[0].dtype,
size=time_steps_t,
element_shape=model.outputs[0].shape,
tensor_array_name='output_ta_0')
time = tf.constant(0, dtype='int32', name='time')
return input_ta, output_ta, time, time_steps_t
Examples & validating:
Case design: we feed the same input twice, which enables certain stateful vs stateless comparisons; results also hold for differing inputs.
- Case 0: control; other cases must match this.
- Case 1: fail; gradients don't match, even though outputs and loss do. Backprop fails when feeding the halved sequence.
- Case 2: gradients match case 1. It may seem we've used only one
tf.while_loop, but SimpleRNN uses one of its own for the 3 timesteps, and writes to aTensorArraythat's discarded; this won't do. A workaround is to implement the SimpleRNN logic ourselves. - Case 3: perfect match.
Note that there's no such thing as a stateful RNN cell; statefulness is implemented in the RNN base class, and we've recreated it in model_rnn. This is likewise how any other layer is to be handled - feeding one step slice at a time for every forward pass.
import random
import numpy as np
import tensorflow as tf
from tensorflow.keras.layers import Input, SimpleRNN, SimpleRNNCell
from tensorflow.keras.models import Model
def reset_seeds():
random.seed(0)
np.random.seed(1)
tf.compat.v1.set_random_seed(2) # graph-level seed
tf.random.set_seed(3) # global seed
def print_report(case, model, outs, loss, tape, idx=1):
print("\nCASE #%s" % case)
print("LOSS", loss)
print("GRADS:\n", tape.gradient(loss, model.layers[idx].weights[0]))
print("OUTS:\n", outs)
#%%# Make data ###############################################################
reset_seeds()
x0 = y0 = tf.constant(np.random.randn(2, 3, 4))
x0_2 = y0_2 = tf.concat([x0, x0], axis=1)
x00 = y00 = tf.stack([x0, x0], axis=0)
#%%# Case 0: Complete forward pass; control case #############################
reset_seeds()
ipt = Input(batch_shape=(2, 6, 4))
out = SimpleRNN(4, return_sequences=True)(ipt)
model0 = Model(ipt, out)
model0.compile('sgd', 'mse')
#%%#############################################################
with tf.GradientTape(persistent=True) as tape:
outs = model0(x0_2, training=True)
loss = model0.compiled_loss(y0_2, outs)
print_report(0, model0, outs, loss, tape)
#%%# Case 1: Two passes, stateful RNN, direct feeding ########################
reset_seeds()
ipt = Input(batch_shape=(2, 3, 4))
out = SimpleRNN(4, return_sequences=True, stateful=True)(ipt)
model1 = Model(ipt, out)
model1.compile('sgd', 'mse')
#%%#############################################################
with tf.GradientTape(persistent=True) as tape:
outs0 = model1(x0, training=True)
tape.watch(outs0) # cannot even diff otherwise
outs1 = model1(x0, training=True)
tape.watch(outs1)
outs = tf.concat([outs0, outs1], axis=1)
tape.watch(outs)
loss = model1.compiled_loss(y0_2, outs)
print_report(1, model1, outs, loss, tape)
#%%# Case 2: Two passes, stateful RNN, model_rnn #############################
reset_seeds()
ipt = Input(batch_shape=(2, 3, 4))
out = SimpleRNN(4, return_sequences=True, stateful=True)(ipt)
model2 = Model(ipt, out)
model2.compile('sgd', 'mse')
#%%#############################################################
with tf.GradientTape(persistent=True) as tape:
outs, _ = model_rnn(model2, x00, swap_batch_timestep=False)
outs = tf.concat(list(outs), axis=1)
loss = model2.compiled_loss(y0_2, outs)
print_report(2, model2, outs, loss, tape)
#%%# Case 3: Single pass, stateless RNN, model_rnn ###########################
reset_seeds()
ipt = Input(batch_shape=(2, 4))
sipt = Input(batch_shape=(2, 4))
out, state = SimpleRNNCell(4)(ipt, sipt)
model3 = Model([ipt, sipt], [out, state])
model3.compile('sgd', 'mse')
#%%#############################################################
with tf.GradientTape(persistent=True) as tape:
outs, _ = model_rnn(model3, x0_2)
outs = tf.transpose(outs, (1, 0, 2))
loss = model3.compiled_loss(y0_2, outs)
print_report(3, model3, outs, loss, tape, idx=2)
Vertical flow: we've validated horizontal, timewise-backpropagation; what about vertical?
To this end, we implement a stacked stateful RNN; results below. All outputs on my machine, here.
We've hereby validated both vertical and horizontal stateful backpropagation. This can be used to implement arbitrarily complex forward-prop logic with correct backprop. Applied example here.
#%%# Case 4: Complete forward pass; control case ############################
reset_seeds()
ipt = Input(batch_shape=(2, 6, 4))
x = SimpleRNN(4, return_sequences=True)(ipt)
out = SimpleRNN(4, return_sequences=True)(x)
model4 = Model(ipt, out)
model4.compile('sgd', 'mse')
#%%
with tf.GradientTape(persistent=True) as tape:
outs = model4(x0_2, training=True)
loss = model4.compiled_loss(y0_2, outs)
print("=" * 80)
print_report(4, model4, outs, loss, tape, idx=1)
print_report(4, model4, outs, loss, tape, idx=2)
#%%# Case 5: Two passes, stateless RNN; model_rnn ############################
reset_seeds()
ipt = Input(batch_shape=(2, 6, 4))
out = SimpleRNN(4, return_sequences=True)(ipt)
model5a = Model(ipt, out)
model5a.compile('sgd', 'mse')
ipt = Input(batch_shape=(2, 4))
sipt = Input(batch_shape=(2, 4))
out, state = SimpleRNNCell(4)(ipt, sipt)
model5b = Model([ipt, sipt], [out, state])
model5b.compile('sgd', 'mse')
#%%
with tf.GradientTape(persistent=True) as tape:
outs = model5a(x0_2, training=True)
outs, _ = model_rnn(model5b, outs)
outs = tf.transpose(outs, (1, 0, 2))
loss = model5a.compiled_loss(y0_2, outs)
print_report(5, model5a, outs, loss, tape)
print_report(5, model5b, outs, loss, tape, idx=2)
来源：https://stackoverflow.com/questions/63222770/backpropagating-through-multiple-forward-passes