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discrete_flows.py
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discrete_flows.py
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# coding=utf-8
# Copyright 2024 The Edward2 Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Reversible layers."""
from edward2.tensorflow import random_variable
from edward2.tensorflow import transformed_random_variable
from edward2.tensorflow.layers import utils
import tensorflow as tf
# TODO(trandustin): Move Reverse to another module(?).
class Reverse(tf.keras.layers.Layer):
"""Swaps the forward and reverse transformations of a layer."""
def __init__(self, reversible_layer, **kwargs):
super(Reverse, self).__init__(**kwargs)
if not hasattr(reversible_layer, 'reverse'):
raise ValueError('Layer passed-in has not implemented "reverse" method: '
'{}'.format(reversible_layer))
self.call = reversible_layer.reverse
self.reverse = reversible_layer.call
class DiscreteAutoregressiveFlow(tf.keras.layers.Layer):
"""A discrete reversible layer.
The flow takes as input a one-hot Tensor of shape `[..., length, vocab_size]`.
The flow returns a Tensor of same shape and dtype. (To enable gradients, the
input must have float dtype.)
For the forward pass, the flow computes in serial:
```none
outputs = []
for t in range(length):
new_inputs = [outputs, inputs[..., t, :]]
net = layer(new_inputs)
loc, scale = tf.split(net, 2, axis=-1)
loc = tf.argmax(loc, axis=-1)
scale = tf.argmax(scale, axis=-1)
new_outputs = (((inputs - loc) * inverse(scale)) % vocab_size)[..., -1, :]
outputs.append(new_outputs)
```
For the reverse pass, the flow computes in parallel:
```none
net = layer(inputs)
loc, scale = tf.split(net, 2, axis=-1)
loc = tf.argmax(loc, axis=-1)
scale = tf.argmax(scale, axis=-1)
outputs = (loc + scale * inputs) % vocab_size
```
The modular arithmetic happens in one-hot space.
If `x` is a discrete random variable, the induced probability mass function on
the outputs `y = flow(x)` is
```none
p(y) = p(flow.reverse(y)).
```
The location-only transform is always invertible ([integers modulo
`vocab_size` form an additive group](
https://en.wikipedia.org/wiki/Modular_arithmetic)). The transform with a scale
is invertible if the scale and `vocab_size` are coprime (see
[prime fields](https://en.wikipedia.org/wiki/Finite_field)).
"""
def __init__(self, layer, temperature, **kwargs):
"""Constructs flow.
Args:
layer: Two-headed masked network taking the inputs and returning a
real-valued Tensor of shape `[..., length, 2*vocab_size]`.
Alternatively, `layer` may return a Tensor of shape
`[..., length, vocab_size]` to be used as the location transform; the
scale transform will be hard-coded to 1.
temperature: Positive value determining bias of gradient estimator.
**kwargs: kwargs of parent class.
"""
super(DiscreteAutoregressiveFlow, self).__init__(**kwargs)
self.layer = layer
self.temperature = temperature
def build(self, input_shape):
input_shape = tf.TensorShape(input_shape)
self.vocab_size = input_shape[-1]
if self.vocab_size is None:
raise ValueError('The last dimension of the inputs to '
'`DiscreteAutoregressiveFlow` should be defined. Found '
'`None`.')
self.built = True
def __call__(self, inputs, *args, **kwargs):
if not isinstance(inputs, random_variable.RandomVariable):
return super(DiscreteAutoregressiveFlow, self).__call__( # pytype: disable=attribute-error # typed-keras
inputs, *args, **kwargs)
return transformed_random_variable.TransformedRandomVariable(inputs, self)
def call(self, inputs, **kwargs):
"""Forward pass for left-to-right autoregressive generation."""
inputs = tf.convert_to_tensor(inputs)
length = inputs.shape[-2]
if length is None:
raise NotImplementedError('length dimension must be known.')
# Form initial sequence tensor of shape [..., 1, vocab_size]. In a loop, we
# incrementally build a Tensor of shape [..., t, vocab_size] as t grows.
outputs = self._initial_call(inputs[..., 0, :], length, **kwargs)
# TODO(trandustin): Use tf.while_loop. Unrolling is memory-expensive for big
# models and not valid for variable lengths.
for t in range(1, length):
outputs = self._per_timestep_call(outputs,
inputs[..., t, :],
length,
t,
**kwargs)
return outputs
def _initial_call(self, new_inputs, length, **kwargs):
"""Returns Tensor of shape [..., 1, vocab_size].
Args:
new_inputs: Tensor of shape [..., vocab_size], the new input to generate
its output.
length: Length of final desired sequence.
**kwargs: Optional keyword arguments to layer.
"""
inputs = new_inputs[..., tf.newaxis, :]
# TODO(trandustin): To handle variable lengths, extend MADE to subset its
# input and output layer weights rather than pad inputs.
batch_ndims = inputs.shape.ndims - 2
padded_inputs = tf.pad(
inputs, paddings=[[0, 0]] * batch_ndims + [[0, length - 1], [0, 0]])
net = self.layer(padded_inputs, **kwargs)
if net.shape[-1] == 2 * self.vocab_size:
loc, scale = tf.split(net, 2, axis=-1)
loc = loc[..., 0:1, :]
loc = tf.cast(utils.one_hot_argmax(loc, self.temperature), inputs.dtype)
scale = scale[..., 0:1, :]
scale = tf.cast(utils.one_hot_argmax(scale, self.temperature),
inputs.dtype)
inverse_scale = utils.multiplicative_inverse(scale, self.vocab_size)
shifted_inputs = utils.one_hot_minus(inputs, loc)
outputs = utils.one_hot_multiply(shifted_inputs, inverse_scale)
elif net.shape[-1] == self.vocab_size:
loc = net
loc = loc[..., 0:1, :]
loc = tf.cast(utils.one_hot_argmax(loc, self.temperature), inputs.dtype)
outputs = utils.one_hot_minus(inputs, loc)
else:
raise ValueError('Output of layer does not have compatible dimensions.')
return outputs
def _per_timestep_call(self,
current_outputs,
new_inputs,
length,
timestep,
**kwargs):
"""Returns Tensor of shape [..., timestep+1, vocab_size].
Args:
current_outputs: Tensor of shape [..., timestep, vocab_size], the so-far
generated sequence Tensor.
new_inputs: Tensor of shape [..., vocab_size], the new input to generate
its output given current_outputs.
length: Length of final desired sequence.
timestep: Current timestep.
**kwargs: Optional keyword arguments to layer.
"""
inputs = tf.concat([current_outputs,
new_inputs[..., tf.newaxis, :]], axis=-2)
# TODO(trandustin): To handle variable lengths, extend MADE to subset its
# input and output layer weights rather than pad inputs.
batch_ndims = inputs.shape.ndims - 2
padded_inputs = tf.pad(
inputs,
paddings=[[0, 0]] * batch_ndims + [[0, length - timestep - 1], [0, 0]])
net = self.layer(padded_inputs, **kwargs)
if net.shape[-1] == 2 * self.vocab_size:
loc, scale = tf.split(net, 2, axis=-1)
loc = loc[..., :(timestep+1), :]
loc = tf.cast(utils.one_hot_argmax(loc, self.temperature), inputs.dtype)
scale = scale[..., :(timestep+1), :]
scale = tf.cast(utils.one_hot_argmax(scale, self.temperature),
inputs.dtype)
inverse_scale = utils.multiplicative_inverse(scale, self.vocab_size)
shifted_inputs = utils.one_hot_minus(inputs, loc)
new_outputs = utils.one_hot_multiply(shifted_inputs, inverse_scale)
elif net.shape[-1] == self.vocab_size:
loc = net
loc = loc[..., :(timestep+1), :]
loc = tf.cast(utils.one_hot_argmax(loc, self.temperature), inputs.dtype)
new_outputs = utils.one_hot_minus(inputs, loc)
else:
raise ValueError('Output of layer does not have compatible dimensions.')
outputs = tf.concat([current_outputs, new_outputs[..., -1:, :]], axis=-2)
if not tf.executing_eagerly():
outputs.set_shape([None] * batch_ndims + [timestep+1, self.vocab_size])
return outputs
def reverse(self, inputs, **kwargs):
"""Reverse pass returning the inverse autoregressive transformation."""
if not self.built:
self._maybe_build(inputs)
net = self.layer(inputs, **kwargs)
if net.shape[-1] == 2 * self.vocab_size:
loc, scale = tf.split(net, 2, axis=-1)
scale = tf.cast(utils.one_hot_argmax(scale, self.temperature),
inputs.dtype)
scaled_inputs = utils.one_hot_multiply(inputs, scale)
elif net.shape[-1] == self.vocab_size:
loc = net
scaled_inputs = inputs
else:
raise ValueError('Output of layer does not have compatible dimensions.')
loc = tf.cast(utils.one_hot_argmax(loc, self.temperature), inputs.dtype)
outputs = utils.one_hot_add(loc, scaled_inputs)
return outputs
def log_det_jacobian(self, inputs):
return tf.cast(0, inputs.dtype)
class DiscreteBipartiteFlow(tf.keras.layers.Layer):
"""A discrete reversible layer.
The flow takes as input a one-hot Tensor of shape `[..., length, vocab_size]`.
The flow returns a Tensor of same shape and dtype. (To enable gradients, the
input must have float dtype.)
For the forward pass, the flow computes:
```none
net = layer(mask * inputs)
loc, scale = tf.split(net, 2, axis=-1)
loc = tf.argmax(loc, axis=-1)
scale = tf.argmax(scale, axis=-1)
outputs = ((inputs - (1-mask) * loc) * (1-mask) * inverse(scale)) % vocab_size
```
For the reverse pass, the flow computes:
```none
net = layer(mask * inputs)
loc, scale = tf.split(net, 2, axis=-1)
loc = tf.argmax(loc, axis=-1)
scale = tf.argmax(scale, axis=-1)
outputs = ((1-mask) * loc + (1-mask) * scale * inputs) % vocab_size
```
The modular arithmetic happens in one-hot space.
If `x` is a discrete random variable, the induced probability mass function on
the outputs `y = flow(x)` is
```none
p(y) = p(flow.reverse(y)).
```
The location-only transform is always invertible ([integers modulo
`vocab_size` form an additive group](
https://en.wikipedia.org/wiki/Modular_arithmetic)). The transform with a scale
is invertible if the scale and `vocab_size` are coprime (see
[prime fields](https://en.wikipedia.org/wiki/Finite_field)).
"""
def __init__(self, layer, mask, temperature, **kwargs):
"""Constructs flow.
Args:
layer: Two-headed masked network taking the inputs and returning a
real-valued Tensor of shape `[..., length, 2*vocab_size]`.
Alternatively, `layer` may return a Tensor of shape
`[..., length, vocab_size]` to be used as the location transform; the
scale transform will be hard-coded to 1.
mask: binary Tensor of shape `[length]` forming the bipartite assignment.
temperature: Positive value determining bias of gradient estimator.
**kwargs: kwargs of parent class.
"""
super(DiscreteBipartiteFlow, self).__init__(**kwargs)
self.layer = layer
self.mask = mask
self.temperature = temperature
def build(self, input_shape):
input_shape = tf.TensorShape(input_shape)
self.vocab_size = input_shape[-1]
if self.vocab_size is None:
raise ValueError('The last dimension of the inputs to '
'`DiscreteBipartiteFlow` should be defined. Found '
'`None`.')
self.built = True
def __call__(self, inputs, *args, **kwargs):
if not isinstance(inputs, random_variable.RandomVariable):
return super(DiscreteBipartiteFlow, self).__call__( # pytype: disable=attribute-error # typed-keras
inputs, *args, **kwargs)
return transformed_random_variable.TransformedRandomVariable(inputs, self)
def call(self, inputs, **kwargs):
"""Forward pass for bipartite generation."""
inputs = tf.convert_to_tensor(inputs)
batch_ndims = inputs.shape.ndims - 2
mask = tf.reshape(tf.cast(self.mask, inputs.dtype),
[1] * batch_ndims + [-1, 1])
masked_inputs = mask * inputs
net = self.layer(masked_inputs, **kwargs)
if net.shape[-1] == 2 * self.vocab_size:
loc, scale = tf.split(net, 2, axis=-1)
loc = tf.cast(utils.one_hot_argmax(loc, self.temperature), inputs.dtype)
scale = tf.cast(utils.one_hot_argmax(scale, self.temperature),
inputs.dtype)
inverse_scale = utils.multiplicative_inverse(scale, self.vocab_size)
shifted_inputs = utils.one_hot_minus(inputs, loc)
masked_outputs = (1. - mask) * utils.one_hot_multiply(shifted_inputs,
inverse_scale)
elif net.shape[-1] == self.vocab_size:
loc = net
loc = tf.cast(utils.one_hot_argmax(loc, self.temperature), inputs.dtype)
masked_outputs = (1. - mask) * utils.one_hot_minus(inputs, loc)
else:
raise ValueError('Output of layer does not have compatible dimensions.')
outputs = masked_inputs + masked_outputs
return outputs
def reverse(self, inputs, **kwargs):
"""Reverse pass for the inverse bipartite transformation."""
if not self.built:
self._maybe_build(inputs)
inputs = tf.convert_to_tensor(inputs)
batch_ndims = inputs.shape.ndims - 2
mask = tf.reshape(tf.cast(self.mask, inputs.dtype),
[1] * batch_ndims + [-1, 1])
masked_inputs = mask * inputs
net = self.layer(masked_inputs, **kwargs)
if net.shape[-1] == 2 * self.vocab_size:
loc, scale = tf.split(net, 2, axis=-1)
scale = tf.cast(utils.one_hot_argmax(scale, self.temperature),
inputs.dtype)
scaled_inputs = utils.one_hot_multiply(inputs, scale)
elif net.shape[-1] == self.vocab_size:
loc = net
scaled_inputs = inputs
else:
raise ValueError('Output of layer does not have compatible dimensions.')
loc = tf.cast(utils.one_hot_argmax(loc, self.temperature), inputs.dtype)
masked_outputs = (1. - mask) * utils.one_hot_add(loc, scaled_inputs)
outputs = masked_inputs + masked_outputs
return outputs
def log_det_jacobian(self, inputs):
return tf.cast(0, inputs.dtype)
class SinkhornAutoregressiveFlow(tf.keras.layers.Layer):
"""A discrete reversible layer using Sinkhorn normalization for permutations.
The flow takes as input a one-hot Tensor of shape `[..., length, vocab_size]`.
The flow returns a Tensor of same shape and dtype. (To enable gradients, the
input must have float dtype.)
"""
def __init__(self, layer, temperature, **kwargs):
"""Constructs flow.
Args:
layer: Masked network taking inputs with shape `[..., length, vocab_size]`
and returning a real-valued Tensor of shape
`[..., length, vocab_size ** 2]`. Sinkhorn iterations are applied to
each `layer` output to produce permutation matrices.
temperature: Positive value determining bias of gradient estimator.
**kwargs: kwargs of parent class.
"""
super(SinkhornAutoregressiveFlow, self).__init__(**kwargs)
self.layer = layer
self.temperature = temperature
def build(self, input_shape):
input_shape = tf.TensorShape(input_shape)
self.vocab_size = input_shape[-1]
if self.vocab_size is None:
raise ValueError('The last dimension of the inputs to '
'`DiscreteAutoregressiveFlow` should be defined. Found '
'`None`.')
self.built = True
def __call__(self, inputs, *args, **kwargs):
if not isinstance(inputs, random_variable.RandomVariable):
return super(SinkhornAutoregressiveFlow, self).__call__( # pytype: disable=attribute-error # typed-keras
inputs, *args, **kwargs)
return transformed_random_variable.TransformedRandomVariable(inputs, self)
def call(self, inputs, **kwargs):
"""Forward pass for left-to-right autoregressive generation."""
inputs = tf.convert_to_tensor(inputs)
length = inputs.shape[-2]
if length is None:
raise NotImplementedError('length dimension must be known.')
# Form initial sequence tensor of shape [..., 1, vocab_size]. In a loop, we
# incrementally build a Tensor of shape [..., t, vocab_size] as t grows.
outputs = self._initial_call(inputs[..., 0, :], length, **kwargs)
for t in range(1, length):
outputs = self._per_timestep_call(outputs,
inputs[..., t, :],
length,
t,
**kwargs)
return outputs
def _initial_call(self, new_inputs, length, **kwargs):
"""Returns Tensor of shape [..., 1, vocab_size].
Args:
new_inputs: Tensor of shape [..., vocab_size], the new input to generate
its output.
length: Length of final desired sequence.
**kwargs: Optional keyword arguments to layer.
"""
inputs = new_inputs[..., tf.newaxis, :]
# TODO(trandustin): To handle variable lengths, extend MADE to subset its
# input and output layer weights rather than pad inputs.
batch_ndims = inputs.shape.ndims - 2
padded_inputs = tf.pad(
inputs, paddings=[[0, 0]] * batch_ndims + [[0, length - 1], [0, 0]])
temperature = 1.
logits = self.layer(padded_inputs / temperature, **kwargs)
logits = logits[..., 0:1, :]
logits = tf.reshape(
logits,
logits.shape[:-1].concatenate([self.vocab_size, self.vocab_size]))
soft = utils.sinkhorn(logits)
hard = tf.cast(utils.soft_to_hard_permutation(soft), inputs.dtype)
hard = tf.reshape(hard, logits.shape)
# Inverse of permutation matrix is its transpose.
# inputs is [batch_size, timestep + 1, vocab_size].
# hard is [batch_size, timestep + 1, vocab_size, vocab_size].
outputs = tf.matmul(inputs[..., tf.newaxis, :],
hard,
transpose_b=True)[..., 0, :]
return outputs
def _per_timestep_call(self,
current_outputs,
new_inputs,
length,
timestep,
**kwargs):
"""Returns Tensor of shape [..., timestep+1, vocab_size].
Args:
current_outputs: Tensor of shape [..., timestep, vocab_size], the so-far
generated sequence Tensor.
new_inputs: Tensor of shape [..., vocab_size], the new input to generate
its output given current_outputs.
length: Length of final desired sequence.
timestep: Current timestep.
**kwargs: Optional keyword arguments to layer.
"""
inputs = tf.concat([current_outputs,
new_inputs[..., tf.newaxis, :]], axis=-2)
# TODO(trandustin): To handle variable lengths, extend MADE to subset its
# input and output layer weights rather than pad inputs.
batch_ndims = inputs.shape.ndims - 2
padded_inputs = tf.pad(
inputs,
paddings=[[0, 0]] * batch_ndims + [[0, length - timestep - 1], [0, 0]])
logits = self.layer(padded_inputs, **kwargs)
logits = logits[..., :(timestep+1), :]
logits = tf.reshape(
logits,
logits.shape[:-1].concatenate([self.vocab_size, self.vocab_size]))
soft = utils.sinkhorn(logits / self.temperature)
hard = tf.cast(utils.soft_to_hard_permutation(soft), inputs.dtype)
hard = tf.reshape(hard, logits.shape)
# Inverse of permutation matrix is its transpose.
# inputs is [batch_size, timestep + 1, vocab_size].
# hard is [batch_size, timestep + 1, vocab_size, vocab_size].
new_outputs = tf.matmul(inputs[..., tf.newaxis, :],
hard,
transpose_b=True)[..., 0, :]
outputs = tf.concat([current_outputs, new_outputs[..., -1:, :]], axis=-2)
if not tf.executing_eagerly():
outputs.set_shape([None] * batch_ndims + [timestep+1, self.vocab_size])
return outputs
def reverse(self, inputs, **kwargs):
"""Reverse pass returning the inverse autoregressive transformation."""
if not self.built:
self._maybe_build(inputs)
logits = self.layer(inputs, **kwargs)
logits = tf.reshape(
logits,
logits.shape[:-1].concatenate([self.vocab_size, self.vocab_size]))
soft = utils.sinkhorn(logits / self.temperature, n_iters=20)
hard = utils.soft_to_hard_permutation(soft)
hard = tf.reshape(hard, logits.shape)
# Recover the permutation by right-multiplying by the permutation matrix.
outputs = tf.matmul(inputs[..., tf.newaxis, :], hard)[..., 0, :]
return outputs
def log_det_jacobian(self, inputs):
return tf.cast(0, inputs.dtype)