invariant_slot_attention/modules/misc.py

# coding=utf-8
# Copyright 2023 The Google Research 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
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"""Miscellaneous modules."""

from typing import Any, Callable, Dict, Iterable, Mapping, Optional, Sequence, Tuple, Union

from flax import linen as nn
import jax
import jax.numpy as jnp

from invariant_slot_attention.lib import utils

Shape = Tuple[int]

DType = Any
Array = Any  # jnp.ndarray
ArrayTree = Union[Array, Iterable["ArrayTree"], Mapping[str, "ArrayTree"]]  # pytype: disable=not-supported-yet
ProcessorState = ArrayTree
PRNGKey = Array
NestedDict = Dict[str, Any]


class Identity(nn.Module):
  """Module that applies the identity function, ignoring any additional args."""

  @nn.compact
  def __call__(self, inputs, **args):
    return inputs


class Readout(nn.Module):
  """Module for reading out multiple targets from an embedding."""

  keys: Sequence[str]
  readout_modules: Sequence[Callable[[], nn.Module]]
  stop_gradient: Optional[Sequence[bool]] = None

  @nn.compact
  def __call__(self, inputs, train = False):
    num_targets = len(self.keys)
    assert num_targets >= 1, "Need to have at least one target."
    assert len(self.readout_modules) == num_targets, (
        "len(modules) and len(keys) must match.")
    if self.stop_gradient is not None:
      assert len(self.stop_gradient) == num_targets, (
          "len(stop_gradient) and len(keys) must match.")
    outputs = {}
    for i in range(num_targets):
      if self.stop_gradient is not None and self.stop_gradient[i]:
        x = jax.lax.stop_gradient(inputs)
      else:
        x = inputs
      outputs[self.keys[i]] = self.readout_modules[i]()(x, train)  # pytype: disable=not-callable
    return outputs


class MLP(nn.Module):
  """Simple MLP with one hidden layer and optional pre-/post-layernorm."""

  hidden_size: int
  output_size: Optional[int] = None
  num_hidden_layers: int = 1
  activation_fn: Callable[[Array], Array] = nn.relu
  layernorm: Optional[str] = None
  activate_output: bool = False
  residual: bool = False

  @nn.compact
  def __call__(self, inputs, train = False):
    del train  # Unused.

    output_size = self.output_size or inputs.shape[-1]

    x = inputs

    if self.layernorm == "pre":
      x = nn.LayerNorm()(x)

    for i in range(self.num_hidden_layers):
      x = nn.Dense(self.hidden_size, name=f"dense_mlp_{i}")(x)
      x = self.activation_fn(x)
    x = nn.Dense(output_size, name=f"dense_mlp_{self.num_hidden_layers}")(x)

    if self.activate_output:
      x = self.activation_fn(x)

    if self.residual:
      x = x + inputs

    if self.layernorm == "post":
      x = nn.LayerNorm()(x)

    return x


class GRU(nn.Module):
  """GRU cell as nn.Module."""

  @nn.compact
  def __call__(self, carry, inputs,
               train = False):
    del train  # Unused.
    carry, _ = nn.GRUCell()(carry, inputs)
    return carry


class Dense(nn.Module):
  """Dense layer as nn.Module accepting "train" flag."""

  features: int
  use_bias: bool = True

  @nn.compact
  def __call__(self, inputs, train = False):
    del train  # Unused.
    return nn.Dense(features=self.features, use_bias=self.use_bias)(inputs)


class PositionEmbedding(nn.Module):
  """A module for applying N-dimensional position embedding.

  Attr:
    embedding_type: A string defining the type of position embedding to use. One
      of ["linear", "discrete_1d", "fourier", "gaussian_fourier"].
    update_type: A string defining how the input is updated with the position
      embedding. One of ["proj_add", "concat"].
    num_fourier_bases: The number of Fourier bases to use. For embedding_type ==
      "fourier", the embedding dimensionality is 2 x number of position
      dimensions x num_fourier_bases. For embedding_type == "gaussian_fourier",
      the embedding dimensionality is 2 x num_fourier_bases. For embedding_type
      == "linear", this parameter is ignored.
    gaussian_sigma: Standard deviation of sampled Gaussians.
    pos_transform: Optional transform for the embedding.
    output_transform: Optional transform for the combined input and embedding.
    trainable_pos_embedding: Boolean flag for allowing gradients to flow into
      the position embedding, so that the optimizer can update it.
  """

  embedding_type: str
  update_type: str
  num_fourier_bases: int = 0
  gaussian_sigma: float = 1.0
  pos_transform: Callable[[], nn.Module] = Identity
  output_transform: Callable[[], nn.Module] = Identity
  trainable_pos_embedding: bool = False

  def _make_pos_embedding_tensor(self, rng, input_shape):
    if self.embedding_type == "discrete_1d":
      # An integer tensor in [0, input_shape[-2]-1] reflecting
      # 1D discrete position encoding (encode the second-to-last axis).
      pos_embedding = jnp.broadcast_to(
          jnp.arange(input_shape[-2]), input_shape[1:-1])
    else:
      # A tensor grid in [-1, +1] for each input dimension.
      pos_embedding = utils.create_gradient_grid(input_shape[1:-1], [-1.0, 1.0])

    if self.embedding_type == "linear":
      pass
    elif self.embedding_type == "discrete_1d":
      pos_embedding = jax.nn.one_hot(pos_embedding, input_shape[-2])
    elif self.embedding_type == "fourier":
      # NeRF-style Fourier/sinusoidal position encoding.
      pos_embedding = utils.convert_to_fourier_features(
          pos_embedding * jnp.pi, basis_degree=self.num_fourier_bases)
    elif self.embedding_type == "gaussian_fourier":
      # Gaussian Fourier features. Reference: https://arxiv.org/abs/2006.10739
      num_dims = pos_embedding.shape[-1]
      projection = jax.random.normal(
          rng, [num_dims, self.num_fourier_bases]) * self.gaussian_sigma
      pos_embedding = jnp.pi * pos_embedding.dot(projection)
      # A slightly faster implementation of sin and cos.
      pos_embedding = jnp.sin(
          jnp.concatenate([pos_embedding, pos_embedding + 0.5 * jnp.pi],
                          axis=-1))
    else:
      raise ValueError("Invalid embedding type provided.")

    # Add batch dimension.
    pos_embedding = jnp.expand_dims(pos_embedding, axis=0)

    return pos_embedding

  @nn.compact
  def __call__(self, inputs):

    # Compute the position embedding only in the initial call use the same rng
    # as is used for initializing learnable parameters.
    pos_embedding = self.param("pos_embedding", self._make_pos_embedding_tensor,
                               inputs.shape)

    if not self.trainable_pos_embedding:
      pos_embedding = jax.lax.stop_gradient(pos_embedding)

    # Apply optional transformation on the position embedding.
    pos_embedding = self.pos_transform()(pos_embedding)  # pytype: disable=not-callable

    # Apply position encoding to inputs.
    if self.update_type == "project_add":
      # Here, we project the position encodings to the same dimensionality as
      # the inputs and add them to the inputs (broadcast along batch dimension).
      # This is roughly equivalent to concatenation of position encodings to the
      # inputs (if followed by a Dense layer), but is slightly more efficient.
      n_features = inputs.shape[-1]
      x = inputs + nn.Dense(n_features, name="dense_pe_0")(pos_embedding)
    elif self.update_type == "concat":
      # Repeat the position embedding along the first (batch) dimension.
      pos_embedding = jnp.broadcast_to(
          pos_embedding, shape=inputs.shape[:-1] + pos_embedding.shape[-1:])
      # concatenate along the channel dimension.
      x = jnp.concatenate((inputs, pos_embedding), axis=-1)
    else:
      raise ValueError("Invalid update type provided.")

    # Apply optional output transformation.
    x = self.output_transform()(x)  # pytype: disable=not-callable
    return x


class RelativePositionEmbedding(nn.Module):
  """A module for applying embedding of input position relative to slots.

  Attr
    update_type: A string defining how the input is updated with the position
      embedding. One of ["proj_add", "concat"].
    embedding_type: A string defining the type of position embedding to use.
      Currently only "linear" is supported.
    num_fourier_bases: The number of Fourier bases to use. For embedding_type ==
      "fourier", the embedding dimensionality is 2 x number of position
      dimensions x num_fourier_bases. For embedding_type == "gaussian_fourier",
      the embedding dimensionality is 2 x num_fourier_bases. For embedding_type
      == "linear", this parameter is ignored.
    gaussian_sigma: Standard deviation of sampled Gaussians.
    pos_transform: Optional transform for the embedding.
    output_transform: Optional transform for the combined input and embedding.
    trainable_pos_embedding: Boolean flag for allowing gradients to flow into
      the position embedding, so that the optimizer can update it.
  """

  update_type: str
  embedding_type: str = "linear"
  num_fourier_bases: int = 0
  gaussian_sigma: float = 1.0
  pos_transform: Callable[[], nn.Module] = Identity
  output_transform: Callable[[], nn.Module] = Identity
  trainable_pos_embedding: bool = False
  scales_factor: float = 1.0

  def _make_pos_embedding_tensor(self, rng, input_shape):

    # A tensor grid in [-1, +1] for each input dimension.
    pos_embedding = utils.create_gradient_grid(input_shape[1:-1], [-1.0, 1.0])

    # Add batch dimension.
    pos_embedding = jnp.expand_dims(pos_embedding, axis=0)

    return pos_embedding

  @nn.compact
  def __call__(self, inputs, slot_positions,
               slot_scales = None,
               slot_rotm = None):

    # Compute the position embedding only in the initial call use the same rng
    # as is used for initializing learnable parameters.
    pos_embedding = self.param("pos_embedding", self._make_pos_embedding_tensor,
                               inputs.shape)

    if not self.trainable_pos_embedding:
      pos_embedding = jax.lax.stop_gradient(pos_embedding)

    # Relativize pos_embedding with respect to slot positions
    # and optionally slot scales.
    slot_positions = jnp.expand_dims(
        jnp.expand_dims(slot_positions, axis=-2), axis=-2)
    if slot_scales is not None:
      slot_scales = jnp.expand_dims(
          jnp.expand_dims(slot_scales, axis=-2), axis=-2)

    if self.embedding_type == "linear":
      pos_embedding = pos_embedding - slot_positions
      if slot_rotm is not None:
        pos_embedding = self.transform(slot_rotm, pos_embedding)
      if slot_scales is not None:
        # Scales are usually small so the grid might get too large.
        pos_embedding = pos_embedding / self.scales_factor
        pos_embedding = pos_embedding / slot_scales
    else:
      raise ValueError("Invalid embedding type provided.")

    # Apply optional transformation on the position embedding.
    pos_embedding = self.pos_transform()(pos_embedding)  # pytype: disable=not-callable

    # Define intermediate for logging.
    pos_embedding = Identity(name="pos_emb")(pos_embedding)

    # Apply position encoding to inputs.
    if self.update_type == "project_add":
      # Here, we project the position encodings to the same dimensionality as
      # the inputs and add them to the inputs (broadcast along batch dimension).
      # This is roughly equivalent to concatenation of position encodings to the
      # inputs (if followed by a Dense layer), but is slightly more efficient.
      n_features = inputs.shape[-1]
      x = inputs + nn.Dense(n_features, name="dense_pe_0")(pos_embedding)
    elif self.update_type == "concat":
      # Repeat the position embedding along the first (batch) dimension.
      pos_embedding = jnp.broadcast_to(
          pos_embedding, shape=inputs.shape[:-1] + pos_embedding.shape[-1:])
      # concatenate along the channel dimension.
      x = jnp.concatenate((inputs, pos_embedding), axis=-1)
    else:
      raise ValueError("Invalid update type provided.")

    # Apply optional output transformation.
    x = self.output_transform()(x)  # pytype: disable=not-callable
    return x

  @classmethod
  def transform(cls, rot, coords):
    # The coordinate grid coords is in the (y, x) format, so we need to swap
    # the coordinates on the input and output.
    coords = jnp.stack([coords[Ellipsis, 1], coords[Ellipsis, 0]], axis=-1)
    # Equivalent to inv(R) * coords^T = R^T * coords^T = (coords * R)^T.
    # We are multiplying by the inverse of the rotation matrix because
    # we are rotating the coordinate grid *against* the rotation of the object.
    new_coords = jnp.einsum("...hij,...jk->...hik", coords, rot)
    # Swap coordinates again.
    return jnp.stack([new_coords[Ellipsis, 1], new_coords[Ellipsis, 0]], axis=-1)